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Using biomechanics to understand how an individual accomplishes a task in a variety of contexts

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Using biomechanics to understand how an individual accomplishes a task in a variety of contexts

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Content Copyright 2022 Casey Wiens

Using biomechanics to understand how an individual accomplishes a task in a variety of
contexts

by

Casey Wiens

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(INTEGRATIVE AND EVOLUTIONARY BIOLOGY)

December 2022
ii

Dedication
To my family, for their love, support, and guidance.
iii

Table of Contents
Dedication ............................................................................................................................................................ ii
List of Tables .......................................................................................................................................................... vi
List of Figures ....................................................................................................................................................... vii
Abstract .......................................................................................................................................................... xv
Chapter 1 Introduction .................................................................................................................................. 1
1.1 Basketball ............................................................................................................................................... 3
1.2 Database .................................................................................................................................................. 8
1.3 Completed Set of Experiments ....................................................................................................... 9
Chapter 2 Methods ........................................................................................................................................10
2.1 Experimental Procedures ...............................................................................................................10
2.1.1 Basketball collections ............................................................................................................. 10
2.2 Reference System ..............................................................................................................................12
2.3 Data collected ......................................................................................................................................13
2.3.1 Video ............................................................................................................................................. 13
2.3.2 Force ............................................................................................................................................. 14
2.3.3 Kinematics .................................................................................................................................. 14
2.3.4 Segment angles ......................................................................................................................... 14
2.3.5 Segment angular velocities .................................................................................................. 15
2.4 Variable Definitions ..........................................................................................................................15
2.4.1 Ball release ................................................................................................................................. 15
2.4.2 Ball entry into the hoop ......................................................................................................... 16
2.4.3 Ball release velocity ................................................................................................................ 16
2.4.4 Ball release height ................................................................................................................... 16
2.4.5 Ball release distance ............................................................................................................... 16
2.4.6 Ground departure .................................................................................................................... 17
2.4.7 Net impulse ................................................................................................................................ 17
2.4.8 Center of mass velocity at ground departure ............................................................... 18
2.4.9 Center of mass velocity at ball release............................................................................. 19
2.4.10 Center of mass velocity contribution ............................................................................... 20
2.4.11 Arm velocity contribution .................................................................................................... 20
2.4.12 Time of center of mass apex ................................................................................................ 21
2.4.13 Time of ball release relative to ground departure ...................................................... 21
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2.4.14 Time of ball release relative to center of mass apex .................................................. 21
Chapter 3 Characterizing the effect of personalized wheelchair adjustments on
posture and upper extremity mechanics during overground wheelchair propulsion ............22
3.1 Introduction .........................................................................................................................................22
3.2 Methods .................................................................................................................................................25
3.2.1 Statistics ...................................................................................................................................... 29
3.3 Results ....................................................................................................................................................32
3.3.1 Resultant shoulder NJM impulse during push .............................................................. 35
3.3.2 Torso angle at wrist top-dead-center of wheel ............................................................ 36
3.3.3 Elbow angle at wrist top-dead-center of wheel ........................................................... 37
3.3.4 Relationship between torso and elbow angle at wrist-top-dead-center of
wheel ......................................................................................................................................................... 38
3.4 Discussion .............................................................................................................................................38
3.5 Conclusion ............................................................................................................................................42
Chapter 4 The effect of shot distance on the whole body center of mass velocity
regulation in the basketball shot ..................................................................................................................43
4.1 Introduction .........................................................................................................................................43
4.2 Methods .................................................................................................................................................47
4.3 Results ....................................................................................................................................................52
4.4 Discussion .............................................................................................................................................60
Chapter 5 The effect of shot distance on the arm velocity regulation in the basketball
shot ..........................................................................................................................................................66
5.1 Introduction .........................................................................................................................................66
5.2 Methods .................................................................................................................................................71
5.2.1 Participants ................................................................................................................................ 71
5.3 Results ....................................................................................................................................................75
5.4 Discussion .............................................................................................................................................84
Chapter 6 The strategies of generating ball velocity in the basketball jump shot across
shot distances .......................................................................................................................................................89
6.1 Introduction .........................................................................................................................................89
6.2 Ball Entry Angle ..................................................................................................................................94
6.3 Whole Body’s Contribution ...........................................................................................................96
6.4 Arm’s Contribution ...........................................................................................................................99
6.5 Conclusion ......................................................................................................................................... 101
6.5.1 How did they achieve the high entry angle?................................................................ 101
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6.5.2 How can they increase their entry angle? .................................................................... 101
Chapter 7 Regulation of ball velocity at release with increases in shot distance in
wheelchair basketball .................................................................................................................................... 104
7.1 Introduction ...................................................................................................................................... 104
7.2 Methods .............................................................................................................................................. 106
7.3 Results ................................................................................................................................................. 109
7.4 Discussion .......................................................................................................................................... 116
Chapter 8 Improving human performance over time using an integrated
biomechanical informatics system with embedded data visualization tools ........................... 120
8.1 Introduction ...................................................................................................................................... 120
8.2 Methods .............................................................................................................................................. 123
8.3 Results ................................................................................................................................................. 129
8.4 Discussion .......................................................................................................................................... 132
Chapter 9 Conclusion ................................................................................................................................ 138
9.1 Personalized wheelchair fitting ................................................................................................ 138
9.2 Whole body velocity regulation across shot distance in basketball shooting ........ 139
9.3 Arm velocity regulation across shot distance in basketball shooting ........................ 139
9.4 Arm velocity regulation across shot distance in wheelchair basketball shooting 139
9.5 Database, integration of data, and tracking progressions .............................................. 140
9.6 Future directions ............................................................................................................................ 140
References ....................................................................................................................................................... 141

vi

List of Tables
Table 3.1: Scoring summary explanation for each variable of interest. x1: Pre; x2: Post. ..... 31

Table 3.2: Wheelchair adjustments in seatback, axle position relative to seatback, and
seat height for each participant from pre- to post-WC reconfiguration and scoring of
posture, elbow, and shoulder NJM impulse outcomes. ................................................................ 33

Table 3.3: Probability estimate and 95% confidence intervals for each possible score
for variables of interest. ........................................................................................................................... 35

Table 4.1: Collection procedure. .................................................................................................................. 48

Table 5.1: Collection procedure. .................................................................................................................. 72

vii

List of Figures

Figure 1.1: There are multiple ball flight trajectories that can result in a successful shot.
Exemplar successful trajectories by multiple participants (color) and two different
distances (4.19 m, 6.02 m). ........................................................................................................................ 2
Figure 1.2: The reference system and basketball variables. Position is relative to the
location on the floor directly beneath the center of the hoop (origin). Linear velocity
is defined within the plane YZ and angular velocity about the X-axis. ...................................... 4
Figure 1.3: Filmstrip of key events during the basketball shot with three different
techniques. Start of impulse: When the individual applies force contributing to the
shot. Arm swing: Beginning of the upper arm counter-clockwise rotation. Arm shot
initiation: Beginning of arm rotation that contributes to the ball release velocity.
End of Impulse: When the individual is no longer applying force into the ground,
also referred to as ground departure. Ball Release: Last frame in which the person
is in contact with the ball. CM Apex: The individual’s center of mass trajectory apex. ...... 5
Figure 1.4: The center of mass vertical velocity (CM Vv) is greater when releasing the
ball earlier (purple) relative to the center of mass. .......................................................................... 6
Figure 1.5: The center of mass velocity during the basketball shot is a result of the net
impulse generated by the legs. Once the shooter leaves the ground, gravity
accelerates the body toward the ground, reducing their center of mass velocity. The
center of mass velocity at the time of ball release is the amount contributed to the
ball release velocity. ...................................................................................................................................... 7
Figure 1.6: An outline of the set of experiments conducted in this body of work. ...................... 9
Figure 2.1: Data acquired from these three collections were incorporated into a
database to track performance over time. ........................................................................................ 10
Figure 2.2: Basketball shots will be taken from three distances from the center of the
hoop: 4.19 m, 6.02 m, 7.24 m. Camera and force plate set up. The two portable force
plates will be moved to the condition’s shot location. ................................................................. 11
Figure 2.3: The gym reference system. The origin (0, 0) is located on the floor directly
beneath the center of the hoop. Positive x is in the direction of the hoop. Positive y
is in the direction to the left of the hoop from the shooter’s perspective. Positive z is
up. Positive angular velocity about the y-axis is clockwise. ....................................................... 13
Figure 2.4: The center of mass vertical and horizontal velocity at ball release. ........................ 19
Figure 2.5: The shooter’s center of mass and arms contribute to the ball velocity. ................ 20
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Figure 2.6: Time of ball release relative to ground departure is the time between the
participant no long applying force into the ground and when the ball is released.
Time of ball release relative to center of mass apex is the time between ball release
and the highest vertical position of the center of mass (apex). ................................................ 21
Figure 3.1: Selection of key events during task: a) start of push; b) wrist top-dead-
center; c) peak RF magnitude; d) peak elbow extension angular velocity; e) end of
push using variables of interest for an exemplar participant. .................................................. 28
Figure 3.2: Torso angle was defined as the anterior angle created by the right
horizontal and the line from the shoulder joint center and the wheel axle. Elbow
angle was defined as the anteriorinterior angle between the long axes of the upper
arm and forearm. ........................................................................................................................................ 29
Figure 3.3: Comparison of Resultant shoulder NJM impulse (Nms) during push pre-post
WC reconfiguration for each participant. Data shown for individual cycles within
Pre (black circles)-Post (gray circles) data collection sessions. ............................................... 36
Figure 3.4: Comparison of Torso angle at wrist top-dead-center during push pre-post
WC reconfiguration for each participant. Data shown for individual cycles within
Pre (black circles)-Post (gray circles) data collection sessions. ............................................... 37
Figure 3.5: Comparison of Elbow angle at wrist top-dead-center during push pre-post
WC reconfiguration for each participant. Data shown for individual cycles within
Pre (black circles)-Post (gray circles) data collection sessions. ............................................... 38
Figure 4.1: The ball resultant velocity at release (brown) can be attributed to the body
CM velocity (purple) and the velocity generated by the arms (gold). .................................... 44
Figure 4.2: The CM velocity during the basketball shot is a result of the net impulse
generated by the legs. Once the shooter leaves the ground, gravity accelerates the
body toward the ground, reducing their CM velocity. The CM velocity at the time of
ball release is the amount contributed to the ball release velocity. Filmstrip of key
events and phases during the basketball shot. Start of impulse: When the individual
applies force contributing to the shot. Arm swing: Beginning of the upper arm
counterclockwise rotation. Arm shot initiation: Beginning of arm rotation that
contributes to the ball release velocity. End of Impulse: When the individual is no
longer applying force into the ground, also referred to as ground departure. Ball
Release: Last frame in which the person is in contact with the ball. CM Apex: The
individual’s CM trajectory apex. ............................................................................................................ 45
Figure 4.3: Dimensions of a basketball court and the reference system used to describe
shot location on the court. Shot distance was characterized by the distance from the
center of the hoop to lines on the court: free throw (4.19 m, gold); American high
school three-point (6.02 m, blue); NBA three-point (7.24, purple). The origin of the
reference system was located on the floor, directly beneath the center of the hoop. ..... 49
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Figure 4.4: The CM vertical (top row) and horizontal (bottom row) velocity at release
increases with an increase in shot distance (gold: 4.19 m; blue: 6.02 m; purple:
7.24 m). * p < 0.5; ** p < 0.01; *** p < 0.001; **** p < 0.0001. ................................................... 54
Figure 4.5: The CM vertical (top row) and horizontal (bottom row) velocity
contribution to velocity at release increases with an increase in shot distance (gold:
4.19 m; blue: 6.02 m; purple: 7.24 m). * p < 0.5; ** p < 0.01; *** p < 0.001; **** p <
0.0001. ............................................................................................................................................................. 56
Figure 4.6: The time of release occurs earlier relative to the CM jump apex as shot
distance increases (gold: 4.19 m; blue: 6.02 m; purple: 7.24 m). * p < 0.5; ** p < 0.01;
*** p < 0.001; **** p < 0.0001. ................................................................................................................ 57
Figure 4.7: The net vertical impulse generated during the shot increases as shot
distance increases, while the net horizontal impulse magnitude decreases in the
negative direction as shot distance increases (gold: 4.19 m; blue: 6.02 m; purple:
7.24 m). * p < 0.5; ** p < 0.01; *** p < 0.001; **** p < 0.0001. ................................................... 59
Figure 4.8: The time in the air before release decreases when shooting at 4.19 m and
6.02 m relative to 4.19 m (gold: 4.19 m; blue: 6.02 m; purple: 7.24 m). * p < 0.5; ** p
< 0.01; *** p < 0.001; **** p < 0.0001. ................................................................................................. 60
Figure 4.9: Three exemplar control strategies used by participants to regulate CM
vertical velocity contributions to ball vertical velocity at release with increases in
shot distance (gold: 4.19 m; blue: 6.02 m; purple: 7.24 m). The individuals
generating relatively low but progressively greater CM vertical velocity at Ground
Departure across shot distances (Column 1) tended to release ball much earlier in
flight enabling the player to maximize contribution of CM vertical velocity at
Ground Departure to ball velocity at release when the CM vertical position was
relatively low. The individuals effective in generating substantial CM vertical
velocity at Ground Departure (> 1.75 m/s across distances, Column 2) released the
ball earlier in flight with increased shot distance which enabled the player to use
more of their CM vertical velocity generated during the shot. The individuals
effective in generating substantial CM vertical velocity at Ground Departure (> 1.75
m/s) and increased the magnitude of CM vertical velocity at Ground departure
across shot distances (Column 3) also released the ball earlier in flight with
increased shot distance, enabling the player to use more of their CM vertical
velocity at Ground Departure. ............................................................................................................... 64
Figure 5.1: Events and phases characterizing a jump shot initiated from the foul line.
The context in which a jump shot occurs may change the multijoint coordination in
this exemplar jump shot. For example, a shot initiated from a greater distance from
the hoop requires a greater ball velocity at release. In order to satisfy the increased
velocity demand with shot distance coordination of the legs, trunk, and arms may
change. ............................................................................................................................................................ 67
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Figure 5.2: Filmstrip of key events during the basketball shot with three different
techniques. Start of impulse generation: When the individual applies force
contributing to the shot. Arm swing: Beginning of the upper arm counter-clockwise
rotation. Arm contribution to shot initiation: Beginning of arm rotation that
contributes to the ball velocity at release. End of Impulse generation: When the
individual is no longer applying force into the ground, referred in this study as
ground departure. Ball Release: Last frame in which the person is in contact with
the ball. CM Apex: The apex of an individual’s center of mass during the flight phase
of the jump shot. .......................................................................................................................................... 70
Figure 5.3: Reference system the locations of the three jump shots relative to the center
of the hoop: free throw (4.19 m, gold); American high school three-point (6.02 m,
blue); NBA three-point (7.24 m, purple)). The reference system’s origin was located
directly beneath the hoop and on the floor. ..................................................................................... 72
Figure 5.4: The arm velocity contribution to ball vertical (top row) and horizontal
(bottom row) velocity at release increased with an increase in shot distance (gold:
4.19 m; blue: 6.02 m; purple: 7.24 m). * p < 0.5; ** p < 0.01; *** p < 0.001; **** p <
0.0001. Participants are sorted by the median arm contribution to ball vertical
velocity at release in the 4.19 m shots. ............................................................................................... 76
Figure 5.5: The arm velocity contribution to ball vertical (top row) and horizontal
(bottom row) velocity at release increased with an increase in shot distance (gold:
4.19 m; blue: 6.02 m; purple: 7.24 m). * p < 0.5; ** p < 0.01; *** p < 0.001; **** p <
0.0001. Participants are sorted by the median arm contribution to ball vertical
velocity at release in the 4.19 m shots. ............................................................................................... 80
Figure 5.6: The upper arm angular velocity at release (top row) increased with an
increase in shot distance (gold: 4.19 m; blue: 6.02 m; purple: 7.24 m). The forearm
angular velocity at release was lowest at 4.19 m and greatest at 6.02 m. * p < 0.5; **
p < 0.01; *** p < 0.001; **** p < 0.0001. Note the bottom row y-axis is reversed.
Participants are sorted by the median arm contribution to ball vertical velocity at
release in the 4.19 m shots. ..................................................................................................................... 82
Figure 5.7: The upper arm angle (top row) increased with shot distance while the
forearm angle (bottom row) decreased with shot distance (gold: 4.19 m; blue: 6.02
m; purple: 7.24 m). * p < 0.5; ** p < 0.01; *** p < 0.001; **** p < 0.0001. Participants
are sorted by the median arm contribution to ball vertical velocity at release in the
4.19 m shots. ................................................................................................................................................. 84
Figure 5.8: It isn’t just about achieving angular velocities at release but doing so at key
positions. The more horizontal the upper arm at release, the more vertical the
elbow relative resultant velocity (top left). Individuals can achieve the same upper
arm angular velocity at release (bottom left and right column, row 1), but due to
their upper arm position at release (right column, row 2), they achieve different
elbow relative vertical velocities at release (right column, row 3). This example
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illustrates that a player can achieve a greater vertical velocity contribution from the
upper arm by releasing the ball with a more horizontal upper arm. ..................................... 87
Figure 5.9: The greater the ball velocity entry angle, the greater room for error.
Methods of increasing the ball velocity entry angle include increasing the ball
velocity release angle and/or increasing the ball release height. ............................................ 88
Figure 6.1: There are multiple ball flight trajectories that can result in a successful shot.
Exemplar successful trajectories by multiple participants (color) and two different
distances (4.19 m, 6.02 m). ..................................................................................................................... 90
Figure 6.2: The center of mass velocity during the basketball shot is a result of the net
impulse generated by the legs. Once the shooter leaves the ground, gravity
accelerates the body toward the ground, reducing their center of mass velocity. The
center of mass velocity at the time of ball release is the amount contributed to the
ball release velocity. ................................................................................................................................... 91
Figure 6.3: The greater the ball velocity entry angle, the greater the room for error. The
minimum ball velocity entry angle that the ball does not hit the rim is 32.72 degrees
when shooting with a men’s ball (size 7) and 30.28 degrees with a women’s ball
(size 6) (Hay, 1985). .................................................................................................................................. 93
Figure 6.4: A player can achieve a high ball velocity entry angle by a combination of
high CM vertical velocity at release, high arm contribution to ball vertical velocity at
release, and high ball vertical position at release. Lower values in two or more of
those variables likely decreases your ball velocity entry angle. Note that within each
group, the participants are ordered by median ball entry angle from shots at the
free throw line from lowest to highest. .............................................................................................. 95
Figure 6.5: Three main strategies of regulating the center of mass vertical velocity at
release exist when increasing shot distance (gold: 4.19 m; blue: 6.02 m; purple: 7.24
m). The ‘CM Vv at Ground Departure’ group releases the ball early in the air, which
forces them to have to achieve a greater amount of center of mass vertical velocity
at ground departure in order to increase the center of mass vertical velocity at
release. The ‘Time in the Air before Release’ group consistently achieves a great
amount of center of mass vertical velocity at ground departure across shot
distances, and chooses to regulate the time in the air before release to increase
their center of mass vertical velocity at release. The ‘Both’ group generates
regulates both their center of mass vertical velocity at ground departure and when
they release the ball in the air. Note that within each group, the participants are
ordered by the body CM contribution to ball vertical velocity at release from lowest
to highest. ....................................................................................................................................................... 98
Figure 6.6: Upper arm angular velocity at release increased and upper arm angle at
release decreased with increasing shot distance (gold: 4.19 m; blue: 6.02 m; purple:
7.24 m). These participants tended to regulate the same across shot distances, but
the main separation was what their strategy affords them. The ‘Release Height/Set
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Position’ group prioritized using the upper arm for a greater release height and set
position for the forearm to rotate. The ‘Vertical Velocity’ group relied heavily on the
upper arm’s contribution to ball vertical velocity at release by having a high upper
arm angular velocity when the upper arm angle was small. The ‘Both’ group
achieved an average amount of vertical velocity contribution from the upper arm
by having both average upper arm angular velocity and upper arm angle at release.
Note that within each group, the participants were ordered by the arm contribution
to ball vertical velocity at release from lowest to highest. ....................................................... 100
Figure 6.7: Comparison of the primary causes for high and low ball entry angles.
Participant 2 (gold) achieved a high ball entry angle by having a large arm velocity
contribution, large whole body velocity contribution, and a high release height.
Participant 8 (silver) had a low ball entry angle due to a lower release height, low
arm velocity contribution, and an average whole body velocity contribution. ................ 103
Figure 7.1: Example of the ball flight when shooting from a seated position. The ball
must travel a greater vertical distance than standing basketball shots, which
increases the demand on the arms that are already tasked in generating majority of
the ball velocity. ......................................................................................................................................... 105
Figure 7.2: The arm velocity contribution to ball vertical (top row) and horizontal
(bottom row) velocity at release increased with an increase in shot distance (gold:
4.19 m; blue: 6.02 m; purple: 7.24 m). * p < 0.5; ** p < 0.01; *** p < 0.001; **** p <
0.0001. Participants are sorted by the median arm contribution to ball vertical
velocity at release in the 4.19 m shots. ............................................................................................. 110
Figure 7.3: The arm velocity contribution to ball vertical (top row) and horizontal
(bottom row) velocity at release increased with an increase in shot distance (gold:
4.19 m; blue: 6.02 m; purple: 7.24 m). * p < 0.5; ** p < 0.01; *** p < 0.001; **** p <
0.0001. Participants are sorted by the median arm contribution to ball vertical
velocity at release in the 4.19 m shots. ............................................................................................. 112
Figure 7.4: The upper arm angular velocity at release (top row) increased with an
increase in shot distance (gold: 4.19 m; blue: 6.02 m; purple: 7.24 m). The forearm
angular velocity at release was lowest at 4.19 m and greatest at 6.02 m. * p < 0.5; **
p < 0.01; *** p < 0.001; **** p < 0.0001. Note the bottom row y-axis is reversed.
Participants are sorted by the median arm contribution to ball vertical velocity at
release in the 4.19 m shots. ................................................................................................................... 114
Figure 7.5: The upper arm angle (top row) increased with shot distance while the
forearm angle (bottom row) decreased with shot distance (gold: 4.19 m; blue: 6.02
m; purple: 7.24 m). * p < 0.5; ** p < 0.01; *** p < 0.001; **** p < 0.0001. Participants
are sorted by the median arm contribution to ball vertical velocity at release in the
4.19 m shots. ............................................................................................................................................... 115
Figure 7.6: Example trial of Participant 4 (top). To begin the shot, the elbow was raised
high and the upper arm is set. The forearm then began to rotate about the elbow
xiii

joint until ball release. Example trial of Participant 5 (bottom). To begin the shot,
the elbow was set slightly below horizontal. During the shot, as the forearm rotated
forward toward the hoop, the upper arm also rotated upward, resulting in a greater
elbow vertical velocity relative vertical velocity at release than Participant 5. ............... 118
Figure 8.1: Workflow supporting the Integrated Biomechanics Informatics System
(IBIS). ............................................................................................................................................................. 124
Figure 8.2: Position on the runway relative to the scratch line during the Jump
Preparation Phase. Horizontal position of toes at final contact are expressed
relative to the scratch line (0,0). ......................................................................................................... 125
Figure 8.3: Support and Flight Phase Durations during the Jump Preparation Phase.
Durations are calculated by determining the change in time between Initial Contact
(IC) and Final Contact (FC). ................................................................................................................... 125
Figure 8.4: Momentum regulation during the Jump Preparation Phase. Center of mass
(CM) horizontal velocities calculated by determining the change in CM horizontal
position divided by the change in time between Final Contact (FC) and Initial
Contact (IC). ................................................................................................................................................ 126
Figure 8.5: Data structure for force and video collected for each athlete and use of data
in calculations of variables of interest. Cleaning of the data prior to analysis
involves cropping of the video records, conversion of measures into units, event
identification, normalization of quantities based on body mass or contact duration,
and attenuation of noise in source signals through filtering or curve fitting. ................... 128
Figure 8.6: Visualizing performance over time can assist in monitoring an individual’s
progression. ................................................................................................................................................ 130
Figure 8.7: Post competition reporting of key attributes of triple jump performance
using data in IBIS. ..................................................................................................................................... 131
Figure 8.8: Comparison of triple jump performances over time during competition and
in practice using data visualization tools in IBIS. ......................................................................... 131
Figure 8.9: Combining multiple data sources together can provide an informative
analysis. This visual highlights the differences in the mechanical demand on the
jumper for two different jumps. .......................................................................................................... 132
Figure 8.10: Continued advances in markerless motion capture technology will further
leverage these data base resources for improved validation estimates of CM
velocities based on kinematic source data, comparing and contrasting momentum
regulation mechanisms within athlete over time, as well as utilization of multilink
model simulation to assess ‘what if’ scenarios (e.g., model simulation of non-
contact, and impact and post impact phases during activities of daily living by
(Amezcua-Cerda, McNitt-Gray, & Flashner, 2022; McNitt-Gray, Requejo, Flashner, &
xiv

Held, 2004; Munaretto, McNitt-Gray, Flashner, & Requejo, 2012, 2013; Requejo,
McNitt-Gray, & Flashner, 2004; Wagner, 2018)). ......................................................................... 134
Figure 8.11: The Flight Phase Simulator allows coaches to determine how best to use
and develop an individual athlete’s abilities to improve their performance. For
example, to achieve a center of mass (CM) displacement during flight of 5.6 m (light
blue line reflects the combination of CM horizontal and vertical velocities needed to
achieve this displacement), an athlete can achieve this by using their horizontal
velocity (black text and arrows) or by using their ability convert horizontal to
vertical momentum (purple text and arrows) during last contact prior to the flight
phase of the long jump. ........................................................................................................................... 135
Figure 8.12: Interactive features allow coaches and athletes to contribute to the data
base by adding their own video clips using a fixed camera set up and data
acquisition ‘help’ documentation. In addition, the Flight Phase Simulator based on
projectile motion equation allows coaches and athletes to simulate center of mass
(CM) trajectory during flight phases of long jump and triple jump using “what if”
scenarios (e.g., if I can increase my speed by 0.2 m/s at Final Contact prior to flight,
how will this add to my CM displacement during flight). ......................................................... 136
Figure 8.13: Integration of video and force information (force vector synchronized in
time with the video images at key instances or as a force time-curve) shows how
the forces generated by the individual athlete causes the observed motion and how
an individual converts their horizontal velocity to vertical velocity during the last
contact prior to flight............................................................................................................................... 137

xv

Abstract
An individual’s performance is more than what they did but also how they did it.
While the performance outcome is useful as it typically defines success, it does not describe
how the individual achieved that outcome. It is possible to achieve a given outcome through
multiple strategies. For example, in the basketball shot, more than one ball flight trajectory
can result in a success. What causes the differences in the ball flight are differences in the
ball velocity at release. Not only are there more than one way to achieve a task, but it is
likely that individual characteristics exist. Individuals can successfully perform tasks using
their own control strategies, which may shift depending on the context and affordance of
the environment (e.g., less space) or physiological state of the system (e.g., fatigued). This is
the true beauty of human movement, as each individual has their own control strategies,
like a motor signature. This may make it more challenging to understand performance, but
the generalization of strategies across many individuals can be detrimental. Identifying
individual’s how an individual performs an activity can serve as the basis of individual-
specific rehabilitation and training. This is further helpful when the individual’s tendencies
are captured within the context of the task.
The collective research presented in this document present individual strategies in
contextually-relevant situations. By analyzing individuals in the field (Chapter 3, 4, 5, 7), we
can get a better understanding of individual-specific tendencies that exist in real world
scenarios. Understanding the underlying mechanics of the movement allows us to identify
what can be modified. We can then “fit” the feedback/response to the individual, whether
that be personalized fitting a wheelchair (Chapter 3) or technique feedback (Chapter 6).
xvi

Through the use of a database and similar tools (Chapter 8), we can track the individual’s
progression over time. This allows for more meaningful questions to be asked and skill
progressions to be tracked and refined.
Future research can expand on the work presented here by applying the same
within-individual analyses to a broader group of people, such as gender, skill-level, and
mobility. This may help shed light onto why there may be differences, and how the
individual can improve. Another future direction is to track the hand during the basketball
shot. Likely due to the group analyses, there are mixed results suggesting how the hand
segment impacts the shot. By adding the hand to the arm system, it would give a more
detailed picture into how the individual uses the arms to generate the ball velocity at
release.

1

Chapter 1 Introduction
An individual’s performance is more than what they did but also how they did it.
While the performance outcome is useful as it typically defines success, it does not describe
how the individual achieved that outcome. It is possible to achieve a given outcome through
multiple strategies. For example, in the basketball shot, more than one ball flight trajectory
can result in a success (Figure 1.1). What causes the differences in the ball flight are
differences in the ball velocity at release. Not only are there more than one way to achieve a
task, but it is likely that individual characteristics exist. Individuals can successfully
perform tasks using their own control strategies, which may shift depending on the context
and affordance of the environment (e.g., less space) or physiological state of the system
(e.g., fatigued). This is the true beauty of human movement, as each individual has their
own control strategies, like a motor signature (Horst, Janssen, Beckmann, & Schöllhorn,
2020). This may make it more challenging to understand performance, but the
generalization of strategies across many individuals can be detrimental (Fisher, Medaglia,
& Jeronimus, 2018). Identifying individual’s how an individual performs an activity can
serve as the basis of individual-specific rehabilitation and training. This is further helpful
when the individual’s tendencies are captured within the context of the task.
2

Figure 1.1: There are multiple ball flight trajectories that can result in a successful shot.
Exemplar successful trajectories by multiple participants (color) and two different distances
(4.19 m, 6.02 m).
Analyzing performance in “real-world” contexts provides the ability to understand
individual control strategies that exist within their everyday activities. For example,
wheelchair propulsion on an ergometer may contribute to different propulsion technique
patterns compared to overground propulsion due to the constraints of the setup (Ian M.
Russell, 2018). Understanding how the individual propels overground may be more
representative of their everyday activity. In team sports, not only is it important to
understand how the individual accomplishes the mechanical demands of the task, but also
how it is executed during contextually relevant scenarios, such as when defended by an
opposing player. Analyzing the individual within contextually relevant situations may lead
to more informed decision making that may increase its impact on future performance.
3

Analyzing the movement over time provides further context of the mechanisms used by the
individual to complete the task and allows methods of assessing progressions. A robust
database allows not only the maintenance of the data but also the ability to link multiple
data sources together to show the how the individual achieved the performance outcome.
1.1 Basketball
The basketball shot has a clear performance objective: put the ball in the hoop. To
achieve this, the ball must be released with a resultant ball velocity magnitude and angle
that results in a ball flight trajectory that enters the hoop (Figure 1.2). The ball velocity at
release is a result of the shooter’s center of mass and arms contributions (Hay, 1985).
Previous research has suggested a range of ball release parameters (Brancazio, 1981;
Hamilton & Reinschmidt, 1997; Hay, 1985; Mortimer, 1951; Nakano, Fukashiro, &
Yoshioka, 2020; Tran & Silverberg, 2008), as well as investigate arm joint configuration and
angular velocities during successful shots (Miller & Bartlett, 1996; Miller & Bartlett, 1993;
Okazaki & Rodacki, 2012). However, there is likely no general kinematic determinants that
are associated with a success shot (Coves, Caballero, & Moreno, 2020) as there are
practically an unlimited amount of arm joint configurations and velocities that result in a
successful shot (Okubo & Hubbard, 2016). It is likely the determinants of success in the
basketball shot are individualistic (Coves, Caballero, & Moreno, 2020). Figure 1.3 illustrates
the progression of the basketball shot and highlights three different shooting techniques.
Therefore, it is clear the importance of analyzing the individual tendencies in generating
ball velocity at release, especially in contexts that may influence ball release parameters
such as different shot distances (Miller & Bartlett, 1996; Miller & Bartlett, 1993; Nakano,
4

Fukashiro, & Yoshioka, 2020; Okazaki & Rodacki, 2012) and shooting while defended
(Gorman & Maloney, 2016; Rojas, Cepero, Ona, & Gutierrez, 2000).

Figure 1.2: The reference system and basketball variables. Position is relative to the location
on the floor directly beneath the center of the hoop (origin). Linear velocity is defined within
the plane YZ and angular velocity about the X-axis.
5

Figure 1.3: Filmstrip of key events during the basketball shot with three different techniques.
Start of impulse: When the individual applies force contributing to the shot. Arm swing:
Beginning of the upper arm counter-clockwise rotation. Arm shot initiation: Beginning of arm
rotation that contributes to the ball release velocity. End of Impulse: When the individual is no
longer applying force into the ground, also referred to as ground departure. Ball Release: Last
frame in which the person is in contact with the ball. CM Apex: The individual’s center of mass
trajectory apex.
When increasing the shot distance, the ball release velocity at release must increase
in order to be successful. A greater contribution likely comes from the center of mass
velocity (B. Elliot, 1992), as the center of mass vertical velocity increases with an increase
in shot distance (Miller & Bartlett, 1996; Miller & Bartlett, 1993; Okazaki & Rodacki, 2012;
Walters, Hudson, & Bird, 1990; Wiens & McNitt-Gray, 2020). A greater center of mass
vertical velocity is achieved by releasing the ball earlier relative to the center of mass
6

trajectory apex (Figure 1.4) (B. Elliot, 1992; B. C. Elliot & White, 1989; Miller & Bartlett,
1993).

Figure 1.4: The center of mass vertical velocity (CM Vv) is greater when releasing the ball
earlier (purple) relative to the center of mass.
In the jump shot - when the shooter leaves the ground - the potential for releasing
the ball earlier relative to the center of mass apex is defined by the center of mass vertical
velocity at ground departure. The greater the center of mass vertical velocity at ground
departure, the higher the center of mass apex and the more time the shooter is in the air.
The center of mass velocity at ground departure is defined by the impulse generated during
the ground contact and any momentum the shooter had prior to the shot preparation
(Figure 1.5). Therefore, the shooter can modify their center of mass velocity at ball release
by initiating the shooting motion with more momentum (e.g., stepping into the shot),
7

generating more impulse during ground contact, and releasing the ball earlier in the jump
(decrease gravity’s effect).

Figure 1.5: The center of mass velocity during the basketball shot is a result of the net impulse
generated by the legs. Once the shooter leaves the ground, gravity accelerates the body
toward the ground, reducing their center of mass velocity. The center of mass velocity at the
time of ball release is the amount contributed to the ball release velocity.
When increasing shot distance, it is probable that the shooter releases the ball
earlier relative to ground departure (Miller & Bartlett, 1993; Nakano, Fukashiro, &
Yoshioka, 2020) and generates a greater impulse. However, it is not known if there are
individual strategies in achieving the greater center of mass velocity at ball release. If the
shooter needs to achieve a greater ball release velocity, analyzing how the individual
regulates the whole body velocity reveals how the individual solves the problem and
8

potentially presents options for improvement. Given that if you have center of mass
velocity at ball release, you use it, any individual characteristics in the center of mass
velocity at ball release will also influence the shooter’s ball velocity contribution. It is
unknown if individuals have similar velocity contributions from the center of mass and
arms, and if these are consistent across shot distances. It may be helpful to identify if an
individual relies more on the arms at greater distances so strategies can be implemented to
increase the center of mass velocity’s contribution.
Individuals participating in wheelchair basketball have limited options in generating
the ball velocity at release. Generation of center of mass vertical velocity and CM vertical
position at ball release is limited when initiating a basketball shot from a seated position.
As a result, arm contributions to ball velocity at release is expected to be greater when
initiating the shot from a seated position as compared to a standing position. It is unknown
how body and arm contributions to ball velocity at release change with increases in shot
distance.
1.2 Database
A database is only as useful as the data within it. By going beyond the performance
outcome and tracking how the individual is performing tasks in realistic contexts, more
meaningful questions can be investigated, and more mechanistic tendencies can be tracked
over time. Incorporating these biomechanical data into the database provides meaningful
context regarding mechanical factors that influence performance outcomes. These data can
then be leveraged to improve performance through the design of more personalized skill
9

progressions. Over time, skill progressions leading to an intended performance outcome
can be assessed and further refined as athletes prepare to play.
1.3 Completed Set of Experiments
This body of work (Figure 1.6) seeks to provide evidence of how an individual
generates ball release velocity in the basketball shot and how it may change based on the
context (e.g., change in distance). Due to the increased ball release velocity required to
successful make a shot from an increased shot distance, changing the shot distances will
allow the analysis of how individuals must generate more ball velocity at release. The
generation of the ball release velocity requires multijoint control. By exploring the
individual’s multijoint coordination and how it may change with an increase in shot
distance, we can explore the individual’s multijoint control strategies in different
mechanical requirements. An understanding of each individual’s tendencies can inform
training and feedback to improve accuracy. Finally, it will also include the foundation of
creating a robust database to track the mechanics of an individual’s performance over time.

Figure 1.6: An outline of the set of experiments conducted in this body of work.
10

Chapter 2 Methods
2.1 Experimental Procedures
The series of studies were completed over three collections (Figure 2.1).

Figure 2.1: Data acquired from these three collections were incorporated into a database to
track performance over time.
2.1.1 Basketball collections
2.1.1.1 Standing basketball collection
Recreational basketball players were asked to participate in the standing basketball
collections. Participants were recruited from university club teams and campus
recreational leagues teams. Participants provided informed consent in accordance with the
USC Institutional Review Board.
Participants shot from the following shot locations: 4.19 m, 6.02 m, 7.24 m (Figure
2.2). The first two distances were chosen due to the frequency of shots taken at those
11

locations during a game. The furthest distance was chosen to analyze performance likely
near an individual’s limits. The participants were given at least 10 minutes to perform a
self-guided warm-up prior to starting the collection.

Figure 2.2: Basketball shots will be taken from three distances from the center of the hoop:
4.19 m, 6.02 m, 7.24 m. Camera and force plate set up. The two portable force plates will be
moved to the condition’s shot location.
2.1.1.2 Wheelchair basketball collection
Experienced wheelchair basketball players were asked to participate in the
wheelchair basketball collection. Participants were recruited from a wheelchair basketball
team that competes at the national level. Participants provided informed consent in
12

accordance with the Rancho Research Institute Institutional Review Board for research
involving human subjects.
Each participant shot from two of the three possible locations from the hoop: 3.35 m, 4.19
m, 6.02 m. The two shot locations were chosen based on the position and role of the
participant on their team (inside player: 3.35 m and 4.19 m; outside player: 4.19 m and
6.02 m). Participants attempted shots from two shot locations in a stationary position and
while rolling. Participants were given at least 10 minutes to perform a self-guided warm-up
before the session started.
2.2 Reference System
The gym’s reference system is illustrated in Figure 2.3. The origin (0, 0) is located on
the floor, directly beneath the center of the hoop. The shot locations will be measured from
that location. From the shooter’s perspective, positive x, y, and z are towards the hoop, to
the left, and up, respectively. Vertical will refer to the z-axis, and horizontal will refer to the
x-axis.
13

Figure 2.3: The gym reference system. The origin (0, 0) is located on the floor directly beneath
the center of the hoop. Positive x is in the direction of the hoop. Positive y is in the direction to
the left of the hoop from the shooter’s perspective. Positive z is up. Positive angular velocity
about the y-axis is clockwise.
2.3 Data collected
2.3.1 Video
The motion of the participant and ball kinematics were recorded by eight high speed
video cameras (120 Hz, Prime Color, OptiTrack, Corvallis, OR) (Figure 2.2). Three-
dimensional kinematics of the body motion were calculated using a markerless motion
capture software (Theia Markerless Inc., Kingston, ON, Canada) (Kanko et al., 2021; Kanko,
Laende, Davis, Selbie, & Deluzio, 2021; Kanko, Laende, Selbie, & Deluzio, 2021). The ball
position was detected using a neural network (Mathis et al., 2018; Nath et al., 2019) trained
14

on a subset of images from each collection from each camera view. The ball position in
three-dimensional gym reference system was calculated using a custom Python code.
2.3.2 Force
Two portable force plates (1200 Hz, Kistler, Amherst, NY, USA) measured ground
reaction forces generated by each leg during the shot (Figure 2.2. The reference system of
the force plates was transformed to match the gym reference system. Ground reaction
forces were only measured in the standing basketball collection.
2.3.3 Kinematics
Body kinematic data were calculated using a deep learning algorithm-based
software (Theia Markerless Inc., Kingston, ON, Canada) (Kanko et al., 2021; Kanko, Laende,
Davis, Selbie, & Deluzio, 2021; Kanko, Laende, Selbie, & Deluzio, 2021). The software was
provided video data from eight synchronized cameras, and it estimated the locations of key
anatomical features. The software then applied an articulated multi-body model scaled to
the participant-specific anatomical landmark positions in three-dimensional space. Inverse
kinematics estimated the participant’s three-dimensional pose.
2.3.4 Segment angles
Upper arm angle was expressed as the upper arm angle relative to the right
horizontal in the Y-axis of the gym reference system (Figure 2.3) where
0
∘
= upper arm parallel with the horizontal line
> 0
∘
= the distal endpoint (elbow) was at a more vertical position than the proximal
endpoint (shoulder)
< 0
∘
= the proximal endpoint (shoulder) was at a more vertical position than the distal
15

endpoint (elbow)

Forearm angle was expressed as the forearm angle relative to the right horizontal Y-
axis of the gym reference system (Figure 2.3) where
0
∘
= forearm parallel with the horizontal line
> 0
∘
= the distal endpoint (wrist) was at a more vertical position than the proximal
endpoint (elbow)
< 0
∘
= the proximal endpoint (elbow) was at a more vertical position than the distal
endpoint (shoulder)

2.3.5 Segment angular velocities
Upper arm angular velocity was expressed as the upper arm angular velocity about
the X-axis of the gym reference system (Figure 2.3).
Forearm angular velocity was expressed as the forearm angular velocity about the
X-axis of the gym reference system (Figure 2.3).
2.4 Variable Definitions
Horizontal refers to data along the y-axis and vertical refers to data along the z-axis
in the gym reference system (Figure 2.3).
2.4.1 Ball release
Ball release was the last frame the individual was in contact with the ball before its
flight toward the hoop (Figure 2.3). This event in time was identified manually.
16

2.4.2 Ball entry into the hoop
Ball entry frame was automatically identified using a custom Python script that
identified when the ball is 0.169 meters above the hoop (men’s ball radius is 0.119 m).
2.4.3 Ball release velocity
Ball release velocity was calculated using equations of motion, the timing of ball
release and ball entry into the hoop, and the ball vertical and horizontal position at release
and entry. The ball position data were smoothed with a dual-pass 2nd-order Butterworth
filter with a cutoff frequency of 4 Hz. Ball velocity was will be measured in the three-
dimensional space (Figure 2.3).
𝑣 𝑣 = (𝛥𝑧 − 0.5 ∗ 𝑔 ∗ 𝛥 𝑡 2
/𝛥𝑡 )
𝑣 ℎ
= 𝛥𝑦 /𝛥𝑡
𝑣 is the ball release velocity
𝛥𝑧 is the change in vertical position from the ball entry frame to the ball release frame
𝛥𝑦 is the change in horizontal position from the ball entry frame to the ball release
frame
𝛥𝑡 is the ball flight time from ball release to ball entry frame
𝑔 is gravity
2.4.4 Ball release height
Ball release height was defined as the vertical distance from the center of the ball to
the floor (Figure 2.3).
2.4.5 Ball release distance
Ball release distance (shot distance) was defined as the horizontal distance from the
center of the ball to the point on the floor directly beneath the center of the hoop (origin of
reference system) (Figure 2.3).
17

2.4.6 Ground departure
Ground departure occurred when the individual was no longer applying force into
the ground. It was measured by the vertical reaction forces and was defined when the
vertical reaction forces were less than 30 Newtons.
2.4.7 Net impulse
Impulse was calculated using the reaction forces measured by portable force plates
during the ground contact of the shot. Net vertical impulse was calculated using the
equation below and net horizontal impulse by the equation below.
∫ 𝑅 𝑡 2
𝑡 1
𝐹𝑧 𝑑𝑡 + ∫ 𝐵 𝑡 2
𝑡 1
𝑊 𝑑𝑡
∫ 𝑅 𝑡 2
𝑡 1
𝐹 𝑦 𝑑𝑡
𝑅𝐹 is reaction forces generated by both legs (N)
𝐵𝑊 is the shooter’s body weight (N)
Start of the shot (𝑡 1
) was defined at the minimum whole body center of mass
vertical velocity prior to the shot. This starting point was chosen due to the participants
stepping onto the force plates after starting off of them. It was the most consistently
identified instance across all participants and shot distances. The minimum whole body
center of mass vertical velocity is also when the individual begins to redirect their center of
mass vertical position upwards. End of impulse generation (𝑡 2
) was defined as ground
departure (described above). In the shot attempts that a participant did not leave the
ground, the end of impulse generation was defined as ball release.
18

2.4.8 Center of mass velocity at ground departure
Center of mass vertical velocity at ground departure was identified (Figure 2.3).
Center of mass horizontal velocity at ground departure will be calculated using the net
horizontal impulse generated during the ground contact of the shot (Figure 2.3).
∫ 𝑅 𝑡 2
𝑡 1
𝐹𝑧 𝑑𝑡 + ∫ 𝐵 𝑡 2
𝑡 1
𝑊 𝑑𝑡 = 𝑚 𝑣 𝑧 ,𝑡 2
− 𝑚 𝑣 𝑧 ,𝑡 1

∫ 𝑅 𝑡 2
𝑡 1
𝐹 𝑦 𝑑𝑡 = 𝑚 𝑣 𝑦 ,𝑡 2
− 𝑚 𝑣 𝑦 ,𝑡 1

𝑅𝐹 is reaction forces generated by both legs (N)
𝐵𝑊 is the shooter’s body weight (N)
𝑚 is the shooter’s body mass (kg)
𝑣 is the shooter’s center of mass velocity (m/s)
Due to the individual being static at the start of the impulse generation, 𝑚 𝑣 𝑡 1
is 0.
This allows us to calculate the center of mass velocity when the individual no longer is
applying force into the ground (e.g., ground departure).
19

Figure 2.4: The center of mass vertical and horizontal velocity at ball release.
2.4.9 Center of mass velocity at ball release
Center of mass horizontal and vertical velocity at ball release were calculated using
the model. Center of mass horizontal velocity at ball release was equal to the center of mass
horizontal velocity at ground departure (Figure 2.6) based on the assumption that the body
center of mass was not accelerating in the horizontal direction while in the air (neglecting
air resistance).
𝐶 𝑀 𝑟𝑒𝑙𝑒𝑎𝑠𝑒 ,𝑧 ̇ = 𝐶 𝑀 𝑑𝑒𝑝𝑎𝑟𝑡𝑢𝑟𝑒 ,𝑧 ̇ + 𝑔 ∗ 𝑡 𝑎𝑖𝑟
𝐶 𝑀 𝑟𝑒𝑙𝑒𝑎𝑠𝑒 ,𝑦 ̇ = 𝐶 𝑀 𝑑𝑒𝑝𝑎𝑟𝑡𝑢𝑟𝑒 ,𝑦 ̇
𝐶 𝑀 𝑟𝑒𝑙𝑒𝑎𝑠𝑒 ̇ is the center of mass velocity at release
𝐶 𝑀 𝑑𝑒𝑝𝑎𝑟𝑡𝑢𝑟𝑒 ̇ is the center of mass velocity at ground departure
𝑔 is gravity
𝑡 𝑎𝑖𝑟 is time of ball release relative to ground departure
20

2.4.10 Center of mass velocity contribution
The center of mass velocity contribution was defined in both the magnitude and
percent contribution to ball velocity at release (Figure 2.5). The magnitude was the center
of mass velocity magnitude at ball release. The percent contribution was the ratio of center
of mass velocity magnitude at ball release to the ball release velocity magnitude. It was
defined in the vertical and horizontal directions.

Figure 2.5: The shooter’s center of mass and arms contribute to the ball velocity.
2.4.11 Arm velocity contribution
The arm velocity contribution was defined in both the magnitude and percent
contribution to ball velocity at release (Figure 2.5). The magnitude was the ball release
velocity minus the center of mass velocity magnitude at ball release (Hay, 1985). The
21

percent contribution was the ratio of arm velocity contribution magnitude at ball release to
the ball release velocity magnitude. It was defined in the vertical and horizontal directions.
2.4.12 Time of center of mass apex
The time of center of mass apex was calculated using equations of motion and the
center of mass vertical velocity at ground departure.
𝑇𝑖𝑚𝑒 𝑜𝑓 𝐶𝑒𝑛𝑡𝑒𝑟 𝑜𝑓 𝑀𝑎𝑠𝑠 𝐴𝑝𝑒𝑥 (𝑠 ) = 𝑣 𝑧 /9.81 𝑚 /𝑠 2

𝑣 𝑧 is the center of mass’ vertical velocity at ground departure.
2.4.13 Time of ball release relative to ground departure
The duration between ground departure and ball release defined time of ball release
relative to ground departure (Figure 2.6).

Figure 2.6: Time of ball release relative to ground departure is the time between the
participant no long applying force into the ground and when the ball is released. Time of ball
release relative to center of mass apex is the time between ball release and the highest
vertical position of the center of mass (apex).
2.4.14 Time of ball release relative to center of mass apex
The duration between center of mass apex and ball release defined time of ball
release relative to center of mass apex (Figure 2.6).
22

Chapter 3 Characterizing the effect of personalized wheelchair adjustments on posture
and upper extremity mechanics during overground wheelchair propulsion
3.1 Introduction
The configuration of a wheelchair can affect the mechanical demand imposed on the
upper extremity during push (Mulroy et al., 2005; Munaretto, McNitt-Gray, Flashner, &
Requejo, 2012, 2013; Ian M. Russell et al., 2015; L. H. van der Woude, Veeger, Rozendal, &
Sargean, 1989), individual’s push technique (Boninger et al., 2002; L. van der Woude et al.,
2009; L. H. van der Woude, Veeger, Rozendal, & Sargean, 1989), muscular activation
(Gutierrez, Mulroy, Newsam, Gronley, & Perry, 2005), cardio-respiratory parameters (L.
van der Woude et al., 2009; L. H. van der Woude, Veeger, Rozendal, & Sargean, 1989), and
stability (Majaess, Kirby, Ackroyd-Stolarz, & Charlebois, 1993). Personalized configuration,
such as of a WC consistent with clinical guidelines, requires the ability to modify seat
height, seat dump, seatback angle, and axle position. Strategic adjustments in these features
through personalized WC fitting contributes to improved posture, balance, propulsion
energetics and mitigate detrimental mechanical loading of the shoulder during activities an
individual performs during their daily life, thereby improving function and reducing injury
risk (energetics (Brubaker, 1986; L. H. van der Woude, Veeger, Rozendal, & Sargean, 1989);
push technique (Boninger et al., 2002; Boninger, Baldwin, Cooper, Koontz, & Chan, 2000;
Hughes, Weimar, Sheth, & Brubaker, 1992; Masse, Lamontagne, & O’Riain, 1992; L. H. van
der Woude, Veeger, Rozendal, & Sargean, 1989)). Currently, this level of adjustability is
only found in ultralight weight manual WCs (“Preservation of Upper Limb Function
Following Spinal Cord Injury,” 2005).
23

Based on previous research, ergonomics, and recommendations from experienced
clinicians, clinical practice guidelines have been established to promote - amongst other
areas - shoulder health, posture, and stability (“Preservation of Upper Limb Function
Following Spinal Cord Injury,” 2005). When configuring the WC, seated posture and
stability is considered a priority, while keeping the individual’s balance and stability needs
in mind (“Preservation of Upper Limb Function Following Spinal Cord Injury,” 2005). It is
also recommended that the elbow angle be between 100-120 degrees when the hand is
located top-dead-center of the wheel for effective propulsion energetics (“Preservation of
Upper Limb Function Following Spinal Cord Injury,” 2005).
While personalized WC fitting is becoming more prevalent, particularly in sport
(Haydon & Pinder, 2020; Haydon, Pinder, Grimshaw, & Robertson, 2018; Haydon, Pinder,
Grimshaw, & Robertson, 2019), current approaches to WC fitting rely heavily on the
expertise of the clinician. The clinician must understand the need and function of the
individual while making any modifications to the WC configuration. This is generally
accomplished by speaking with the individual, observing how they sit in their WC, and
analyzing how they perform functional activities of daily living. As decisions regarding WC
adjustments are made by the clinician (e.g., lowering the seat, altering back rest, tilting of
the seat, shifting the axle etc.), the clinician also needs to consider how these WC
adjustments often made in combination affect other necessary requirements related to
posture, pressure relief, and WC stability, as well as external limiting factors (e.g.,
environmental challenges including obstacles, inclines, surfaces, work place ergonomics
etc.) are also satisfied.
24

In this study, we investigated how personalized adjustments to WC seating, made by
a seating center clinician in accordance with clinical guidelines, would affect posture, upper
extremity kinematics, and the mechanical demand imposed on the shoulder during manual
WC propulsion on a level sidewalk at self-selected fast speeds. Mechanical demand
imposed on the shoulder was indicated by the shoulder net joint moment (NJM) generated
during the push phase (NJM impulse). In accordance with clinical guidelines, we
hypothesized these personalized adjustments made by the seating center clinician would
lead to more upright posture, indicated by a more vertical torso angle and upper extremity
kinematics with an elbow angle between 100- 120 degrees when the wrist was at top-
dead-center without an increase in shoulder NJM impulse during push. Each individual’s
median difference in posture, elbow angles, and shoulder NJM impulse between pre- and
post-WC reconfiguration were scored based on alignment with clinical guidelines and
statistical analysis was used to determine the probability of positive outcomes with WC
reconfiguration by using 95% confidence intervals for each variable of interest. An
outcome was considered positive if the WC reconfiguration contributed to results within or
more aligned with clinical guidelines. The results of this pilot work is expected to inform
the use of low-cost technology and personalized model simulation to inform clinical-guided
refinements in WC seating for an individual manual WC user with paraplegia. By
incorporating sensitivity of mechanical loading to modifications in WC configuration, we
expect that these insights when provided to clinicians can lead to improvements in function
and reduced risk of injury in manual WC users.
25

3.2 Methods
Manual wheelchair users (25 male, 1 female) with paraplegia (T2-L3) volunteered
to participate. The participants were recruited from Ranchos Los Amigos National
Rehabilitation Center and provided consent in accordance with the Institutional Review
Board. The mean (standard deviation) weight and age of the participants were 79.71
(18.58) kg and 33 (range: 18-56) years, respectively. The time since injury occurrence
ranged from 2 months to 25 years. All participants had been using their new or
replacement wheelchair at baseline for at least one month.
Individuals with paraplegia from complete spinal cord injury (level: thoracic or
lower, American Spinal Cord Injury Association A or B with no motor function below spinal
cord injury level) were included if they: were using their own wheelchair for minimum one
month, were free of shoulder pain at entry into study that interferes with daily activities or
requires medical intervention, and had a total score on the Wheelchair Users Shoulder Pain
Index of 10 or less. Individuals with positive Hawkins-Kennedy test and painful arc in
shoulder abduction or flexion (positive impingement signs), biceps tendonitis (positive
Speed’s test), adhesive capsulitis, cervical radiculopathy at initial evaluation, shoulder
injury or surgery history or orthopedic or neurological disorder (other than spinal cord
injury) that impacts arm function were excluded.
Wheelchair propulsion was performed on a level sidewalk in the courtyard outside
of the Seating Center at the Ranchos Los Amigos National Rehabilitation Center. Each trial
was initiated from a stationary position and individuals continued to propel their WC for
26

approximately 10 meters at a self-selected free and fast pace. A fast pace was described to
the participant as “if you are in a hurry to not miss an important appointment.”
Reaction force (RF) generated at the push rim were measured using an
instrumented wheel secured to the individual’s WC (240 Hz; strain gauges, SmartWheel,
Three Rivers Holdings, Mesa AZ, USA). Frontal and sagittal plane kinematics were recorded
simultaneously (60 Hz video). Wearable inertial measurement unit sensors (APDM,
Portland, OR) secured to the wrist and upper arm measured upper extremity segment
acceleration and angular velocity kinematics during manual WC propulsion. Kinematic data
were filtered using a 4th order Butterworth recursive filter (6 Hz cut-off frequency)
synchronized at the time of hand contact with the push rim and interpolated to 240 Hz as
to match the force sampling frequency.
Frontal plane video confirmed that when the hand applies a RF greater than five
Newtons to the pushrim that the elbow was in plane with the wrist, and the shoulder offset
from the wrist and elbow was consistent throughout the propulsion cycle. Inverse
dynamics using the upper extremity segments of fixed lengths, body segment parameters
(de Leva, 1996) and RF applied between the wrist and the pushrim were used to calculate
the resultant elbow and shoulder net joint moments (inverse dynamics, custom script in
MATLAB).
Push was defined as the interval when the moment about the wheel axle exceeded
five Newton-meters (Figure 3.1). RF orientation relative to forearm was defined as the
angle between the RF vector in the sagittal plane and the long axis of the forearm. A RF
aligned with the forearm was considered 0 degree, and a positive RF orientation angle
27

indicates the RF vector was anterior to the forearm. Resultant shoulder net joint moment
(NJM) impulse was calculated by integrating the resultant shoulder net joint moment
during the push duration (flexor NJM +).
Shifts in posture and technique pre- and post-WC fitting were characterized by
changes in torso and elbow angle at wrist top-dead-center of the wheel in relation to
clinical guidelines (“Preservation of Upper Limb Function Following Spinal Cord Injury,”
2005). Torso angle was defined as the anterior angle created by the intersection of the line
from the shoulder joint center to the wheel axle and the line through the wheel axle parallel
to the ground (right horizontal) (Figure 3.2). Elbow angle was defined as the anterior angle
between the long axes of the upper arm and forearm (Figure 3.2). Clinical guidelines for
WC fitting recommend an upright posture, characterized in this study by a torso angle of 90
(+/-5) degrees relative to horizontal (Figure 3.2 & Table 3.1). Based on energetics (REF),
the recommended upper extremity configuration when the wrist is at top-dead-center of
the push rim is an elbow angle of 110 (+/-10 degrees) (Figure 3.2 & Table 3.1). A functional
difference in mechanical demand imposed on the shoulder during push corresponded the
observed difference in shoulder NJM impulse at free and self-selected fast paces during
manual WC propulsion on a level sidewalk (Table 3.1).
28

Figure 3.1: Selection of key events during task: a) start of push; b) wrist top-dead-center; c)
peak RF magnitude; d) peak elbow extension angular velocity; e) end of push using variables
of interest for an exemplar participant.
29

Figure 3.2: Torso angle was defined as the anterior angle created by the right horizontal and
the line from the shoulder joint center and the wheel axle. Elbow angle was defined as the
anteriorinterior angle between the long axes of the upper arm and forearm.
3.2.1 Statistics
In this analysis, WC propulsion, performed at a self-selected fast speed at baseline
and one-month post-WC reconfiguration, were characterized using measurements from 6-
10 propulsion cycles at performed at pace by each participant. Posture, upper extremity
configuration, and mechanical demand imposed on the shoulder during push were
compared within participant pre- (at baseline) and post-WC reconfiguration. To compare
propulsion characteristics pre- and post-configuration, differences in median values of
torso angle and elbow angle at wrist top-dead-center as well as shoulder NJM impulse
during push were calculated for each participant. Changes in the median values of these
variables of interest, from pre- to post-WC reconfiguration, were scored based on levels of
change in relation to clinical guidelines. score of 0 indicated no significant functional
change using the defined thresholds whereas scores of +1 (more aligned) or -1 (less
30

aligned) reflected alignment with clinical guidelines (Table 3.1). The thresholds for each
variable were approximately half the standard deviation of the measured variable
(resultant shoulder NJM impulse: 2 Nms, torso angle at wrist top-dead-center: 2 degrees,
elbow angle at wrist top-dead-center: 5 degrees).
For resultant shoulder NJM impulse, torso angle at wrist top-dead-center, and elbow
angle at wrist top-dead-center, 95% Confidence intervals for the probability associated
with each scoring outcome were computed using R. We then tested if a decision can be
made about which scoring outcome had the highest probability with an 𝛼 = 0.05.

31

Table 3.1: Scoring summary explanation for each variable of interest. x1: Pre; x2: Post.
Pre (x1) Post (x2) Score Reason
Resultant Shoulder NJM Impulse
x2-x1 <= -threshold 1
Decreased in magnitude by
more than threshold
x2-x1 >= threshold -1
Increased in magnitude by
more than threshold
Other 0 No change more than threshold
Torso Angle at Wrist Top-Dead-Center
85 <= x1 <= 90 85 <= x2 <= 90 1 Stayed within guideline
|x2-x1| >= thresh -1
Left guideline range and
change was more than
threshold
Other 0
Left guideline range but change
was less than threshold
x1 <= 85 or x1 >= 90 |x2-x1| <= thresh 0
Started outside guideline range
and change was less than
threshold
85 <= x2 <= 90 1
Moved to within guideline range
and change was more than
threshold
x2-x1 < 0 and x1 > 90 1
Started higher than guideline
range and moved within range
x2-x1 > 0 and x1 < 85 1
Started lower than guideline
range and moved within range
Other -1
Started outside range and
change was further from range
and greater than threshold
Elbow Angle at Wrist Top-Dead-Center
100 <= x1 <= 120 100 <= x2 <= 120 1 Stayed within guideline
|x2-x1| >= thresh -1
Left guideline range and
change was more than
threshold
32

Pre (x1) Post (x2) Score Reason
Other 0
Left guideline range but change
was less than threshold
x1 <= 100 or x1 >= 120 |x2-x1| <= thresh 0
Started outside guideline range
and change was less than
threshold
100 <= x2 <= 120 1
Moved to within guideline range
and change was more than
threshold
x2-x1 < 0 and x1 > 120 1
Started higher than guideline
range and moved within range
x2-x1 > 0 and x1 < 100 1
Started lower than guideline
range and moved within range
Other -1
Started outside range and
change was further from range
and greater than threshold
3.3 Results
Differences in posture, upper extremity configuration, and mechanical demand
imposed on the shoulder during push were observed during manual WC propulsion on a
level sidewalk at self-selected fast speeds before and after WC reconfiguration (Table 3.2).
Resultant shoulder NJM impulse during push likely remained unchanged from pre-WC
configuration to post-WC configuration (Figure 3.3). Across participants, torso angles,
when wrists were positioned at top-dead-center of the wheel, were found to likely be more
upright or unchanged after WC reconfiguration as compared to their initial WC
configuration (Figure 3.4). Across participants, elbow angles when wrists were positioned
top-dead-center of the wheel during propulsion either stayed within the suggested range
(100
∘
-120
∘
) or shifted towards or into the range after personalized WC configuration
33

(Figure 3.5). Table 3.3 lists the probability and 95% confidence intervals for each scoring
outcome for the variables of interest.

Table 3.2: Wheelchair adjustments in seatback, axle position relative to seatback, and seat
height for each participant from pre- to post-WC reconfiguration and scoring of posture,
elbow, and shoulder NJM impulse outcomes.
1 2 3 4 5 6 7 8 9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
2
1
2
2
2
3
2
4
2
5
2
6
Seatback
Angle
a
V V V R V V V V R V V V V V
Height
b
R R L R L L L R
Position
c
B F F F F F F
Axle Position Relative to Seatback
Axle
c
B B B B B B B B B
Seat Height
Rear
b
R R R R R R R R R R R R R R R R
Front
b
R R R R R R R R R R
Outcome Scores
34

1 2 3 4 5 6 7 8 9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
2
1
2
2
2
3
2
4
2
5
2
6
Shoulde
r NJM
Impulse
during
Push

1

0

0

1

0

0

0

0

0
-
1

0

0

0

0

0

0

0

0

0

0
-
1

0

0

0

0

1
Torso
Angle at
Wrist
Top-
Dead-
Center

1

1

0

1

1

0

0

1

0

1

0

1

1

1

0

0

1

1

1

0

0

1

0

1
-
1

0
Elbow
Angle at
Wrist
Top-
Dead-
Center

1

1

1

1

1

0
-
1

1

1

1

1

1

1

1

1

1

1
-
1

1

1

1
-
1

1

1

1

1
a
V: more vertical; R: more reclined
b
R: raised; L: lowered
c
B: backward; F: forward

35

Table 3.3: Probability estimate and 95% confidence intervals for each possible score for
variables of interest.
Score Estimate 95% CI
Resultant Shoulder NJM Impulse during
Push
-1 0.077 [0.01, 0.25]
0 0.808 [0.62, 0.92]
P

1 0.115 [0.03, 0.3]
Torso Angle at Wrist Top-Dead-Center
-1 0.038 [0, 0.19]
0 0.423 [0.25, 0.62]
1 0.538 [0.34, 0.72]
Elbow Angle at Wrist Top-Dead-Center
-1 0.115 [0.03, 0.3]
0 0.038 [0, 0.19]
1 0.846 [0.66, 0.95]
P

P
Significantly larger than the other
scores
3.3.1 Resultant shoulder NJM impulse during push
In this study, resultant shoulder NJM impulse during push was found likely to
remain unchanged from pre-WC configuration to post-WC configuration (Figure 3.3). The
greatest probability estimate was for a score of 0 (E(X) = 0.808, CI [0.62, 0.92]), and it was
significantly larger (p = 0.004) than the probability of the other scores (-1: E(X) = 0.077, CI
[0.01, 0.25]; 1: E(X) = 0.115, CI [0.03, 0.3]). Five of the 26 participants had different
resultant shoulder NJM impulse during push between sessions, based on our scoring
criteria (Figure 3.3). Factors contributing to these observed differences in shoulder NJM
36

impulse within participants include push duration, RF magnitude, RF orientation relative to
forearm (reflecting the elbow NJM contribution to control of the upper extremity) during
push.

Figure 3.3: Comparison of Resultant shoulder NJM impulse (Nms) during push pre-post WC
reconfiguration for each participant. Data shown for individual cycles within Pre (black
circles)-Post (gray circles) data collection sessions.
3.3.2 Torso angle at wrist top-dead-center of wheel
Across participants, torso angles were found likely be more upright or remain
within guidelines after WC reconfiguration as compared to their initial WC configuration
(Figure 3.4). A score of 1 had the greatest probability estimate (E(X) = 0.538, CI [0.34,
0.72]). However, it was not significantly larger (p = 0.66) than the probability of the other
scores (-1: E(X) = 0.038, CI [0, 0.19]; 0: E(X) = 0.423, CI [0.25, 0.62]).
37

Figure 3.4: Comparison of Torso angle at wrist top-dead-center during push pre-post WC
reconfiguration for each participant. Data shown for individual cycles within Pre (black
circles)-Post (gray circles) data collection sessions.
3.3.3 Elbow angle at wrist top-dead-center of wheel
Across participants, elbow angles when wrists were positioned top-dead-center of
the wheel during propulsion were likely to remain within the suggested range (100
∘
-120
∘
)
or shift towards or into the recommended range after personalized WC configuration
(Figure 3.5). A score of 1 had the greatest probability estimate (E(X) = 0.846, CI [0.66,
0.95]). It was significantly larger (p = 0.004) than the probability of the other scores (-1:
E(X) = 0.115, CI [0.03, 0.3]; 0: E(X) = 0.038, CI [0, 0.19]).
38

Figure 3.5: Comparison of Elbow angle at wrist top-dead-center during push pre-post WC
reconfiguration for each participant. Data shown for individual cycles within Pre (black
circles)-Post (gray circles) data collection sessions.
3.3.4 Relationship between torso and elbow angle at wrist-top-dead-center of wheel
Torso Angle and Elbow Angle
All 6 of the participants whose median torso angle at wrist top-dead-center
increased more than the threshold also increased their elbow angle at wrist top-dead-
center by more than the threshold. Of the 2 participants whose median torso angle at wrist
top-dead-center decreased more than the threshold, neither had a change in elbow angle at
wrist top-dead-center.
3.4 Discussion
Personalized WC configuration is a promising approach for improving posture,
upper extremity kinematics associated with propulsion energetics, and mitigating
mechanical demand imposed on the shoulder during manual WC propulsion. In this study,
we hypothesized personalized adjustments to the individual’s WC made by the seating
center clinician would lead to more effective interaction with the WC during propulsion at
39

self-selected fast speeds on a level sidewalk. Across participants, torso angles were found
to likely be more upright or unchanged after WC reconfiguration and elbow angles either
stayed within or shifted towards the recommended range after personalized WC
configuration. Resultant shoulder NJM impulse during push likely remained unchanged
from pre-WC configuration to post-WC configuration. The results demonstrate that
personalized WC configuration can positively affect upper extremity kinematics during
push, without detrimental increases in shoulder demand or shifts in posture when
compared to pre-WC configuration. Taken together, these results suggest personalized WC
configurations that aligns with clinical guidelines can likely yields positive results for
posture and propulsion energetics without significant changes in mechanical demand
imposed on the shoulder.
In this pilot project, participants volunteering to be part of this longitudinal study
were primarily male and being fitted for their chair for the first time. While males
represent approximately 78% of new spinal cord injury cases (“National spinal cord injury
statistical center, facts and figures at a glance,” 2019), this study only included one female,
representing about 4% of the study population. Therefore, care must be taken when
applying these results to different populations. As access to wearable technology increases,
it will become more feasible for future studies to include more activities of daily living in
real world settings, more cycles, under different conditions (e.g., slope, terrain, with
obstacles, etc.). Additional insights to system dynamics and right-left symmetry would also
likely benefit if both wheels used in the study were instrumented. We also acknowledge the
elbow angle in the guidelines was assumes a static condition (“Preservation of Upper Limb
Function Following Spinal Cord Injury,” 2005); in that it provides a easily repeatable task in
40

the clinic (“Preservation of Upper Limb Function Following Spinal Cord Injury: A Clinical
Practice Guideline for Health-Care Professionals” 2005); however, in our pilot work we
learned that posture in the sitting position can be considerably different than posture
during manual WC propulsion. We elected to use the more contextually relevant elbow
angle when the wrist was at top dead center of the pushrim in that it better reflected the
body configuration when initiating push mechanics in context. Future work may also
benefit from modifying the thresholds used to score outcomes in relation to current clinical
recommendations. Instead of using a % of the observed standard deviation in these
participants, future work the threshold could be set a % of what is deemed a functional
difference from a clinical perspective for individuals with paraplegia with different
capacities to generate shoulder flexor NJMs.
Personalized WC configuration likely did not change the demand on the shoulder,
indicated by a score of 0 (no change greater than the threshold). Three of the participants
had a reduction in their resultant shoulder NJM impulse, while two had an increase. Several
factors may have lead to these changes, for example, push duration, resultant reaction force
magnitude, and reaction force angle relative to the forearm (Munaretto, McNitt-Gray,
Flashner, & Requejo, 2012, 2013; Papp, Russell, Requejo, Furumasu, & McNitt-Gray, 2019).
Previous research has also shown no effects on shoulder demand with changes in seat
angle while maintaining axle position (Desroches, Aissaoui, & Bourbonnais, 2006). As the
authors point out, and in conjunction with our results, it is possible that changes to the WC
can be made to improve functionality without increasing shoulder demand.
41

WC reconfiguration decisions resulted more vertical postures across participants.
Specifically, 14 participants experienced positive changes - or maintenance - in torso angle
at wrist top-dead-center while nine had no change, leaving only two participants that had
changes in torso angle further from guidelines. While a vertically aligned trunk may
facilitate theoretical placement of body center of mass relative to the base of support (rear
and front wheels), trunk orientation may also assist in force generation used by individuals
when generating reaction forces applied to the pushrim. Future analysis of propulsion
patterns used by participants will examine torso-elbow coordination during reaction force
generation during push and how reorientation of the shoulder position affects the proximal
and distal moments created by the Net Joint Forces at the elbow and shoulder on the upper
arm.
The effects of personalized WC configuration on upper extremity kinematics were
likely positive, as evidenced by elbow angles aligning with clinical guidelines (all but 3
participants maintained or improved) (“Preservation of Upper Limb Function Following
Spinal Cord Injury,” 2005) formulated from previous work (Boninger, Baldwin, Cooper,
Koontz, & Chan, 2000; L. H. van der Woude, Veeger, Rozendal, & Sargean, 1989) and later
re-affirmed (L. van der Woude et al., 2009) An elbow angle between 100-120
∘
, or even 100-
130
∘
(L. van der Woude et al., 2009), when the wrist is at top-dead-center of the wheel was
associated with better cardio-respiratory parameters and mechanical efficiency (L. van der
Woude et al., 2009; L. H. van der Woude, Veeger, Rozendal, & Sargean, 1989). Again, this
variable was measured in these studies under static condition, but as seen in this study,
changes in posture may occur when generating the reaction forces needed to perform a
functional task.
42

3.5 Conclusion
Personalized WC configuration was likely to lead to positive changes - or
maintenance - in elbow angle at wrist top-dead-center while also not affecting the demand
on the shoulder. Although no decision could be made about changes in torso angle set at
the study threshold, 24 of the 26 participants had positive changes or maintenance. Taken
together, it is likely that personalizing WC configuration by having the ability to modify
axle, seatback, and seat height, as a clinician is able to do with a K0005 WC, will be
beneficial for posture, upper extremity kinematics associated with energetics, and
mechanical loading of the shoulder.

43

Chapter 4 The effect of shot distance on the whole body center of mass velocity
regulation in the basketball shot
4.1 Introduction
The objective of a basketball shot is to put the ball into the hoop. To accomplish this
task, the player must release the ball with a resultant velocity that produces a ball
trajectory that results in the ball entering the hoop. The ball position and velocity at release
from the hands determines the flight trajectory of the ball relative to the hoop. Both the
body center of mass (CM) velocity at release and the velocity generated by the arms
relative to the body contribute to the ball CM velocity at release (Hay, 1985) (Figure 4.1). In
the context of a game, shots are taken from various distances from the hoop. As the shot
distance increases, the magnitude of the ball velocity at release required for a successful
shot increases.
For a given distance from the hoop, more than one ball velocity at release can result
in a successful shot. A range of ball velocity angles for successful shots have been suggested
(Brancazio, 1981, 1981; Hamilton & Reinschmidt, 1997; Hay, 1985; Mortimer, 1951;
Nakano, Inaba, Fukashiro, & Yoshioka, 2020, 2020; Tran & Silverberg, 2008). The shooter
then has options - within the context of the situation – to impart the required force onto the
ball that will result in favorable release conditions for a successful attempt.
44

Figure 4.1: The ball resultant velocity at release (brown) can be attributed to the body CM
velocity (purple) and the velocity generated by the arms (gold).
Generation of the ball velocity at release involves the whole body. The whole body
and arms work together to generate the ball velocity at release. The availability of body CM
velocity at the time of ball release is a result of the net vertical impulse generated by the
player during contact with the ground and when the player chooses to release the ball
(time in the air before ball release). Multijoint control of the upper extremity relative to the
body also contributes to ball velocity magnitude and direction at release. Previous research
suggest that the upper arm velocity is likely to contribute to the vertical velocity of the ball
at release, while the lower arm and hand likely contribute to the horizontal velocity of the
ball at release (Okubo & Hubbard, 2015).
Velocity of the body generated prior to the shot preparation phase enables the
player to initiate the shot with momentum (Figure 4.2). Increases in CM vertical velocity at
45

ground departure occur when the net vertical impulse generated during the shot
preparation increases and downward CM vertical velocity at shot initiation decreases. The
sooner the player initiates the shot during flight, the greater the CM velocity contribution to
ball velocity at release. The greater whole body CM velocity at release, the greater it’s

Figure 4.2: The CM velocity during the basketball shot is a result of the net impulse generated
by the legs. Once the shooter leaves the ground, gravity accelerates the body toward the
ground, reducing their CM velocity. The CM velocity at the time of ball release is the amount
contributed to the ball release velocity. Filmstrip of key events and phases during the
basketball shot. Start of impulse: When the individual applies force contributing to the shot.
Arm swing: Beginning of the upper arm counterclockwise rotation. Arm shot initiation:
Beginning of arm rotation that contributes to the ball release velocity. End of Impulse: When
the individual is no longer applying force into the ground, also referred to as ground
departure. Ball Release: Last frame in which the person is in contact with the ball. CM Apex:
The individual’s CM trajectory apex.

46

relative contribution to the ball velocity at release (B. Elliot, 1992; Wiens & McNitt-Gray,
2020) in relation to the arms.
There are contextually relevant situations during a basketball game that can
influence when an individual chooses to release the ball (e.g., presence of a quickly closing
defender, time running out on the shot or game clocks, etc.). When taking shots from
greater distances from the hoop, the contributions of the body CM vertical velocity at
release tends to increase (B. Elliot, 1992; Miller & Bartlett, 1996; Miller & Bartlett, 1993;
Okazaki & Rodacki, 2012; Walters, Hudson, & Bird, 1990; Wiens & McNitt-Gray, 2020). This
increase in CM vertical velocity at ball release with shot distance can be a result of the
player choosing to release the ball earlier in the flight phase of the jump (B. Elliot, 1992; B.
C. Elliot & White, 1989; Miller & Bartlett, 1993; Wiens & McNitt-Gray, 2020), which likely
leads to a greater body CM velocity contribution to the ball velocity at release (B. Elliot,
1992; Wiens & McNitt-Gray, 2020). Analyzing how individuals generate ball velocity at
release advances our understanding of an individual’s shot tendencies when generating
ball velocity at release in shots taken from different locations relative to the hoop.
Knowledge of how an individual regulates ball velocity at release in successful shots from
different distances will provide a basis for individualizing interventions for improving shot
performance.
The potential for CM vertical velocity to contribute to ball velocity at release is
determined by the CM vertical velocity the individual has at last contact with the ground.
While an increase in net vertical impulse during the shot has been theorized as the reason
for an increased CM vertical velocity at release, it is unclear how player decisions in flight
47

and arm contributions prior to ball release affect the contributions of CM vertical velocity
to ball velocity at release. While it has been observed that players release the ball sooner
after ground departure with increases in shot distance (Miller & Bartlett, 1996; Miller &
Bartlett, 1993; Nakano, Fukashiro, & Yoshioka, 2020), it is unclear whether the tendencies
within individual reflect reported results for the group. Identifying how the individual
creates their CM velocity at release, through impulse or timing of ball release, can help
identify individual priorities and inform individual-specific training.
The purpose of this study was to determine how the whole body CM velocity
contributes to ball velocity at release with increases in shot distance in successful
basketball shots. We hypothesized that a) an individual’s body CM vertical velocity at
release will increase with an increase in shot distance; b) the contribution of an individual’s
CM horizontal and vertical velocity to the ball horizontal and vertical velocity at release will
increase with an increase in shot distance; c) increases in CM vertical velocity at release
will be achieved by releasing the ball earlier in flight (less time in the air prior to release)
and/or a result of greater net vertical impulse generated during ground contact and d) an
individual’s net horizontal impulse generated toward the hoop during ground contact will
increase with an increase in shot distance. These hypotheses were tested across shot
distances using a within-individual analysis.
4.2 Methods
Eleven individuals participated in the study (11 male; 79.0 (9.4) kg). Basketball
players from university recreational and club teams volunteered to participate and
48

provided informed consent in accordance with the Institutional Review Board for research
involving human participants.
Participants attempted jump shots from three locations on the court (Table 4.1). The
shot locations were expressed as the distance from a point on the floor directly beneath the
center of the hoop to the free throw line (4.19 m), American high school three-point line
(6.02 m), and NBA three-point line (7.24 m) (Figure 4.3). These shot distances are
commonly performed during practice and competition and progressively challenge the
capabilities of the player to generate the ball velocity at release needed for a successful
shot. Participants attempted at least 30 shots from each shot distance or until they
successfully performed 8 shots at each shot location. Participants shot regulation-sized
balls as they would use during competition (size 7, 0.75 m circumference). Before the
collection began, each participant was given at least 10 minutes of self-directed warm-up.
The participants were informed what types of shots they were to perform during the
experiment, so they could prepare accordingly.
Table 4.1: Collection procedure.
Distance Shots Order
4.19 m 30 1
6.02 m 30 2
7.24 m 30 3
49

Figure 4.3: Dimensions of a basketball court and the reference system used to describe shot
location on the court. Shot distance was characterized by the distance from the center of the
hoop to lines on the court: free throw (4.19 m, gold); American high school three-point (6.02
m, blue); NBA three-point (7.24, purple). The origin of the reference system was located on the
floor, directly beneath the center of the hoop.
To begin each trial, a researcher started the data capture software that triggered the
start of the force plate and video recordings. An experienced basketball player (participant
or researcher) located near under the hoop passed the ball to the player who performed
the shot. Once the ball landed on the floor after the shot attempt, the cameras and force
plates were triggered off. This process was repeated until the participant completed all the
shots from each shot distance. Only shot attempts that were successful (ball entered the
hoop without first hitting the backboard) were included in this analysis.
50

Horizontal and vertical reaction forces generated by each leg were measured by two
portable force plates (1200 Hz, 0.6 x 0.4 m, Kistler, Amherst, NY, USA). Ball position and
three-dimensional body kinematics were recorded by eight high-speed cameras (120 Hz, Prime
Color, OptiTrack, Corvallis, OR). The ball position was detected by a neural network (Mathis et
al., 2018; Nath et al., 2019) trained on a subset of images from each collection from each
camera view. The ball position in the three-dimensional gym reference system (Figure 4.3) was
calculated using custom Python code. Three-dimensional body position was estimated using a
markerless motion capture software (Theia Markerless Inc., Kingston, ON, Canada) (Kanko et
al., 2021; Kanko, Laende, Davis, Selbie, & Deluzio, 2021; Kanko, Laende, Selbie, & Deluzio,
2021). Figure 4.3 illustrates the position of the portable force plates and the camera
locations to the basket for all shot locations. The camera placements were the same
throughout the entire collection, while the force plate locations moved depending on the
shot location.
Net horizontal and vertical impulse were calculated from the time of minimum CM
vertical velocity and until the vertical reaction forces are below 15 Newtons (N) (ground
departure, Figure 4.2).The minimum CM vertical velocity occurred after participants
stepped on the plates to receive the pass. This instant in time was easily and consistently
identified in each trial and corresponded with the initiation of lower body joint extension.
The net impulse generated during the shot was calculated by summing the forces measured
from both force plates. Time to apex of the body CM trajectory during flight (CM jump apex)
is influenced by the magnitude of the CM vertical velocity at ground departure and was
identified as the time of maximum vertical position of the CM during the jump. CM vertical
and horizontal position were measured using a built-in Visual3D (C-Motion Inc.,
51

Germantown, MD) model designed for Theia3D output. CM vertical and horizontal velocity
were calculated as the first derivative of the CM position over time. Ball and body position
was expressed relative to the origin of the court (Figure 4.3). Ball vertical and horizontal
velocities at release were expressed as the velocity along the z and y axes, respectively
(Figure 4.3). Ball release was identified manually as the last frame of contact between the
hand and ball.
The contribution of the CM vertical and horizontal velocity to ball vertical and
horizontal velocity at release were the CM vertical and horizontal velocity at release,
respectively. The arm vertical and horizontal velocity contribution to ball vertical and
horizontal velocity at release were calculated as the difference between ball vertical and
horizontal velocity at release minus the CM vertical and horizontal velocity at release,
respectively. Both the CM and arm contributions to ball vertical and horizontal velocity at
release were represented as a percentage of the ball vertical and horizontal at release.
Time in the air before release was calculated by subtracting the time of last contact with
the ground or the local minimum in the measured vertical reaction force after ball release
(i.e., participant did not leave the ground during the shot) from the time of ball release.
Time of ball release relative to the CM jump apex was calculated by subtracting the time to
the apex of the CM trajectory during flight (jump apex)
Within-individual differences were tested by comparing trimmed means using a percentile
bootstrap method and with an 𝛼 = 0.05 (R. Wilcox, 2017; R. R. Wilcox & Schönbrodt, 2021).
Group differences between the three shot distances were tested using percentile
bootstrapped trimmed means with an 𝛼 = 0.05 (R. Wilcox, 2017).
52

4.3 Results
Ball vertical velocity at release increased with an increase in shot distance. As a
group, the ball vertical velocity at release increased when increasing shot distance from
4.19 m to 6.02 m (p < 0.001, 𝑝 ̂ = -0.87, CI [-0.94, -0.8]), from 4.19 m to 7.24 m (p < 0.001, 𝑝 ̂ =
-1.48, CI [-1.57, -1.4]), and from 6.02 m to 7.24 m (p < 0.001, 𝑝 ̂ = -0.61, CI [-0.71, -0.51]).
Within the 11 participants, when increasing shot distance from 4.19 m to 6.02 m, all 11
participants significantly increased the ball vertical velocity at release. When increasing
shot distance from 4.19 m to 7.24 m, all 11 participants significantly increased the ball
vertical velocity at release. When increasing shot distance from 6.02 m to 7.24 m, 10
participants significantly increased the ball vertical velocity at release.
Ball horizontal velocity at release increased with an increase in shot distance. As a
group, the ball horizontal velocity at release increased when increasing shot distance from
4.19 m to 6.02 m (p < 0.001, 𝑝 ̂ = -0.87, CI [-0.94, -0.8]), from 4.19 m to 7.24 m (p < 0.001, 𝑝 ̂ =
-1.48, CI [-1.57, -1.4]), and from 6.02 m to 7.24 m (p < 0.001, 𝑝 ̂ = -0.61, CI [-0.71, -0.51]).
Within the 11 participants, when increasing shot distance from 4.19 m to 6.02 m, all 11
participants significantly increased the ball horizontal velocity at release. When increasing
shot distance from 4.19 m to 7.24 m, all 11 participants significantly increased the ball
horizontal velocity at release. When increasing shot distance from 6.02 m to 7.24 m, all 11
participants significantly increased the ball horizontal velocity at release.
The body CM vertical velocity at release increased with an increase in shot distance
(Figure 4.4). As a group, the CM vertical velocity at release increased when increasing shot
distance from 4.19 m to 6.02 m (p < 0.001, 𝑝 ̂ = -0.53, CI [-0.57, -0.49]), from 4.19 m to 7.24
53

m (p < 0.001, 𝑝 ̂ = -0.77, CI [-0.81, -0.73]), and from 6.02 m to 7.24 m (p < 0.001, 𝑝 ̂ = -0.24, CI
[-0.27, -0.2]). Within the 11 participants, when increasing shot distance from 4.19 m to 6.02
m, all 11 participants significantly increased the CM vertical velocity at release. When
increasing shot distance from 4.19 m to 7.24 m, all 11 participants significantly increased
the CM vertical velocity at release. When increasing shot distance from 6.02 m to 7.24 m, 10
participants significantly increased the CM vertical velocity at release.
The body CM horizontal velocity at release increased with an increase in shot
distance (Figure 4.4). As a group, the CM horizontal velocity at release increased when
increasing shot distance from 4.19 m to 6.02 m (p < 0.001, 𝑝 ̂ = -0.09, CI [-0.12, -0.07]), from
4.19 m to 7.24 m (p < 0.001, 𝑝 ̂ = -0.17, CI [-0.21, -0.13]), and from 6.02 m to 7.24 m (p <
0.001, 𝑝 ̂ = -0.08, CI [-0.12, -0.03]). Within the 11 participants, when increasing shot
distance from 4.19 m to 6.02 m, 9 participants significantly increased the CM horizontal
velocity at release. When increasing shot distance from 4.19 m to 7.24 m, all 11 participants
significantly increased the CM horizontal velocity at release. When increasing shot distance
from 6.02 m to 7.24 m, 8 participants significantly increased the CM horizontal velocity at
release.
54

Figure 4.4: The CM vertical (top row) and horizontal (bottom row) velocity at release
increases with an increase in shot distance (gold: 4.19 m; blue: 6.02 m; purple: 7.24 m). * p <
0.5; ** p < 0.01; *** p < 0.001; **** p < 0.0001.
The contribution of the CM vertical velocity to ball vertical velocity at release
increased with an increase in shot distance (Figure 4.5). As a group, the contribution of the
CM vertical velocity to ball vertical velocity at release increased when increasing shot
distance from 4.19 m to 6.02 m (p < 0.001, 𝑝 ̂ = -0.06, CI [-0.07, -0.06]), from 4.19 m to 7.24
m (p < 0.001, 𝑝 ̂ = -0.08, CI [-0.09, -0.07]), and from 6.02 m to 7.24 m (p < 0.001, 𝑝 ̂ = -0.02, CI
55

[-0.03, -0.01]). Within the 11 participants, when increasing shot distance from 4.19 m to
6.02 m, all 11 participants significantly increased the contribution of the CM vertical
velocity to ball vertical velocity at release. When increasing shot distance from 4.19 m to
7.24 m, all 11 participants significantly increased the contribution of the CM vertical
velocity to ball vertical velocity at release. When increasing shot distance from 6.02 m to
7.24 m, 9 participants significantly increased the contribution of the CM vertical velocity to
ball vertical velocity at release.
The contribution of the CM horizontal velocity to ball horizontal velocity at release
increased with an increase in shot distance (Figure 4.5). As a group, the contribution of the
CM horizontal velocity to ball horizontal velocity at release increased when increasing shot
distance from 4.19 m to 6.02 m (p < 0.001, 𝑝 ̂ = -0.06, CI [-0.07, -0.06]), from 4.19 m to 7.24
m (p < 0.001, 𝑝 ̂ = -0.08, CI [-0.09, -0.07]), and from 6.02 m to 7.24 m (p < 0.001, 𝑝 ̂ = -0.02, CI
[-0.03, -0.01]). Within the 11 participants, when increasing shot distance from 4.19 m to
6.02 m, 9 participants significantly increased the contribution of the CM horizontal velocity
to ball horizontal velocity at release. When increasing shot distance from 4.19 m to 7.24 m,
10 participants significantly increased the contribution of the CM horizontal velocity to ball
horizontal velocity at release. When increasing shot distance from 6.02 m to 7.24 m, 4
participants significantly increased the contribution of the CM horizontal velocity to ball
horizontal velocity at release.
56

Figure 4.5: The CM vertical (top row) and horizontal (bottom row) velocity contribution to
velocity at release increases with an increase in shot distance (gold: 4.19 m; blue: 6.02 m;
purple: 7.24 m). * p < 0.5; ** p < 0.01; *** p < 0.001; **** p < 0.0001.
The ball was released earlier relative to the time of CM jump apex with an increase
in shot distance (Figure 4.6). As a group, ball release occurred earlier relative to the time of
CM jump apex when increasing shot distance from 4.19 m to 6.02 m (p < 0.001, 𝑝 ̂ = 0.06, CI
[0.05, 0.06]), from 4.19 m to 7.24 m (p < 0.001, 𝑝 ̂ = 0.08, CI [0.08, 0.09]), and from 6.02 m to
7.24 m (p < 0.001, 𝑝 ̂ = 0.03, CI [0.02, 0.03]). Within the 11 participants, when increasing
shot distance from 4.19 m to 6.02 m, all 11 participants significantly released the ball
earlier relative to the time of CM jump apex. When increasing shot distance from 4.19 m to
57

7.24 m, all 11 participants significantly released the ball earlier relative to the time of CM
jump apex. When increasing shot distance from 6.02 m to 7.24 m, 10 participants
significantly released the ball earlier relative to the time of CM jump apex.

Figure 4.6: The time of release occurs earlier relative to the CM jump apex as shot distance
increases (gold: 4.19 m; blue: 6.02 m; purple: 7.24 m). * p < 0.5; ** p < 0.01; *** p < 0.001; ****
p < 0.0001.
Net vertical impulse generated during the shot increased with an increase in shot
distance (Figure 4.7). As a group, net vertical impulse increased when increasing shot
distance from 4.19 m to 6.02 m (p < 0.001, 𝑝 ̂ = -0.3, CI [-0.45, -0.16]), from 4.19 m to 7.24 m
(p < 0.001, 𝑝 ̂ = -0.56, CI [-0.72, -0.4]), and from 6.02 m to 7.24 m (p < 0.001, 𝑝 ̂ = -0.26, CI [-
0.4, -0.13]). Within the 11 participants, when increasing shot distance from 4.19 m to 6.02
m, 9 participant significantly increased net vertical impulse, while 1 participants
significantly decreased net vertical impulse. When increasing shot distance from 4.19 m to
7.24 m, 8 participants significantly increased net vertical impulse. When increasing shot
58

distance from 6.02 m to 7.24 m, 8 participants significantly increased net vertical impulse,
while 1 participant significantly decreased net vertical impulse.
Net horizontal impulse generated during the shot decreased magnitude in the
negative direction with an increase in shot distance (Figure 4.7). As a group, net horizontal
impulse decreased magnitude in the negative direction when increasing shot distance from
4.19 m to 6.02 m (p < 0.001, 𝑝 ̂ = -0.21, CI [-0.25, -0.16]), from 4.19 m to 7.24 m (p < 0.001, 𝑝 ̂
= -0.3, CI [-0.36, -0.24]), and from 6.02 m to 7.24 m (p < 0.001, 𝑝 ̂ = -0.1, CI [-0.16, -0.03]).
Within the 11 participants, when increasing shot distance from 4.19 m to 6.02 m, 9
participants significantly decreased net horizontal impulse magnitude in the negative
direction. When increasing shot distance from 4.19 m to 7.24 m, 8 participants significantly
decreased net horizontal impulse magnitude in the negative direction. When increasing
shot distance from 6.02 m to 7.24 m, 7 participants significantly decreased net horizontal
impulse magnitude in the negative direction.
59

Figure 4.7: The net vertical impulse generated during the shot increases as shot distance
increases, while the net horizontal impulse magnitude decreases in the negative direction as
shot distance increases (gold: 4.19 m; blue: 6.02 m; purple: 7.24 m). * p < 0.5; ** p < 0.01; *** p
< 0.001; **** p < 0.0001.
Time in the air before ball release generally decreased with an increase in shot
distance, although it depended on the individual (Figure 4.8). As a group, the time in the air
before ball release decreased with increasing shot distance from 4.19 m to 6.02 m (p <
0.001, 𝑝 ̂ = 0.02, CI [0.01, 0.04]) and from 4.19 m to 7.24 m (p < 0.001, 𝑝 ̂ = 0.03, CI [0.01,
0.04]). Within the 11 participants, when increasing shot distance from 4.19 m to 6.02 m, 1
60

participant significantly decreased the time in the air before ball release, while 8
participants significantly increased the time in the air before ball release. When increasing
shot distance from 4.19 m to 7.24 m, 7 participants significantly decreased the time in the
air before ball release, while 7 participants significantly increased the time in the air before
ball release. When increasing shot distance from 6.02 m to 7.24 m, 3 participants
significantly decreased the time in the air before ball release, while 4 participants
significantly increased the time in the air before ball release.

Figure 4.8: The time in the air before release decreases when shooting at 4.19 m and 6.02 m
relative to 4.19 m (gold: 4.19 m; blue: 6.02 m; purple: 7.24 m). * p < 0.5; ** p < 0.01; *** p <
0.001; **** p < 0.0001.
4.4 Discussion
In this study, we determined how the ball velocity at release is generated from the
whole body CM during successful shots taken from progressively further distances from
the hoop. Within-participant analyses revealed that each of the basketball players in this
61

study significantly increased body CM vertical velocity at release with increases in shot
distance. In addition, the contribution of the CM vertical and horizontal velocity to the ball
vertical and horizontal velocity at release also increased with shot distance. Increases in
CM vertical velocity at release with shot distance were attributed to increases in net
vertical impulse generated during the shot, releasing the ball earlier in the air, or both.
Increases in CM horizontal velocity at release were attributed to a decreased magnitude in
the net horizontal impulse generated during the shot that opposed movement towards the
hoop.
The results of this study are limited in that they only reflect the control strategies
used by recreational, male basketball players. This contextually relevant approach,
however, can be applied to characterize shot tendencies of basketball players of all
genders, ages, abilities, and skill levels in future work. This approach, when combined with
within-participant design as used in this study, may be particularly helpful in delineating
how CM vertical velocity contribution to the ball vertical velocity at release is greater for
female players than male players when increasing shot distance (B. Elliot, 1992). Future
research would benefit from incorporating shots from different locations on the court and
more contextually relevant situations that exacerbate the need to shoot more quickly (e.g.,
shot or game clock, closing defender).
Findings of this study using a within-participant design are consistent previously reported
group results (B. Elliot, 1992; Miller & Bartlett, 1993; Okazaki & Rodacki, 2012; Walters,
Hudson, & Bird, 1990; Wiens & McNitt-Gray, 2020), that indicate CM contribution to ball
vertical velocity at release increase with shot distance and increases in CM vertical velocity
62

at release were attributed to ball release occurring earlier relative to the CM jump apex (B.
Elliot, 1992; B. C. Elliot & White, 1989; Miller & Bartlett, 1993). The current study provides
additional insights into the individual strategies players use to generate CM velocity during
the shot and the implications of releasing the ball earlier relative to the CM jump apex on
ball velocity at release.
Participants in this study used three primary strategies for regulating CM velocity
contribution to ball velocity at release (Figure 4.9). These exemplar strategies were
identified by how the CM vertical velocity was regulated across shot distances and what it
afforded the individual. Individuals generating relatively low but progressively greater CM
vertical velocity at Ground Departure across shot distances (Figure 4.9, Column 1) tended
to release the ball much earlier in flight relative to the other participants, enabling the
players to maximize contribution of CM vertical velocity at Ground Departure to ball
velocity at release, yet lowering CM vertical position at ball release. The individuals
effective in generating substantial CM vertical velocity at Ground Departure (> 1.75 m/s
across distances, Figure 4.9, Column 2) released the ball earlier in flight with increased shot
distance, which enabled the player to use more of their available CM vertical velocity while
still achieving the same amount of CM vertical velocity at ground departure. The
individuals effective in generating substantial CM vertical velocity at Ground Departure (>
1.75 m/s) who also progressively increased the magnitude of CM vertical velocity at
Ground departure with increases in shot distances (Figure 4.9, Column 3) also released the
ball earlier in flight with increased shot distance, enabling the player to use more of their
CM vertical velocity at Ground Departure. Individuals achieving a relatively large CM
63

vertical velocity at ground departure (Figure 4.9, Columns 2 & 3) tended to be at a
relatively higher CM vertical position at ball release that reduced with shot distance.
Participants in this study used three primary strategies for regulating CM velocity
contribution to ball velocity at release (Figure 4.9).These exemplar strategies were
identified by how the CM vertical velocity was regulated across shot distances and what it
afforded the individual. Individuals generating relatively low but progressively greater CM
Vv at Ground Departure across shot distances (Figure 4.9, Column 1) tended to release the
ball much earlier in flight, enabling the player to maximize contribution of CM Vv at Ground
Departure to ball velocity at release, yet lowering CM vertical position at ball release. The
individuals effective in generating substantial CM Vv at Ground Departure (> 1.75 m/s
across distances, Figure 4.9, Column 2) released the ball earlier in flight with increased shot
distance, which enabled the player to use more of their available CM Vv. The individuals
effective in generating substantial CM Vv at Ground Departure (> 1.75 m/s) who also
progressively increased the magnitude of CM Vv at Ground departure with increases in
shot distances (Figure 4.9, Column 3) also released the ball earlier in flight with increased
shot distance, enabling the player to use more of their CM vertical velocity at Ground
Departure. Individuals achieving a relatively large CM vertical velocity at ground departure
(Figure 4.9, Columns 2 & 3) tended to be at a relatively higher CM vertical position at ball
release that reduced with shot distance.
64

Figure 4.9: Three exemplar control strategies used by participants to regulate CM vertical
velocity contributions to ball vertical velocity at release with increases in shot distance (gold:
4.19 m; blue: 6.02 m; purple: 7.24 m). The individuals generating relatively low but
progressively greater CM vertical velocity at Ground Departure across shot distances (Column
65

1) tended to release ball much earlier in flight enabling the player to maximize contribution
of CM vertical velocity at Ground Departure to ball velocity at release when the CM vertical
position was relatively low. The individuals effective in generating substantial CM vertical
velocity at Ground Departure (> 1.75 m/s across distances, Column 2) released the ball earlier
in flight with increased shot distance which enabled the player to use more of their CM
vertical velocity generated during the shot. The individuals effective in generating substantial
CM vertical velocity at Ground Departure (> 1.75 m/s) and increased the magnitude of CM
vertical velocity at Ground departure across shot distances (Column 3) also released the ball
earlier in flight with increased shot distance, enabling the player to use more of their CM
vertical velocity at Ground Departure.
The body CM vertical velocity contribution to the ball velocity at release is reflected
in the CM velocity at release. By understanding how an individual generates the ball
velocity at release and how CM velocity contributions to ball velocity at release change
when shooting from different shot distances, training and feedback can be specific to the
individual. Understanding how to help players use what they do have will likely increase
success. Increasing the CM vertical velocity at ground departure affords a greater potential
of options and emphasizes the value of impulse generating abilities of the player. With an
increase in CM vertical velocity at ground departure, the player has more options when
overcoming challenges imposed by an opposing player in the context of a game. Likewise,
improving the player’s ability to generate greater CM vertical velocity during ground
contact and delaying ball release until closer to the jump apex, the number of possible
successful ball trajectories increases.

66

Chapter 5 The effect of shot distance on the arm velocity regulation in the basketball shot
5.1 Introduction
A basketball shot is successful when the ball enters the hoop. The trajectory of the
ball during flight is determined by the ball velocity at release from the hands. Ball velocity
at release results from contributions by the center of mass (CM) and the arms (Hay, 1985).
Previous research indicates that the upper arm contributes to the vertical velocity of the
ball at release, while the lower arm and hand contribute to the horizontal ball velocity at
release (Okubo & Hubbard, 2015). During a free throw, arm contribution to ball velocity
begins with the upper arm, followed by the lower arm, and then the hand (Hayes, 1987).
The CM vertical velocity contribution to ball velocity at release increases with shot distance
(Miller & Bartlett, 1996; Miller & Bartlett, 1993; Okazaki & Rodacki, 2012; Walters, Hudson,
& Bird, 1990; Wiens & McNitt-Gray, 2020), and with an increase in CM velocity at ball
release, the arm percent contribution is decreased (B. Elliot, 1992). Changes in multijoint
coordination also occur, as elbow and shoulder angular velocities at ball release increase
(Miller & Bartlett, 1993; Okazaki & Rodacki, 2012). Regulation of ball velocity at release
involves regulation of the body momentum at the whole body level during ground contact
and coordination of the limbs and trunk during shot preparation (Figure 5.1).
67

Figure 5.1: Events and phases characterizing a jump shot initiated from the foul line. The
context in which a jump shot occurs may change the multijoint coordination in this exemplar
jump shot. For example, a shot initiated from a greater distance from the hoop requires a
greater ball velocity at release. In order to satisfy the increased velocity demand with shot
distance coordination of the legs, trunk, and arms may change.
The contribution of whole body CM velocity to ball velocity at release is determined
by the momentum generated prior to shot initiation phase (Figure 5.1), net impulse
generated during shot preparation, and the time in the air before ball release. The options
and outcomes afforded to the individual are determined by the strategy chosen by the
player (Chapter 4). Experimental evidence indicates that the whole body and arms work
together to generate the ball velocity at release, within-participant results indicate that
there are multiple strategies in doing so successfully (Chapter 4). Releasing the ball early
during flight results in a relatively large contribution from the whole body CM velocity to
the ball velocity at release, thereby reducing the required contribution from the arms.
Waiting to release the ball closer to the apex of the body CM trajectory during flight results
in a higher ball height at release; however, the corresponding reduction in body CM
68

velocity results in greater reliance on arm contributions to ball velocity at release.
Characterizing how individuals use their arms to generate ball velocity at release will
further advance our understanding of the individual’s preferred strategies under different
shot conditions and inform player-specific feedback and training.
Numerous ball release conditions can result in a successful shot (Okubo & Hubbard,
2016). Generation of a specific ball velocity at release may also involve various
combinations of shoulder, elbow, and wrist angular velocities across players (Okubo &
Hubbard, 2015). As shot distance increases, individuals regulate ball velocity at release
using various strategies. The arms are the primary contributor to the ball velocity at
release (B. Elliot, 1992; Wiens & McNitt-Gray, 2020). When increasing shot distance, the
whole body CM velocity percent contribution to ball velocity at release increases at a
greater rate than that of the arms (B. Elliot, 1992; Wiens & McNitt-Gray, 2020) (Chapter 4).
Within-group analyses have suggested the elbow angular velocity at release increases with
shot distance; however, mixed results are reported regarding the shoulder angular velocity
at release (Miller & Bartlett, 1993; Okazaki & Rodacki, 2012). Varied control strategies used
by players have also been reported with increases in shot distance (Okazaki & Rodacki,
2012) (Chapter 4). There are numerous ball release conditions that can result in a
successful shot (Okubo & Hubbard, 2016) which involve various combinations of shoulder,
elbow, and wrist angular velocities (Okubo & Hubbard, 2015). These findings emphasize
the value of a within-player analysis to better understand how the individual regulates the
arm contribution to ball velocity at release across increasing shot distances.
69

Arm contributions to ball velocity at release involve the shoulder, elbow, and wrist.
The outcome an individual’s multijoint control strategy is reflected by linear velocities of
the upper extremity segment endpoints expressed relative to the shoulder (Hayes, 1987).
The linear velocities of the segment endpoints are a function of the segment’s angular
velocity and position. Scenarios can occur when comparable joint angular velocities at
release are observed but because of the differences in segment positions at release, the
action of the arms during push can have different effects on the ball velocity at release. How
shot distance affects the joint positions (Diehl, Tant, Coleman, & Osborn, 1993; B. Elliot,
1992; B. C. Elliot & White, 1989; Miller & Bartlett, 1996; Miller & Bartlett, 1993; Okazaki &
Rodacki, 2012) and joint angles at release remain uncertain from reported group data
(Coves, Caballero, & Moreno, 2020). As can be seen in Chapter 4 and Figure 5.2, a within
participant experimental designs was effectively used to characterize how individuals use
body CM velocity at release to regulate ball velocity at release with increases in shot
distances. It is expected that analysis of arm contribution to ball velocity at release with
increases in shot distance would also benefit from a within-participant design.
70

Figure 5.2: Filmstrip of key events during the basketball shot with three different techniques.
Start of impulse generation: When the individual applies force contributing to the shot. Arm
swing: Beginning of the upper arm counter-clockwise rotation. Arm contribution to shot
initiation: Beginning of arm rotation that contributes to the ball velocity at release. End of
Impulse generation: When the individual is no longer applying force into the ground, referred
in this study as ground departure. Ball Release: Last frame in which the person is in contact
with the ball. CM Apex: The apex of an individual’s center of mass during the flight phase of
the jump shot.
The purpose of this study was to determine arm contributions to ball velocity at
release in successful basketball shots taken from different distances. We hypothesized that
a) an individual’s arm contribution to ball velocity at release will increase with shot
distance from the center of the hoop; b) the elbow vertical velocity at release relative to the
shoulder would increase with an increase in shot distance, resulting from an increase in
upper arm angular velocity and a more horizontal upper arm position at release; c) the
wrist horizontal velocity at release would increase with an increase in shot distance,
71

resulting from an increase in forearm angular velocity and a more vertical forearm position
at release. We tested these hypotheses by comparing segment kinematics during the shot
using a within-player experimental design.
5.2 Methods
5.2.1 Participants
Eleven individuals participated in the study (11 male; 79.0 (9.4) kg). Basketball
players were from university recreational and club teams and volunteered in accordance
with the university’s Institutional Review Board for research involving human subjects.
Participants attempted catch and shoot jump shots from three locations on the court (Table
5.1). The shot locations were locations commonly preformed in games and practice and
progressively increased the ball velocity at release required for a successful shot. The shot
locations (distance from the point on the floor directly beneath the center of the hoop)
were the: free throw line (4.19 m), American high school three-point line (6.02 m), and
NBA three-point line (7.24 m) (Figure 5.3). Each participant attempted at least 30 shots
from each shot distance or until they successfully attempted 8 shots at each shot location.
Participants shot with the regulation-sized balls they would use in a competition (size 7,
0.75 m circumference). The participants led a self-guided warm-up of at least 10 minutes
after being informed what the amount, types, and locations of the shots.

72

Table 5.1: Collection procedure.
Distance Shots Order
4.19 m 30 1
6.02 m 30 2
7.24 m 30 3

Figure 5.3: Reference system the locations of the three jump shots relative to the center of the
hoop: free throw (4.19 m, gold); American high school three-point (6.02 m, blue); NBA three-
point (7.24 m, purple)). The reference system’s origin was located directly beneath the hoop
and on the floor.
The data capture software triggered the start of the force plate and video recordings
at the beginning of the trial. The participant was located at the appropriate location for the
trial condition and received a pass from an experienced basketball player (participant or
73

researcher) that was located near under the hoop. Once the participant received the pass,
they performed the shot as if they were in a game. The trial was considered complete and
data capture software was triggered off once the ball hit the floor. All shots from each shot
distance followed this process. For data analyses, only trials that ended in success (e.g., the
ball entered the hoop) were used.
Horizontal and vertical reaction forces generated by each leg were measured by two
portable force plates (1200 Hz, 0.6 x 0.4 m, Kistler, Amherst, NY, USA). Ball position and
three-dimensional body kinematics were recorded by eight high-speed cameras (120 Hz,
Prime Color, OptiTrack, Corvallis, OR). The ball position was detected by a neural network
(Mathis et al., 2018; Nath et al., 2019) trained on a subset of images from each collection
from each camera view. The ball position in the three-dimensional gym reference system
was calculated using a custom Python code. Three-dimensional body position was
estimated using a markerless motion capture software (Theia Markerless Inc., Kingston,
ON, Canada) (Kanko et al., 2021; Kanko, Laende, Davis, Selbie, & Deluzio, 2021; Kanko,
Laende, Selbie, & Deluzio, 2021). The cameras were placed in positions that captured all
shot locations and the force plates were moved when participants moved to a new shot
distance (Figure 5.3).
Ball release was manually identified as the last frame of contact between the hand
and ball. Time was expressed relative to the instant of ball release (time = 0). CM vertical
and horizontal position were measured using a built-in Visual3D (C-Motion Inc.,
Germantown, MD) model designed for Theia3D output. CM vertical and horizontal velocity
were calculated as the first derivative of the CM position. Upper arm angle was the upper
74

arm angle relative to the right horizontal in the Y-axis of the gym reference system (Figure
5.3). Forearm angle was the forearm angle relative to the right horizontal Y-axis of the gym
reference system (Figure 5.3). Upper arm angular velocity was the upper arm angular
velocity about the X-axis of the gym reference system (Figure 5.3; counterclockwise +).
Forearm angular velocity was the forearm angular velocity about the X-axis of the gym
reference system (Figure 5.3; counterclockwise +). Ball and body position was expressed
relative to the origin (Figure 5.3). Ball vertical and horizontal velocities at release were
expressed as the velocity along the z and y axes, respectively (Figure 5.3).
The contribution of the CM vertical and horizontal velocity to ball vertical and
horizontal velocity at release were the CM vertical and horizontal velocity at release,
respectively. The arm vertical and horizontal velocity contribution to ball vertical and
horizontal velocity at release were the ball vertical and horizontal velocity at release minus
the CM vertical and horizontal velocity at release, respectively. Elbow relative velocity at
release was calcuated by subtracting the shoulder joint linear velocity from the elbow joint
linear velocity. Wrist relative velocity at release was calculated by subtracting the elbow
joint linear velocity from the wrist joint linear velocity. Uppear arm angular velocity at
release was calculated as the shooting-side upper arm angular velocity about the x-axis,
with counter-clockwise rotation as positive. Forearm angular velocity at release was
calculated as the shooting-side forearm angular velocity about the x-axis, with counter-
clockwise as positive. Upper arm angle at release was defined as the shooting-side upper
arm’s angle in the y-axis relative to the right horizontal. Forearm angle at release was
defined as the shooting-side forearm’s angle in the y-axis relative to the right horizontal.
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Within-individual differences were tested by comparing trimmed means using a
percentile bootstrap method and with an 𝛼 = 0.05 (R. Wilcox, 2017; R. R. Wilcox &
Schönbrodt, 2021). Group differences between the three shot distances were tested using
percentile bootstrapped trimmed means with an 𝛼 = 0.05 (R. Wilcox, 2017).
5.3 Results
Arm contribution to ball vertical velocity at release increased with an increase in
shot distance (Figure 5.4). As a group, the arm contribution to ball vertical velocity at
release increased when increasing shot distance from 4.19 m to 6.02 m (p < 0.001, 𝑝 ̂ = -
0.37, CI [-0.46, -0.28]), from 4.19 m to 7.24 m (p < 0.001, 𝑝 ̂ = -0.69, CI [-0.8, -0.59]), and
from 6.02 m to 7.24 m (p < 0.001, 𝑝 ̂ = -0.32, CI [-0.44, -0.2]). Within the 11 participants,
when increasing shot distance from 4.19 m to 6.02 m, all 10 participants significantly
increased their arm contribution to ball vertical velocity at release. When increasing shot
distance from 4.19 m to 7.24 m, all 11 participants significantly increased their arm
contribution to ball velocity vertical at release. When increasing shot distance from 6.02 m
to 7.24 m, 9 participants significantly increased their arm contribution to ball vertical
velocity at release.
Arm contribution to ball horizontal velocity at release increased with an increase in
shot distance (Figure 5.4). As a group, the arm contribution to ball horizontal velocity
increased when increasing shot distance from 4.19 m to 7.24 m (p < 0.001, 𝑝 ̂ = -0.92, CI [-
0.99, -0.86]), from 4.19 m to 7.24 m (p < 0.001, 𝑝 ̂ = -0.92, CI [-0.99, -0.86]), and from 6.02 m
to 7.24 m (p < 0.001, 𝑝 ̂ = -0.28, CI [-0.36, -0.2]). Within the 11 participants, when increasing
shot distance from 4.19 m to 6.02 m, all 11 participants significantly increased their arm
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contribution to ball horizontal velocity at release. When increasing shot distance from 4.19
m to 7.24 m, all 11 participants significantly increased their arm contribution to ball
velocity horizontal at release. When increasing shot distance from 6.02 m to 7.24 m, all 11
participants significantly increased their arm contribution to ball horizontal velocity at
release.

Figure 5.4: The arm velocity contribution to ball vertical (top row) and horizontal (bottom
row) velocity at release increased with an increase in shot distance (gold: 4.19 m; blue: 6.02
m; purple: 7.24 m). * p < 0.5; ** p < 0.01; *** p < 0.001; **** p < 0.0001. Participants are sorted
by the median arm contribution to ball vertical velocity at release in the 4.19 m shots.
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Elbow relative vertical velocity at release increased with an increase in shot
distance (Figure 5.5). As a group, the elbow relative vertical velocity at release increased
when increasing shot distance from 4.19 m to 6.02 m (p < 0.001, 𝑝 ̂ = -0.53, CI [-0.62, -0.45]),
from 4.19 m to 7.24 m (p < 0.001, 𝑝 ̂ = -0.68, CI [-0.78, -0.57]), and from 6.02 m to 7.24 m (p
= 0.008, 𝑝 ̂ = -0.15, CI [-0.28, -0.02]). Within the 11 participants, when increasing shot
distance from 4.19 m to 6.02 m, 10 participants increased their elbow relative vertical
velocity at release. When increasing shot distance from 4.19 m to 7.24 m, all 11 participants
increased their elbow relative vertical velocity at release. When increasing shot distance
from 6.02 m to 7.24 m, 7 participants increased their elbow relative vertical velocity at
release, while 2 participants decreased their elbow relative vertical velocity at release.
Elbow relative horizontal velocity at release did not change with an increase in shot
distance (Figure 5.5). As a group, the elbow relative horizontal velocity at release increased
in the negative direction when increasing shot distance from 4.19 m to 7.24 m (p < 0.001, 𝑝 ̂
= 0.14, CI [0.06, 0.2]). There were no differences when increasing shot distance from 4.19
m to 6.02 m (p = 0.068, 𝑝 ̂ = 0.06, CI [-0.02, 0.14]) or from 6.02 m to 7.24 m (p = 0.056, 𝑝 ̂ =
0.07, CI [-0.02, 0.16]). Within the 11 participants, when increasing shot distance from 4.19
m to 6.02 m, 4 participants increased their elbow relative horizontal velocity at release in
the negative direction, while 3 participants decreased their elbow relative horizontal
velocity at release in the negative direction. When increasing shot distance from 4.19 m to
7.24 m, 4 participants increased their elbow relative horizontal velocity at release in the
negative direction, while 4 participants decreased their elbow relative horizontal velocity
at release in the negative direction. When increasing shot distance from 6.02 m to 7.24 m, 2
participants increased their elbow relative horizontal velocity at release in the negative
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direction, while 3 participants decreased their elbow relative horizontal velocity at release
in the negative direction.
Wrist relative vertical velocity at release increased in the negative direction with an
increase in shot distance (Figure 5.5). As a group, the wrist relative vertical velocity at
release increased in the negative direction when increasing shot distance from 4.19 m to
6.02 m (p < 0.001, 𝑝 ̂ = 0.17, CI [0.08, 0.26]) and from 4.19 m to 7.24 m (p < 0.001, 𝑝 ̂ = 0.17,
CI [0.08, 0.26]). There was no difference when increasing shot distance from 6.02 m to 7.24
m (p = 0.964, 𝑝 ̂ < 0.001, CI [-0.11, 0.11]). Within the 11 participants, when increasing shot
distance from 4.19 m to 6.02 m, 7 participants increased their wrist relative vertical
velocity at release in the negative direction, while 2 participants decreased their wrist
relative vertical velocity at release. When increasing shot distance from 4.19 m to 7.24 m, 6
participants increased their wrist relative vertical velocity at release in the negative
direction, while 1 participant decreased their wrist relative vertical velocity at release.
When increasing shot distance from 6.02 m to 7.24 m, 3 participants increased their wrist
relative vertical velocity at release in the negative direction, while 1 participant decreased
their wrist relative vertical velocity at release.
Wrist relative horizontal velocity at release increased with an increase in shot
distance (Figure 5.5). As a group, the wrist relative horizontal velocity at release increased
when increasing shot distance from 4.19 m to 7.24 m (p < 0.001, 𝑝 ̂ = -0.23, CI [-0.33, -0.13])
and from 4.19 m to 7.24 m (p < 0.001, 𝑝 ̂ = -0.23, CI [-0.33, -0.13]). There was no difference
when increasing shot distance from 6.02 m to 7.24 m (p = 0.556, 𝑝 ̂ = -0.02, CI [-0.11, 0.07]).
Within the 11 participants, when increasing shot distance from 4.19 m to 6.02 m, 7
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participants increased their wrist relative horizontal velocity at release, while 1 participant
decreased their wrist relative horizontal velocity at release. When increasing shot distance
from 4.19 m to 7.24 m, 4 participants increased their wrist relative horizontal velocity at
release, while 1 participant decreased their wrist relative horizontal velocity at release.
When increasing shot distance from 6.02 m to 7.24 m, 2 participants increased their wrist
relative horizontal velocity at release, while 4 participants decreased their wrist relative
horizontal velocity at release.
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Figure 5.5: The arm velocity contribution to ball vertical (top row) and horizontal (bottom
row) velocity at release increased with an increase in shot distance (gold: 4.19 m; blue: 6.02
m; purple: 7.24 m). * p < 0.5; ** p < 0.01; *** p < 0.001; **** p < 0.0001. Participants are sorted
by the median arm contribution to ball vertical velocity at release in the 4.19 m shots.

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Upper arm angular velocity at release increased with an increase in shot distance
(Figure 5.6). As a group, the upper arm angular velocity at release increased when
increasing shot distance from 4.19 m to 6.02 m (p < 0.001, 𝑝 ̂ = -95.35, CI [-110.6, -81.39]),
from 4.19 m to 7.24 m (p < 0.001, 𝑝 ̂ = -126.93, CI [-148.39, -107.38]), and from 6.02 m to
7.24 m (p < 0.001, 𝑝 ̂ = -31.58, CI [-52.47, -8.67]). Within the 11 participants, when
increasing shot distance from 4.19 m to 6.02 m, all 11 participants increased their upper
arm angular velocity at release. When increasing shot distance from 4.19 m to 7.24 m, all
11 participants increased their upper arm angular velocity at release. When increasing shot
distance from 6.02 m to 7.24 m, 8 participants increased their upper arm angular velocity
at release, while 2 participants decreased their upper arm angular velocity at release.
Forearm angular velocity at release changes were mixed when increasing shot
distance (Figure 5.6). As a group, the forearm angular velocity at release increased in the
negative direction when increasing shot distance from 4.19 m to 7.24 m (p < 0.001, 𝑝 ̂ =
67.87, CI [26.46, 110.21]) and from 4.19 m to 7.24 m (p < 0.001, 𝑝 ̂ = 67.87, CI [26.46,
110.21]) but decreased from 6.02 m to 7.24 m (p < 0.001, 𝑝 ̂ = -51.09, CI [-91.78, -13.7]).
Within the 11 participants, when increasing shot distance from 4.19 m to 6.02 m, 8
participants increased their forearm angular velocity at release in the negative direction,
while 1 participant decreased their forearm angular velocity at release. When increasing
shot distance from 4.19 m to 7.24 m, 6 participants increased their forearm angular
velocity at release in the negative direction, while 1 participant decreased their wrist
relative horizontal velocity at release. When increasing shot distance from 6.02 m to 7.24
m, 4 participants increased their forearm angular velocity at release in the negative
direction, while 4 participants decreased their forearm angular velocity at release.
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Figure 5.6: The upper arm angular velocity at release (top row) increased with an increase in
shot distance (gold: 4.19 m; blue: 6.02 m; purple: 7.24 m). The forearm angular velocity at
release was lowest at 4.19 m and greatest at 6.02 m. * p < 0.5; ** p < 0.01; *** p < 0.001; **** p
< 0.0001. Note the bottom row y-axis is reversed. Participants are sorted by the median arm
contribution to ball vertical velocity at release in the 4.19 m shots.
Upper arm angle at release decreased with an increase in shot distance (Figure 5.7).
As a group, the upper arm angle at release decreased when increasing shot distance from
4.19 m to 6.02 m (p < 0.001, 𝑝 ̂ = 9.02, CI [6.33, 11.66]) and from 4.19 m to 7.24 m (p <
0.001, 𝑝 ̂ = 9.22, CI [6.56, 12.08]). There was no change in upper arm angle when increasing
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shot distance from 6.02 m to 7.24 m (p = 0.886, 𝑝 ̂ = 0.2, CI [-3.08, 3.5]). Within the 11
participants, when increasing shot distance from 4.19 m to 6.02 m, all 11 participants
decreased their upper arm angle at release. When increasing shot distance from 4.19 m to
7.24 m, all 11 participants decreased their upper arm angle at release. When increasing
shot distance from 6.02 m to 7.24 m, 7 participants decreased their upper arm angle at
release.
Forearm angle at release decreased with an increase in shot distance (Figure 5.7).
As a group, the forearm angle at release decreased when increasing shot distance from 4.19
m to 7.24 m (p < 0.001, 𝑝 ̂ = 4.93, CI [2.29, 7.45]) and from 6.02 m to 7.24 m (p = 0.017, 𝑝 ̂ =
2.77, CI [0.02, 5.54]). Within the 11 participants, when increasing shot distance from 4.19
m to 6.02 m, 4 participants decreased their forearm angle at release, while 2 participants
increased their forearm angle at release. When increasing shot distance from 4.19 m to
7.24 m, all 11 participants decreased their forearm angle at release. When increasing shot
distance from 6.02 m to 7.24 m, 9 participants decreased their forearm angle at release.
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Figure 5.7: The upper arm angle (top row) increased with shot distance while the forearm
angle (bottom row) decreased with shot distance (gold: 4.19 m; blue: 6.02 m; purple: 7.24 m).
* p < 0.5; ** p < 0.01; *** p < 0.001; **** p < 0.0001. Participants are sorted by the median arm
contribution to ball vertical velocity at release in the 4.19 m shots.
5.4 Discussion
In this study, we determined how regulation of the arms contributed to ball velocity
at release when initiating shots from progressively further distances from the center of the
hoop. Within-participant analysis revealed an increase in arm contribution to ball vertical
and horizontal velocity at release with increases in shot distance. The results indicate that
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the increase in upper arm contribution to ball velocity at release was a result of an increase
in upper arm angular velocity and/or a more horizontal upper arm angle at release.
Changes in forearm contribution to ball velocity at release with increases in shot distance
were mixed and reflected differences in individual control strategies. In general, the more
horizontal the upper arm at release, the more vertical the angle of the relative elbow
resultant velocity at release. The more vertical the forearm at release, the more horizontal
the angle of the relative wrist resultant velocity at release.
This study’s results are limited as they only reflect the results and strategies used by
recreational, male basketball players. However, this individualized, contextually-relevant
approach can be applied to all genders, ages, abilities, and skill levels to characterize shot
tendencies. This approach can help uncover how the individual controls their arms to
generate an increased ball velocity at release from greater shot distances, particularly for
female players who exhibit different segment configurations at release(B. Elliot, 1992).
Future work would benefit from incorporating other contextually-relevant scenarios, such
as different shot locations on the court and increased time pressure (e.g., closing defender,
shot or game clock). Future work would also benefit by adding the hand segment into the
analyses.
Findings from this study using a within-participant design are consistent with
previously reported results (Okazaki & Rodacki, 2012) and indicate that individual’s use
different yet relatively consistent strategies within player to regulate ball velocity at
release. The upper arm angular velocities measured in this study are comparable to
previous results indicating the shoulder angular velocity at release increases with shot
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distance (Okazaki & Rodacki, 2012). However, other studies have not come to the same
conclusion (Miller & Bartlett, 1996; Miller & Bartlett, 1993). This may be due to the group
analyses used, as well as a one study grouping together a range of shot locations (Miller &
Bartlett, 1993). By using a within-participant experimental design, the current study
provides further insight how individual players use their arms to generate ball velocity
needed at release to successfully make basketball shots from greater distances.
Individual players in this study increased their upper arm’s contribution to ball
velocity at release by increasing the upper arm angular velocity at release and/or
decreasing their upper arm angle relative to horizontal. The results of this study emphasize
the importance of the kinematic context and arm segment configuration at ball release in
addition to increases in segment angular velocities with shot distance. The magnitude and
direction of the relative elbow resultant velocity angle was found to be associated with the
position of the upper arm at release. These results indicate that a greater proportion of the
elbows relative resultant velocity was directed vertically as the upper arm became more
horizontal. Figure 5.8 illustrates how comparable upper arm angular velocity at release
results in greater relative elbow vertical velocity when the upper arm angle is more
horizontal at release. This result may explain the findings of previous studies indicating a
decrease in shoulder angle at release with increases in shot distance (B. C. Elliot & White,
1989; Miller & Bartlett, 1996; Miller & Bartlett, 1993; Okazaki & Rodacki, 2012). The more
horizontal the upper arm at release, the more the relative elbow resultant velocity is
directed vertically, and, if the upper arm is greater than 0 degrees relative to the horizontal,
the relative elbow resultant velocity’s horizontal component is directed negatively (away
from the hoop). The more vertical the forearm at release, the more the wrist relative wrist
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resultant velocity is directed horizontally, and, if the forearm is less than 90 degrees
relative to the horizontal, the relative wrist resultant velocity’s vertical component is
directed negatively (away from the hoop). For a successful shot, it is clear that individuals
need to control both joint extension and arm position in space order to achieve the
magnitude and direction of ball velocity at release needed for a ball trajectory to enter the
hoop (Okubo & Hubbard, 2016).

Figure 5.8: It isn’t just about achieving angular velocities at release but doing so at key
positions. The more horizontal the upper arm at release, the more vertical the elbow relative
resultant velocity (top left). Individuals can achieve the same upper arm angular velocity at
release (bottom left and right column, row 1), but due to their upper arm position at release
(right column, row 2), they achieve different elbow relative vertical velocities at release (right
column, row 3). This example illustrates that a player can achieve a greater vertical velocity
contribution from the upper arm by releasing the ball with a more horizontal upper arm.
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Results of this study indicate that arm vertical velocity contribution to ball vertical
velocity at release is influenced by the upper arm’s angular velocity and position. By
understanding how the individual generates the ball velocity with their arms and how
different contextually-relevant scenarios may affect the relative contributions of the arms
to ball velocity at release, individualized training and feedback can be given in context (e.g.,
shooting at greater distances, shooting while defended). Increasing the ball vertical velocity
at release can increase the likelihood of success by increasing the margin of error for the
ball to enter the hoop (Figure 5.9). Understanding the player’s tendencies across a range of
shot distances informs what the player can do to improve their ball trajectory and increase
the probability of a successful shot.

Figure 5.9: The greater the ball velocity entry angle, the greater room for error. Methods of
increasing the ball velocity entry angle include increasing the ball velocity release angle
and/or increasing the ball release height.

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Chapter 6 The strategies of generating ball velocity in the basketball jump shot across
shot distances
6.1 Introduction
When shooting the basketball, a goal of the shooter is to release the ball with a
resultant velocity that results in the ball entering the hoop. The ball’s velocity can be
contributed to the shooter’s whole body center of mass (CM) and the arms (Hay, 1985).
Previous research has sought to find the optimal trajectory (Brancazio, 1981; Hamilton &
Reinschmidt, 1997; Hay, 1985; Mortimer, 1951; Nakano, Fukashiro, & Yoshioka, 2020; Tran
& Silverberg, 2008); however, many trajectories can result in a successful shot (Figure 6.1).
Not only are there multiple ball flight trajectories that can be successful, but there are also
numerous joint angular velocities or body configuration that result in a successful shot
(Button, Macleod, Sanders, & Coleman, 2003; Coves, Caballero, & Moreno, 2020; Okubo &
Hubbard, 2015, 2016). The way an individual performs a shot is like their shooting
signature. Individuals have their own strategy in how they release the ball (Okazaki &
Rodacki, 2012), which becomes evident when watching a game. With the range of possible
ball flight trajectories and body and arm contributions to ball velocity, it is important to
analyze at the individual level to better understand the shot tendencies. It is imperative to
know what the individual brings to the table before any adjustments in shooting technique
occurs.
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Figure 6.1: There are multiple ball flight trajectories that can result in a successful shot.
Exemplar successful trajectories by multiple participants (color) and two different distances
(4.19 m, 6.02 m).
The amount the whole body contributes to the ball flight is determined by the whole
body’s CM velocity at the time of release. The whole body CM vertical velocity at release is
the result of how the individual approaches the shot (with or without momentum), how
much force they apply into the ground during the shot (i.e., net vertical impulse), and the
time the player is in the air before release. At further shot distances from the hoop, players
generate greater whole body vertical velocity (B. Elliot, 1992; Miller & Bartlett, 1996; Miller
& Bartlett, 1993; Okazaki & Rodacki, 2012; Walters, Hudson, & Bird, 1990; Wiens & McNitt-
Gray, 2020); however, there are different methods to achieve this (Chapter 4). To achieve a
greater CM vertical velocity at release, the individual must have first generated enough CM
vertical velocity at ground departure (Figure 6.2). After leaving the ground, the player has a
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choice: release the ball earlier in the flight, resulting in a greater whole body contribution
to the ball vertical velocity; or release the ball later in flight, resulting in a greater ball
release height but lower CM vertical velocity contribution to ball vertical velocity. To be
successful, the individual must choose their strategy that best fits their abilities within the
context of the situation (e.g., shot or game clock pressure; closing opposing player
pressure).

Figure 6.2: The center of mass velocity during the basketball shot is a result of the net impulse
generated by the legs. Once the shooter leaves the ground, gravity accelerates the body
toward the ground, reducing their center of mass velocity. The center of mass velocity at the
time of ball release is the amount contributed to the ball release velocity.
The arm contribution to the ball velocity at release is determined by the individual’s
ability to control the upper arm, forearm, and hand. When using all three segments, there
are nearly an unlimited amount of angular velocity and position combinations that result in
a success (Okubo & Hubbard, 2016). Changes in joint angular velocities and positions are
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likely to occur when shooting at greater shot distances, but previous results are mixed
(Diehl, Tant, Coleman, & Osborn, 1993; B. Elliot, 1992; B. C. Elliot & White, 1989; Miller &
Bartlett, 1996; Miller & Bartlett, 1993; Okazaki & Rodacki, 2012). This may be another
example of different strategies used by individuals when generating ball velocity with the
arms when the shot distance is increased (Okazaki & Rodacki, 2012). The arms are
required to generate the remaining velocity that, combined with the whole body’s
contribution, allows the ball to fly through the air and into the hoop. There are many ways
to successfully do this, so understanding how the individual currently controls their arms
can help guide more precise coaching cues and assist in tracking progressions over time.
How the ball enters the hoop determines the amount of margin for error to still be a
success (Figure 6.3). The steeper the ball enters the hoop, the greater the margin for error.
With the release position consistent, a greater ball entry angle is achieved by releasing the
ball at a greater angle (i.e., with more vertical velocity). However, as the release angle
increases, the error caused by changes in release angle for a given release speed increase
(Mortimer, 1951). The ability to control the flight of the ball is more important the higher
the release angle. A range of optimal release angles has been suggested that results in the
margin of error is greater than the possible error produced (Hay, 1985).
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Figure 6.3: The greater the ball velocity entry angle, the greater the room for error. The
minimum ball velocity entry angle that the ball does not hit the rim is 32.72 degrees when
shooting with a men’s ball (size 7) and 30.28 degrees with a women’s ball (size 6) (Hay, 1985).
Although it is common to suggest predefined optimal release angles, it is dependent
on the ball horizontal and vertical position relative to the hoop. In order to suggest a player
should have a certain release angle, the ball release height must be known and even then,
the angle will vary with the shot distance. Imagine Manute Bol and Muggsy Bogues being
told to with the same release angle at the free throw line.
The following sections provide specific examples to advance our understanding of
an individual’s shot mechanics by examining the strategies used by individual players in
generating the ball velocity at release as shot distance increases. We will explore how each
participant controls their whole body and arm contribution to ball velocity at release
across distances, and how these strategies result in a successful ball entry angle. We will
then explore individual-specific approaches to increase the ball entry angle for three
exemplar players.
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6.2 Ball Entry Angle
Within these players, the ball entry angle ranged from 51
∘
-62
∘
. Three groups (low,
medium, and high entry angle) were created. The whole body’s and arm’s contribution to
ball velocity and the vertical distance to the hoop primarily influence the ball entry angle.
So here we will take a look at the whole body (Figure 6.4, Row 1) and arm (Figure 6.4, Row
2) contribution to ball velocity and the ball release height (Figure 6.4, Row 3). In order to
have the ball enter the hoop at a steep angle (which increases the room for error), the
players in the ‘High Entry Angle’ group were above average in at least two of the three
variables that influence ball entry angle. However, it is clear to see there is more than one
way. For example, Participant 5 had the lowest ball release height of any of the players, yet
they had the second highest entry angle. They did so by having the greatest arm
contribution and above average whole body contribution. On the other hand, Participant 2
had third highest entry angle due to them releasing the ball at such a high position. This
reduced how much total vertical velocity they must generate, as they only had average arm
contribution and below average whole body contribution. So what are the mechanisms that
are behind these outcomes and results? Let’s first look at the factors in generating the
whole body velocity contribution.
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Figure 6.4: A player can achieve a high ball velocity entry angle by a combination of high CM
vertical velocity at release, high arm contribution to ball vertical velocity at release, and high
ball vertical position at release. Lower values in two or more of those variables likely
decreases your ball velocity entry angle. Note that within each group, the participants are
ordered by median ball entry angle from shots at the free throw line from lowest to highest.
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6.3 Whole Body’s Contribution
The whole body’s contribution to the ball velocity is impacted by the momentum the
player approaches the shot with (ex., stand-still vs step-in), how much force they apply
while in contact with the ground during the shot (net vertical impulse), and how much time
they are in the air before releasing the ball (Chapter 4). This can be further reduced to what
they do while in while in contact with the ground and when they choose to release the ball.
What the player does before leaving the ground plays a major role in determining the
options available. Generation of a relatively large whole body center of mass vertical
velocity at ground departure affords the player with multiple options, which then affords
choices such as:
• Release quick off the ground:
– Whole body contributes a large amount to the ball velocity
– Arms don’t have to generate as much velocity
• Release later in the jump, closer to the top of the jump:
– Ball is released from a higher position, which
• reduces the vertical distance the ball must travel, which reduces the
how much ball vertical velocity is actually required
• increases the range of possible successful ball flight trajectories
• may allow the player to shoot over a defender
If a player lacks the ability to generate whole body velocity, it limits what is
potential available to them, limiting their versatility to be successful in a variety of contexts
(e.g., time pressure: shot/game clock; space & time pressure: closing defender).
In this group of players, three main strategies were used in controlling their whole
body vertical velocity as shot distance increased (Figure 6.5). The ‘CM Vv at Ground
Departure’ group (Figure 6.5, Column 1) were players who, because they released quick off
the ground, had to increase their whole body vertical velocity at ground departure in order
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to increase it at ball release. Due to their quick release off the ground, their whole body
contributed an above average amount of velocity to the ball. What they did not prioritize
was using the jump to obtain a higher release height. The ‘Time in the Air before Release’
group (Figure 6.5, Column 2) regulated when they released the ball in the air. By leaving
the ground with the same whole body velocity and releasing the ball earlier in the air, they
increased their whole body vertical velocity at release at further shot distances. The ‘Both’
group (Figure 6.5, Column 3) did a mix of both, taking advantage of using the whole body
vertical velocity at ground departure to obtain a higher release height and large velocity
contribution to the ball velocity.
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Figure 6.5: Three main strategies of regulating the center of mass vertical velocity at release
exist when increasing shot distance (gold: 4.19 m; blue: 6.02 m; purple: 7.24 m). The ‘CM Vv at
Ground Departure’ group releases the ball early in the air, which forces them to have to
achieve a greater amount of center of mass vertical velocity at ground departure in order to
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increase the center of mass vertical velocity at release. The ‘Time in the Air before Release’
group consistently achieves a great amount of center of mass vertical velocity at ground
departure across shot distances, and chooses to regulate the time in the air before release to
increase their center of mass vertical velocity at release. The ‘Both’ group generates regulates
both their center of mass vertical velocity at ground departure and when they release the ball
in the air. Note that within each group, the participants are ordered by the body CM
contribution to ball vertical velocity at release from lowest to highest.
6.4 Arm’s Contribution
The arms are the greatest contributor to the ball velocity at release (B. Elliot, 1992).
The upper arm contributes to the ball vertical velocity at release, while the forearm and
hands contribute to the ball horizontal velocity at release (Okubo & Hubbard, 2015).
In this group of players, there were no major differences in how the arm
contribution to ball vertical velocity increased with an increase in shot distance, but the
differences were in individual overall kinematics at release. It wasn’t what they chose to
regulate across shot distances, it was what their strategies afforded them. Three main
groups can again be created (Figure 6.6). The ‘Release Height/Set Position’ group (Figure
6.6, Column 1) received minimal vertical velocity contribution from the upper arm due to
the average upper arm angular velocity and high upper arm angle at release. What their
strategy tended to afford them was a higher ball release height, as well as a base for the
forearm to rotate about the elbow joint. The ‘Vertical Velocity; group (Figure 6.6, Column 2)
had a high vertical velocity contribution from the upper arms. This was a result of large
upper arm angular velocities and low upper arm angle at release. The ’Both’ group (Figure
6.6, Column 3) used a combination of both those strategies.
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Figure 6.6: Upper arm angular velocity at release increased and upper arm angle at release
decreased with increasing shot distance (gold: 4.19 m; blue: 6.02 m; purple: 7.24 m). These
participants tended to regulate the same across shot distances, but the main separation was
what their strategy affords them. The ‘Release Height/Set Position’ group prioritized using
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the upper arm for a greater release height and set position for the forearm to rotate. The
‘Vertical Velocity’ group relied heavily on the upper arm’s contribution to ball vertical velocity
at release by having a high upper arm angular velocity when the upper arm angle was small.
The ‘Both’ group achieved an average amount of vertical velocity contribution from the upper
arm by having both average upper arm angular velocity and upper arm angle at release. Note
that within each group, the participants were ordered by the arm contribution to ball vertical
velocity at release from lowest to highest.
6.5 Conclusion
6.5.1 How did they achieve the high entry angle?
Putting it all together, we can now understand how both Participant 2 and Participant 5
had two of the highest entry angles, yet very different ball release heights:
• Participant 2 (Figure 6.7):
– High release height: Reduces the required vertical velocity for a steep ball
entry angles. He achieved this by:
• Generating a large amount of whole body vertical velocity at ground
departure AND waiting longer in the jump before releasing the ball.
Also had a larger upper arm angle at release.
– Arm contribution
• Participant 5:
– Arm contribution:
• Very high arm angular velocity at release.
• Near horizontal upper arm angle at release.
– Whole body contribution:
• Released the ball quick off the ground
In the next section, we will explore what an individual can do if they have a flat ball
entry angle and are interested in increasing the entry angle of the ball?
6.5.2 How can they increase their entry angle?
Suppose an individual wants to increase their ball entry angle, what can they do? Let’s
examine the two of the players in the ‘Low Entry Angle’ group:

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• Participant 3:
– He already has a high ball release height and average whole body
contribution. What may help is to:
• Increase arm contribution
– Likely can be achieved by increasing the upper arm angular
velocity at release
– Alternative option: release the ball with a more horizontal
upper arm angle
• Participant 8 (Figure 6.7):
– He has an average ball release height, but is limited in the other two
categories. What may help is to:
• Increase whole body contribution:
– Apply more force into the ground during the shot to increase
the whole body velocity at ground departure
• Increase arm contribution:
– Increase the upper arm angular velocity at release and/or
– Release the ball with a more horizontal upper arm angle
In order to improve an individual’s performance, we must meet them where they
are. We need to understand what they bring to the table and what their tendencies are
before we can start suggesting modifications. Once this is done, we now know what their
control patterns are and have a more informed foundation on how to help.

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Figure 6.7: Comparison of the primary causes for high and low ball entry angles. Participant 2
(gold) achieved a high ball entry angle by having a large arm velocity contribution, large
whole body velocity contribution, and a high release height. Participant 8 (silver) had a low
ball entry angle due to a lower release height, low arm velocity contribution, and an average
whole body velocity contribution.

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Chapter 7 Regulation of ball velocity at release with increases in shot distance in
wheelchair basketball
7.1 Introduction
Successful shots in basketball require the player to release the ball with sufficient
velocity so that ball enters the hoop. Basketball shots can occur in a variety of situations
(e.g., guarded/unguarded; jump shot vs layup) and positions on the court (e.g., free throw
vs three point from either standing or seated positions). The ball velocity at release is the
end result of the contributions from the whole body and the arms (Hay, 1985) and, in the
case of wheelchair (WC) basketball, the velocity of the body-chair system.
When increasing the shot distance from the hoop in standing basketball, the whole
body center of mass contribution to ball velocity at release increases (B. Elliot, 1992)
(Chapter 4), reducing the relative contribution of the arms. In WC basketball, the ability to
increase system level contributions to ball velocity at release is limited by the restricted
use of the legs limits the player’s ability to generate center of mass (CM) vertical velocity
(Figure 7.1). Initiating a shot while rolling in the WC increases the horizontal velocity of the
body-chair system at release, which can contribute to the horizontal velocity of the ball at
release. When non-disabled individuals initiated a basketball from a wheelchair, their ball
release height was found to be higher than the release of a tetraplegic group (Nunome,
Doyo, Sakurai, Ikegmai, & Yabe, 2002). The greater vertical displacement required in a
seated shot as compared to a standing shot (Nunome, Doyo, Sakurai, Ikegmai, & Yabe,
2002) requires a greater ball velocity at release to be successful and limits the range of
potentially successful ball flight trajectories (Brancazio, 1981; Hay, 1985).
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Figure 7.1: Example of the ball flight when shooting from a seated position. The ball must
travel a greater vertical distance than standing basketball shots, which increases the demand
on the arms that are already tasked in generating majority of the ball velocity.
WC basketball players, particularly those with limited trunk control, rely their arms
to generate ball velocity at release entire ball velocity. Two strategies to increase the arms
contribution to vertical velocity are increasing the upper arm angular velocity at release
and/or release the ball with a more horizontal upper arm angle (Chapter 5). Both of those
kinematic changes increase the vertical velocity contribution from the upper arm, resulting
in a greater ball vertical velocity at release and a higher CM trajectory. Model simulation
results suggest that shot initiation with the upper arm below horizontal (Schwark,
Mackenzie, & Sprigings, 2004) will provide sufficient range of motion to increase the upper
arm’s velocity contribution to the ball. Understanding how the individual increases their
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arm contribution to the ball velocity at release when increasing shot distance can assist
individual-specific training, potentially leading to a more successful and skillful player.
The purpose of this study was to determine how shot distance affects regulation of
ball velocity at release in the wheelchair basketball shot. We hypothesize a) the arm
contribution to ball vertical and horizontal velocity at release would increase with shot
distance; b) the elbow vertical velocity at release relative to the shoulder would increase
with an increase in shot distance, as a result of an increase in upper arm angular velocity at
release and a more horizontal upper arm position at release. We also hypothesized that c)
the wrist horizontal velocity at release would increase with an increase in shot distance, as
a result of an increase in forearm angular velocity and a more vertical forearm position at
release. We tested these hypotheses by comparing segment kinematics during the shot
using a within-player experimental design.
7.2 Methods
Seven individuals participated in the study (7 male). Participants were from a local
wheelchair basketball club that has teams that competes in Division 1 at a national level
and Division 3 and provided informed consent in accordance with the Institutional Review
Board for research involving human subjects.
Participants attempted shots from two locations on the court depending on their
role on the team. All shot locations (distance from the point on the floor directly beneath
the center of the hoop) were the: paint (3.35 m), free throw line (4.19 m), and the three-
point line (6.02 m). These shot distances are commonly performed during practice and
competition. Inside players shot from the two closest locations (paint and free throw line),
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and perimeter players shot from the two furthest locations (free throw line and three point
line). Participants attempted at least 30 shots from each shot distance. Participants shot
with the regulation-sized balls they would use in a competition (size 7, 0.75 m
circumference).
Each participant was given at least 10 minutes to warm-up prior to the collection.
The participants were informed what types and locations of shots they were to perform
during the experiment, so they could adequately prepare for the collection. Each
participant led their own warm-up.
To start each trial, a researcher started the video capture software. An experienced
basketball player (participant or researcher) located near under the hoop then passed the
ball to the shooter who performed the shot. The cameras were triggered off once the ball
landed on the floor. This process was repeated until each participant completed all the
shots from each shot condition. Participants arrived in pairs and alternated every 10 shots
in effort to reduce fatigue.
The origin of the reference system was located on the floor, directly beneath the
center of the hoop. Ball position and three-dimensional body kinematics were recorded by
eight high-speed cameras (120 Hz, Prime Color, OptiTrack, Corvallis, OR). The ball position
was detected by a neural network (Mathis et al., 2018; Nath et al., 2019) trained on a subset
of images from each collection from each camera view. The ball position in the three-
dimensional gym reference system was calculated using a custom Python code. Three-
dimensional body position was estimated using a markerless motion capture software
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(Theia Markerless Inc., Kingston, ON, Canada) (Kanko et al., 2021; Kanko, Laende, Davis,
Selbie, & Deluzio, 2021; Kanko, Laende, Selbie, & Deluzio, 2021).
Time was expressed relative to the instant of ball release (time = 0). Ball release was
defined as the last contact between the hand and the ball during the shot, and it was
manually identified. Center of mass vertical and horizontal position was measured using a
built-in Visual3D (C-Motion Inc., Germantown, MD) model that is designed for Theia3D
output. Center of mass vertical and horizontal velocity were calculated as the first
derivative of the center of mass position. Ball and body position were expressed relative to
the origin. Ball vertical and horizontal velocities at ball release were expressed as the
velocity along the z and y axes, respectively.
The contribution of the center of mass vertical and horizontal velocity to ball
vertical and horizontal velocity at ball release was the center of mass vertical and
horizontal velocity at ball release, respectively. The arm vertical and horizontal velocity
contribution to ball vertical and horizontal velocity at ball release was the ball vertical and
horizontal velocity at ball release minus the center of mass vertical and horizontal velocity
at ball release, respectively. Both the center of mass and arm contributions to ball vertical
and horizontal velocity at ball release were represented as a percentage of the ball vertical
and horizontal at ball release.
Within-individual differences were tested by comparing trimmed means using a
percentile bootstrap method and with an 𝛼 = 0.05 (R. Wilcox, 2017; R. R. Wilcox &
Schönbrodt, 2021). No group between-distance differences were tested due to the
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heterogeneity of the population, even when shooting the basketball (Goosey-Tolfrey,
Butterworth, & Morriss, 2002; Malone, Gervais, & Steadward, 2002).
7.3 Results
Arm contribution to ball vertical velocity at release increased with an increase in
shot distance (Figure 7.2). Within the 7 participants, when increasing shot distance, all 7
participants significantly increased their arm contribution to ball vertical velocity at
release.
Arm contribution to ball horizontal velocity at release increased with an increase in
shot distance (Figure 7.2). Within the 7 participants, when increasing shot distance, 6
participants significantly increased their arm contribution to ball horizontal velocity at
release.
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Figure 7.2: The arm velocity contribution to ball vertical (top row) and horizontal (bottom
row) velocity at release increased with an increase in shot distance (gold: 4.19 m; blue: 6.02
m; purple: 7.24 m). * p < 0.5; ** p < 0.01; *** p < 0.001; **** p < 0.0001. Participants are sorted
by the median arm contribution to ball vertical velocity at release in the 4.19 m shots.
Elbow relative vertical velocity at release increased with an increase in shot
distance (Figure 7.3). Within the 7 participants, when increasing shot distance, 5
participants increased their elbow relative vertical velocity at release.
Elbow relative horizontal velocity at release decreased magnitude in the negative
direction (Figure 7.3). Within the 7 participants, when increasing shot distance, all 7
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participants decreased their elbow relative horizontal velocity at release in the negative
direction.
Wrist relative vertical velocity at release changed with an increase in shot distance
but was specific to the individual (Figure 7.3). Within the 7 participants, when increasing
shot distance, 4 participants increased their wrist relative vertical velocity at release, while
2 participants decreased their wrist relative vertical velocity at release.
Wrist relative horizontal velocity at release did not change with an increase in shot
distance (Figure 7.3). Within the 7 participants, when increasing shot distance, 1
participant increased their wrist relative horizontal velocity at release, while 2 participants
decreased their wrist relative horizontal velocity at release.
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Figure 7.3: The arm velocity contribution to ball vertical (top row) and horizontal (bottom
row) velocity at release increased with an increase in shot distance (gold: 4.19 m; blue: 6.02
m; purple: 7.24 m). * p < 0.5; ** p < 0.01; *** p < 0.001; **** p < 0.0001. Participants are sorted
by the median arm contribution to ball vertical velocity at release in the 4.19 m shots.
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Upper arm angular velocity at release changed with an increase in shot distance but
it depended on the individual (Figure 7.4). Within the 7 participants, when increasing shot
distance, 3 participants increased their upper arm angular velocity at release, while 2
participants decreased their upper arm angular velocity at release.
Forearm angular velocity at release did not change with an increase in shot distance
(Figure 7.4). Within the 7 participants, when increasing shot distance, 1 participant
increased their forearm angular velocity at release in the negative direction, while 3
participants decreased their forearm angular velocity at release.
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Figure 7.4: The upper arm angular velocity at release (top row) increased with an increase in
shot distance (gold: 4.19 m; blue: 6.02 m; purple: 7.24 m). The forearm angular velocity at
release was lowest at 4.19 m and greatest at 6.02 m. * p < 0.5; ** p < 0.01; *** p < 0.001; **** p
< 0.0001. Note the bottom row y-axis is reversed. Participants are sorted by the median arm
contribution to ball vertical velocity at release in the 4.19 m shots.
Upper arm angle at release decreased with an increase in shot distance (Figure 7.5).
Within the 14 participants, when increasing shot distance, 8 participants decreased their
upper arm angle at release, while 2 participant increased their upper arm angle at release.
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Forearm angle at release decreased with an increase in shot distance (Figure 7.5).
Within the 14 participants, when increasing shot distance, 10 participants decreased their
forearm angle at release, while 2 participants increased their forearm angle at release.

Figure 7.5: The upper arm angle (top row) increased with shot distance while the forearm
angle (bottom row) decreased with shot distance (gold: 4.19 m; blue: 6.02 m; purple: 7.24 m).
* p < 0.5; ** p < 0.01; *** p < 0.001; **** p < 0.0001. Participants are sorted by the median arm
contribution to ball vertical velocity at release in the 4.19 m shots.
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7.4 Discussion
In this study, we determined the effect of shot distance on the arm contribution to
ball velocity at release in wheelchair basketball shots. Within-participant analysis revealed
an increase in arm contribution to ball vertical and horizontal velocity at release with
increases in shot distance. The upper arm vertical velocity contribution was greater at the
further shot distance due to an increased upper arm angular velocity at release and a more
horizontal upper arm angle at release. The elbow relative horizontal velocity decreased
magnitude in the negative direction when increasing shot distance, likely a result of the
more horizontal upper arm angle at release. Majority of the participants release the ball
with a lower forearm angle.
The results from this study are limited as they only reflect male, wheelchair
basketball players. However, this contextually relevant approach for studying shot
tendencies within-participant analysis can be applied to all skill-levels, genders, and
abilities. Applying this approach to more wheelchair basketball players in all classifications
can help further identify how individuals from different classes and with different levels of
trunk control exhibit different shooting tendencies (Goosey-Tolfrey, Butterworth, &
Morriss, 2002; Malone, Gervais, & Steadward, 2002) in order to assist in more personalized
feedback. Future work may benefit from adding a hand segment in the analyses and will
include shots from the side and those contested by a defender.
When increasing shot distance, the upper arm vertical velocity contribution to ball
velocity at release increases, consistent with results for non-disabled, standing basketball
players (Chapter 5). Results indicate that participants in this study increased their upper
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arm vertical velocity contribution at release by increasing their upper arm angular velocity
and/or by releasing the ball with a smaller upper arm angle.
These results indicate that there is more than one way to achieve a successful shot
in WC basketball, consistent with comparable findings in non-disabled players (Okazaki &
Rodacki, 2012) (Chapters 4 & 5) the participants had their own strategies. Although
majority of participants used the same strategy to increase their upper arm vertical
velocity contribution, one participant was unique. Participant 4 had the lowest upper arm
vertical velocity contributions. This was a result of minimal upper arm angular velocity at
release and a large upper arm angle at release. His strategy was to raise his elbow up high,
set his upper arm in place, and rotate the forearm about the elbow joint to generate the ball
velocity at release (Figure 7.6). When increasing shot distance, he was the only participant
to release the ball with a greater forearm angle. By comparison, Participant 5 had a larger
elbow relative vertical velocity at release, as his strategy was to have a lower upper arm set
position and a larger upper arm angular velocity at ball release (Figure 7.6). More
individualized feedback can be provided by analyzing how the individual is regulating their
arm contribution to ball velocity at release and how the position of the ball at release may
be affected when opposed by a defender.
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Figure 7.6: Example trial of Participant 4 (top). To begin the shot, the elbow was raised high
and the upper arm is set. The forearm then began to rotate about the elbow joint until ball
release. Example trial of Participant 5 (bottom). To begin the shot, the elbow was set slightly
below horizontal. During the shot, as the forearm rotated forward toward the hoop, the upper
arm also rotated upward, resulting in a greater elbow vertical velocity relative vertical
velocity at release than Participant 5.
The arm contribution to ball vertical velocity at release increases with shot distance
in wheelchair basketball shooting. The increase in upper arm contribution is a result of
increased upper arm angular velocity and/or decreased upper arm angle at release.
Personalized feedback can be given by understanding how the individual generates the ball
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velocity with their arms. The individualized feedback likely leads to greater success, which
also likely results in more basketball-specific (e.g., skillful in a variety of contexts) and non-
basketball specific (e.g., enjoyment and longevity in the game) outcomes.

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Chapter 8 Improving human performance over time using an integrated biomechanical
informatics system with embedded data visualization tools
8.1 Introduction
Improvement in human performance takes time. To better understand the process
of skill development and performance during competition, it is helpful to track and assess
what is working for the individual and what needs work. An individual’s performance is not
just about what they do but how they do it, in context. By collecting available, relevant data
from multiple sources over time, an individual’s learning pathways and performance
patterns can be better visualized over time. Video recordings of task performances in
different contexts can be found through various sources and media postings that allow
temporal or qualitative analysis of the movement mechanics. High speed video recordings,
acquired from a fixed camera position, ideally leveled, calibrated, and squared with the
performance plane, can be used to better quantify how mechanical objectives needed to
perform the skill were achieved in each phase of the task. Integration of these video
records with performance results and other sources (e.g., electronic patient medical and
training records, injury history, return to play progressions) into an informatics system
provides the infrastructure to track how an individual improves their performance over
time and in context. For athletes ultimately reaching the Olympic level, this can involve the
management and organization of raw data from multiple sources that including training
progressions and injury history gathered over 12-15 years. By integrating and time
synchronizing data acquired into a biomechanical informatics system (IBIS), the gap
between data collected and the information extracted and utilized for skill acquisition and
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improvements in performance can be bridged (B. J. Liu, 2019; J. Liu, Stewart, Wiens, Mcnitt-
Gray, & Liu, 2022; Verma, 2019).
Embedding data visualization tools into the IBIS system allows different end users
to visualize trends over time and query data for statistical analyses. For example, outcomes
of performance at different times during the training cycle or in different context (e.g.,
temperature, wind, elevation) can often be readily obtained by scrubbing information from
website posting of competition results. These data when linked in time to other
information can provide the context needed to interpret shifts in performance over time.
By integrating data acquired during practices leading up the competition, the skill
progressions leading to the performance outcome can be assessed and used to refine
athlete preparation for future competitions. The key challenge is designing a robust
database based on FAIR Guiding Principles (Findability, Accessibility, Interoperability, and
Reuse of digital assets, (“FAIR principles,” n.d.)) in the design, development, and
implementation of effective tools for data pre- and post-processing, data storage, and data
review so that available content can be linked in time and maintained with limited
resources (Le Meur & Torres-Ronda, 2019).
Databases provide a foundation to support decision making by professionals
interested in advancing human performance through sports science (Vincent, Stergiou, &
Katz, 2009) (e.g., “how did the individual achieve the task?” “did my intervention have it’s
intended effect?” “has the individual progressed over the desired timeline?” or “when x and
y occur, what happens to z?” etc.). As the data’s quantity and diversity increase, the
database’s storage design can facilitate the sharing of data across organizations by using
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data formats that eases access across multiple software languages and programs (e.g., R,
Python, MatLab), and queried by key information (e.g., gather all data leading up to London
2012, Rio 2016 and Tokyo 2020 Olympics). Ultimately, data from multiple sources and
models - such as biomechanical, physiological, medical, and performance sources - can be
time synchronized and queried to investigate questions, based on the evidence, ranging
from ‘what just happened’ to ‘what could happen in the future.’
The purpose of this chapter is to present the approach we used for designing,
generating, and implementing an integrated biomechanical informatics system (IBIS) to
monitor improvements in horizontal jump performance of national level athletes in track
and field over the past decade. This project builds on lessons learned from a performance
tracking multimedia informatics system used to track skill acquisition in women’s
volleyball (B. J. Liu, 2019; J. Liu, Stewart, Wiens, McNitt-Gray, & Liu, 2022; Verma, 2019).
Video records of long jump and triple jump performance during practice and competition
were time synchronized and integrated with reaction force data collected during practice
jumps to characterize how individuals achieve their total body linear and angular
momentum at the initiation of flight phase and determine the mechanical demand impose
on the lower extremity of during last contact prior to flight. Data input workflows include
data pre- and post- processing routines where raw data is collected, cropped, cleaned, and
catalogued so data is findable, accessible and in interoperable formats to facilitate reuse for
both improved performance and reduced risk of injury. Data output workflows include
event identification, movement mechanics by phase, and data visualization tools that
illustrate the forces causing the observed motion and the joint kinetics required to control
the lower extremity during ground contact. To illustrate the foundational nature and the
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functionality of IBIS created for USA Track and Field Horizontal Jumpers, exemplar whole
body analysis and joint level case studies are provided for long jump and triple jump
performed by male and female athletes with and without disabilities (Paralympic, Olympic
athletes).
8.2 Methods
Data from high performance level USA track and field athletes participating in the
horizontal jumps (long jump, triple jump) were integrated into the biomechanical
informatics system (IBIS) in accordance with the USC Institutional Review Board for
research involving human participants. To fill the gap between data collected and the
information extraction, unstructured and unsynchronized data were first standardized,
stored, and secured, consistent with HIPAA compliant data sharing protocols. By design,
the IBIS multi-layer infrastructure (Figure 8.1) allows for modifications with time, usage,
and advancements in knowledge and technology (B. J. Liu, 2019; J. Liu, Stewart, Wiens,
McNitt-Gray, & Liu, 2022; Verma, 2019). In layer 1, data is collected from multiple sources.
In layer 2, data is annotated, cleaned, validated, cropped and transferred for use in layer 3.
In layer 3, data analysis, visualization and reporting tools are used to generate knowledge
used for feedback, intervention design, as well as educational and research activities in
layer 4.
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Figure 8.1: Workflow supporting the Integrated Biomechanics Informatics System (IBIS).
In step 1 (Figure 8.1), data related to performance in the horizontal jumps are collected
from multiple sources using varied measurement systems (e.g., force plates, motion
capture, wearable sensors, survey information, competition history, electronic records
from multiple devices. Through the informatics system gateway these data are processed
(e.g., annotated, cleaned, validated etc.) and uploaded to and stored in IBIS. Data can then
be queried and analyzed through web server and decisions support tools for data
visualization, statistical analysis, as well as collaborative analysis. In the final step (6),
analyzed data is then shared with end users with different backgrounds and expertise (e.g.,
coaches, athletes, clinicians, researchers etc.). A data dictionary is provided to clarify
measurements and calculated variables relevant to jump performance. Results are also
shared using contextually relevant graphical representations to facilitate understanding
how and why these measures are relevant to performance outcomes. Figures 2- 4 provide
insights regarding runway management (Figure 8.2), preparation for the jump support and
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flight phase durations relative to regulation of body rigidity during ground contact and
previous center of mass (CM) trajectories (Figure 8.3), as well as momentum regulation
during contact phases represented by changes in momentum in the vertical and horizontal
directions during ground contact (Figure 8.4).

Figure 8.2: Position on the runway relative to the scratch line during the Jump Preparation
Phase. Horizontal position of toes at final contact are expressed relative to the scratch line
(0,0).

Figure 8.3: Support and Flight Phase Durations during the Jump Preparation Phase.
Durations are calculated by determining the change in time between Initial Contact (IC) and
Final Contact (FC).
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Figure 8.4: Momentum regulation during the Jump Preparation Phase. Center of mass (CM)
horizontal velocities calculated by determining the change in CM horizontal position divided
by the change in time between Final Contact (FC) and Initial Contact (IC).
Web Server and Web-based User Interface: The webserver hosts the graphical user
interface (GUI) so that the system can be accesses by authorized users anywhere, any time.
This feature is essential in that coaches, athletes, sports medicine and sports science
service providers are often located on different continents and in different time zones. Data
can be uploaded, downloaded, or open directly on the Web interface using built in data
visualization tools that void the need for local installation of viewing programs. In addition,
authorized users can record notes, annotations as they use customizable discovery and
decision tools. This feature facilitates communication and feedback across all users (e.g.,
athletes, coaches, researchers, clinicians etc.) in that these observations are gathered in one
place and accessible by all. The GUI uses LAMP, an open source Web development platform,
with Apache 2 as the Web server. The client side uses HTML and Javascript and the server-
side uses PHP as the object-oriented scripting language and MySQL as the relational
database management system.
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Security and Privacy: User authentication and specific user access controls have been
implemented to provide access by athletes, coaches, and USATF. The IBIS Web server is
hosted within the ITS firewall that helps track traffic and any questionable activity and
protect against potential cyber attacks.
Data Input Workflow: A relational database model (Codd, 1970) and Structured Query
Language (SQL) was used to manage training and competition data in IBIS for track and
field. A fundamental concept within the database is the relationship between tables.
Primary keys - column(s) that contain unique identifiers for each row - and foreign keys -
column(s) that include the identifiers of the related table’s primary keys - allow for
multiple table connections and enforce the two fundamental design principles, uniqueness
and non-redundancy (Vincent, Stergiou, & Katz, 2009). The primary benefits to this
approach are that data are only stored once (uniqueness) and the size of the data base is
minimized (non-redundancy) in that any data updates (e.g., athlete’s age, height, weight,
coach) occur in only one location (non-redundancy).
Data upload into the centralized database uses a built-in uploader on the Web
platform and incorporates custom upload modules to facilitate data transfers. Data
warehousing is facilitated by the use of secure FTP clients (e.g., Filezilla). Different forms of
data formats (mp4, jpg, dat, text, etc.) are stored including biomechanical variables
calculated using source data (e.g., impulse during impact and post impact phases, contact
time, lower extremity joint kinetics etc.) (Figure 8.5). Specifics needed for data processing,
analysis, and dissemination tend to be unique to each data collection scenario and are
documented using event log sheets.
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Figure 8.5: Data structure for force and video collected for each athlete and use of data in
calculations of variables of interest. Cleaning of the data prior to analysis involves cropping of
the video records, conversion of measures into units, event identification, normalization of
quantities based on body mass or contact duration, and attenuation of noise in source signals
through filtering or curve fitting.
Data Output Workflow: Open source software (e.g., R and Python) were the tools selected
for data visualization and statistical analyses data acquired from jump performances. The
GUI designed for USATF leverages the software’s data visualization and statistical analyses
prowess of the R Shiny application (Chang et al., 2021). Shiny is an interactive application
used for generating customized reports and dashboards. In the initial version, Shiny
applications were developed so that users with limited knowledge of R programming could
use the application by running R locally on their computer. Now that R is integrated within
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IBIS (a secure web-based platform), installation of R on an individual’s computer is no
longer necessary.
8.3 Results
Implementation of the IBIS for top-tier horizontal jumpers has improved
functionality, timeliness of feedback which has had a positive effect on both knowledge
discovery and practice planning. Utilization of IBIS and these tools has reduced the time
required to provide quantitative analysis of jumps performed in competition by more 60%
and has enabled us to provide results to all athletes participating, not just the finalists in an
event, with the same resources. The combination of the database and R provide the ability
to generate interactive data visualizations that has advanced understanding of the
mechanical objectives required in each phase of the skill. A simple yet informative method
of tracking performance is visualizing the performance outcome over time is shown in
Figure 8.1.
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Figure 8.6: Visualizing performance over time can assist in monitoring an individual’s
progression.
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Figure 8.7: Post competition reporting of key attributes of triple jump performance using data
in IBIS.

Figure 8.8: Comparison of triple jump performances over time during competition and in
practice using data visualization tools in IBIS.
By using time synchronized force and high speed video and segment kinematics
during last contact, the mechanical demand imposed on the lower extremity between
attempts can also be visualized (Figure 8.9). The frame-by-frame representation of the
resultant reaction force applied to the foot (vector) and the changing magnitudes of the
ankle, knee, and hip Net Joint Moments during the impact and post impact phase (diameter
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and colors of the circles) allows coaches to better understand how and why the mechanical
demand imposed on the lower extremity changes with each attempt and why the athlete
feels differences between attempts.

Figure 8.9: Combining multiple data sources together can provide an informative analysis.
This visual highlights the differences in the mechanical demand on the jumper for two
different jumps.
8.4 Discussion
In this project, we designed and implemented an integrated biomechanical
informatics system (IBIS) (J. Liu, Stewart, Wiens, Mcnitt-Gray, & Liu, 2022) to monitor
improvements in horizontal jump performance of national level athletes in track and field
over the past decade. Video records of long jump and triple jump performance during
practice and competition were time synchronized and integrated with reaction force data
collected during practice jumps to characterize how individuals achieve their total body
linear and angular momentum at the initiation of flight phase and determine the
mechanical demand impose on the lower extremity of during last contact prior to flight.
133

Data input workflows include data pre- and post- processing routines where raw data is
collected, cropped, cleaned, and catalogued using FAIR principles. Biomechanics related
data visualization workflows include comparison of an individual’s movement mechanics
over time and data visualization tools that illustrate the forces causing the observed motion
and the joint kinetics required to control the lower extremity during ground contact.
The foundational nature and the functionality of IBIS created for USA Track and
Field Horizontal Jumpers is yet to be fully realized. We expect that when combined with
emerging markerless motion capture technology (Figure 8.10), this data base will provide
the source data required for exemplar whole body analysis and joint level case studies to
advance our understanding of control and dynamics of long jumps and triple jumps
performed by male and female athletes with and without disabilities (Paralympic, Olympic
athletes).
Integration and time synchronization of biomechanical measures across multiple
jump attempts performed by the same individual is expected to provide a deeper insight
into how individual athletes achieve the mechanical objectives of tasks performed during
competition and track their improvements over time. For example, if a coach wants their
athlete to achieve a particular center of mass (CM) displacement during flight (Figure 8.11),
experimental results indicate athletes can achieve this mechanical objective in multiple
ways. This allows the coach and athlete consider the individual athletes current capabilities
(e.g., ability to generate fast horizontal speeds and/or convert horizontal to vertical
momentum) during last contact prior to the flight phase of the long jump. Model simulation

134

Figure 8.10: Continued advances in markerless motion capture technology will further
leverage these data base resources for improved validation estimates of CM velocities based
on kinematic source data, comparing and contrasting momentum regulation mechanisms
within athlete over time, as well as utilization of multilink model simulation to assess ‘what if’
scenarios (e.g., model simulation of non-contact, and impact and post impact phases during
activities of daily living by (Amezcua-Cerda, McNitt-Gray, & Flashner, 2022; McNitt-Gray,
Requejo, Flashner, & Held, 2004; Munaretto, McNitt-Gray, Flashner, & Requejo, 2012, 2013;
Requejo, McNitt-Gray, & Flashner, 2004; Wagner, 2018)).
results as well as experimental results from elite female jumpers in IBIS indicate
that with improvements in either of one of these abilities or both through training,
increases in jump performance will result. This provides the coach and athlete with greater
clarity on what attributes to improve during preparation.
135

Figure 8.11: The Flight Phase Simulator allows coaches to determine how best to use and
develop an individual athlete’s abilities to improve their performance. For example, to achieve
a center of mass (CM) displacement during flight of 5.6 m (light blue line reflects the
combination of CM horizontal and vertical velocities needed to achieve this displacement), an
athlete can achieve this by using their horizontal velocity (black text and arrows) or by using
their ability convert horizontal to vertical momentum (purple text and arrows) during last
contact prior to the flight phase of the long jump.
136

Further integration of other sources of data (e.g., medical history, sleep, travel and
time zones, refueling, sports psychology and mindfulness) will continue to provide context
for determining what is working and what needs work. Continued improvements in the
graphical user interfaces as well as introduction of analytical tools like R (Figure 8.12) and
computational codes will improve access to IBIS functionality, particular for coaches,
athletes, and medical providers supporting athlete performance.

Figure 8.12: Interactive features allow coaches and athletes to contribute to the data base by
adding their own video clips using a fixed camera set up and data acquisition ‘help’
documentation. In addition, the Flight Phase Simulator based on projectile motion equation
allows coaches and athletes to simulate center of mass (CM) trajectory during flight phases of
long jump and triple jump using “what if” scenarios (e.g., if I can increase my speed by 0.2 m/s
at Final Contact prior to flight, how will this add to my CM displacement during flight).
137

Figure 8.13: Integration of video and force information (force vector synchronized in time
with the video images at key instances or as a force time-curve) shows how the forces
generated by the individual athlete causes the observed motion and how an individual
converts their horizontal velocity to vertical velocity during the last contact prior to flight.

138

Chapter 9 Conclusion
The collective research presented in this document present individual strategies in
contextually-relevant situations. By analyzing individuals in the field (Chapter 3, 4, 5, 7), we
can get a better understanding of individual-specific tendencies that exist in real world
scenarios. Understanding the underlying mechanics of the movement allows us to identify
what can be modified. We can then “fit” the feedback/response to the individual, whether
that be personalized fitting a wheelchair (Chapter 3) or technique feedback (Chapter 6).
Through the use of a database and similar tools (Chapter 8), we can track the individual’s
progression over time. This allows for more meaningful questions to be asked and skill
progressions to be tracked and refined.
9.1 Personalized wheelchair fitting
Personalized WC configuration is a promising approach for improving posture,
upper extremity kinematics associated with propulsion energetics, and mitigating
mechanical demand imposed on the shoulder during manual WC propulsion. The effects of
personalized WC configuration on upper extremity kinematics were likely positive, as
evidenced by elbow angles aligning with clinical guidelines (23 of 26 participants
maintained or improved). The results demonstrate that personalized WC configuration
afforded by K0005 WCs enabled trained seating center clinicians to positively affect
posture and upper extremity mechanics during push, without detrimental increases in
shoulder demand during WC propulsion.
139

9.2 Whole body velocity regulation across shot distance in basketball shooting
Within-participant analyses revealed that each of the basketball players in this
study significantly increased body CM vertical velocity at release with increases in shot
distance. Increasing the CM vertical velocity at ground departure affords choices and
emphasizes the value of impulse generating abilities of the player. Understanding how to
help players use what they do have will likely increase success.
9.3 Arm velocity regulation across shot distance in basketball shooting
Within-participant analysis revealed an increase in arm contribution to ball vertical
and horizontal velocity at release with increases in shot distance. Individual players in this
study increased their upper arm’s contribution to ball velocity at release by increasing the
upper arm angular velocity at release and/or decreasing their upper arm angle relative to
horizontal. These results emphasize the importance of increasing segment angular
velocities and the achievement of those increased angular velocities at key positions in
space.
9.4 Arm velocity regulation across shot distance in wheelchair basketball shooting
Within-participant analysis revealed an increase in arm contribution to ball vertical
and horizontal velocity at release with increases in shot distance. The arm contribution to
ball vertical velocity at release increases with shot distance in wheelchair basketball
shooting. The increase in upper arm contribution was found to be a result of increased
upper arm angular velocity and/or decreased upper arm angle at release.
140

9.5 Database, integration of data, and tracking progressions
An integrated biomechanical informatics system (IBIS) was designed and
implemented to monitor improvements in horizontal jump performance of national level
athletes in track and field over the past decade. Implementation of the IBIS for top-tier
horizontal jumpers has improved functionality, timeliness of feedback which has had a
positive effect on both knowledge discovery and practice planning.
9.6 Future directions
Future research can expand on the work presented here by applying the same
within-individual analyses to a broader group of people, such as gender, skill-level, and
mobility. This may help shed light onto why there may be differences, and how the
individual can improve. Another future direction is to track the hand during the basketball
shot. Likely due to the group analyses, there are mixed results suggesting how the hand
segment impacts the shot. By adding the hand to the arm system, it would give a more
detailed picture into how the individual uses the arms to generate the ball velocity at
release.

141

References
Amezcua-Cerda, R., McNitt-Gray, J., & Flashner, H. (2022). NACOB.
Angel, E. (2000). Interactive computer graphics : A top-down approach with OpenGL. Boston,
MA: Addison Wesley Longman.
Angel, E. (2001a). Batch-file computer graphics : A bottom-up approach with QuickTime.
Boston, MA: Wesley Addison Longman.
Angel, E. (2001b). Test second book by angel. Boston, MA: Wesley Addison Longman.
Boninger, M. L., Baldwin, M., Cooper, R. A., Koontz, A., & Chan, L. (2000). Manual wheelchair
pushrim biomechanics and axle position. Archives of Physical Medicine and
Rehabilitation, 81(5), 608–613. http://doi.org/10.1016/S0003-9993(00)90043-1
Boninger, M. L., Souza, A. L., Cooper, R. A., Fitzgerald, S. G., Koontz, A. M., & Fay, B. T. (2002).
Propulsion patterns and pushrim biomechanics in manual wheelchair propulsion.
Archives of Physical Medicine and Rehabilitation, 83(5), 718–723.
http://doi.org/10.1053/apmr.2002.32455
Brancazio, P. J. (1981). Physics of basketball. American Journal of Physics, 49(4), 356–365.
http://doi.org/10.1119/1.12511
Brubaker, C. E. (1986). Wheelchair prescription: an analysis of factors that affect mobility
and performance. Journal of Rehabilitation Research and Development, 23(4), 19–26.
Button, C., Macleod, M., Sanders, R., & Coleman, S. (2003). Examining Movement Variability
in the Basketball Free-Throw Action at Different Skill Levels. Research Quarterly for
Exercise and Sport, 74(3), 257–269. http://doi.org/10.1080/02701367.2003.10609090
Chang, W., Cheng, J., Allaire, J., Sievert, C., Schloerke, B., Xie, Y., … Borges, B. (2021). Shiny:
Web application framework for r. Retrieved from https://CRAN.R-
project.org/package=shiny
Codd, E. F. (1970). A Relational Model of Data for Large Shared Data Banks.
Communications of the ACM, 11.
Coves, A., Caballero, C., & Moreno, F. J. (2020). Relationship between kinematic variability
and performance in basketball free-throw. International Journal of Performance Analysis
in Sport, 20(6), 931–941. http://doi.org/10.1080/24748668.2020.1820172
de Leva, P. (1996). Adjustments to Zatsiorsky-Seluyanov’s segment inertia parameters.
Journal of Biomechanics, 29(9), 1223–1230. http://doi.org/10.1016/0021-
9290(95)00178-6
Desroches, G., Aissaoui, R., & Bourbonnais, D. (2006). Effect of system tilt and seat-to-
backrest angles on load sustained by shoulder during wheelchair propulsion. The
142

Journal of Rehabilitation Research and Development, 43(7), 871.
http://doi.org/10.1682/JRRD.2005.12.0178
Diehl, D., Tant, C. L., Coleman, S., & Osborn, R. (1993). 11 International Symposium on
Biomechanics in Sports (pp. 309–312).
Elliot, B. (1992). A kinematic comparison of the male and female two-point and three-point
jump shots in basketball. Australian Journal of Science and Medicine in Sport, 24(4), 111–
117.
Elliot, B. C., & White, E. (1989). A kinematic and kinetic analysis of the female two and three
point jump shots. Australian Journal of Science and Medicine in Sport, 21(2), 7–11.
FAIR principles. (n.d.). Retrieved from https://www.go-fair.org/fair-principles/
Fisher, A. J., Medaglia, J. D., & Jeronimus, B. F. (2018). Lack of group-to-individual
generalizability is a threat to human subjects research. Proceedings of the National
Academy of Sciences, 115(27), E6106–E6115.
http://doi.org/10.1073/pnas.1711978115
Goosey-Tolfrey, V., Butterworth, D., & Morriss, C. (2002). Free Throw Shooting Technique
of Male Wheelchair Basketball Players. Adapted Physical Activity Quarterly, 19(2), 238–
250. http://doi.org/10.1123/apaq.19.2.238
Gorman, A. D., & Maloney, M. A. (2016). Representative design: Does the addition of a
defender change the execution of a basketball shot? Psychology of Sport and Exercise, 27,
112–119. http://doi.org/10.1016/j.psychsport.2016.08.003
Gutierrez, D., Mulroy, S. J., Newsam, C. J., Gronley, J., & Perry, J. (2005). Effect of Fore-Aft
Seat Position on Shoulder Demands During Wheelchair Propulsion:Part2. An
Electromyographic Analysis. The Journal of Spinal Cord Medicine, 28(3), 222–229.
http://doi.org/10.1080/10790268.2005.11753816
Hamilton, G. R., & Reinschmidt, C. (1997). Optimal trajectory for the basketball free throw.
Journal of Sports Sciences, 15(5), 491–504. http://doi.org/10.1080/026404197367137
Hay, J. G. (1985). The biomechanics of sports techniques (3rd ed.). Prentice-Hall.
Haydon, D. S., & Pinder, R. A. (2020). Current methods for optimising sports wheelchairs at
an individual level (1st ed.). Boca Raton, FL : CRC Press, 2020.: CRC Press.
http://doi.org/10.1201/9781351060073
Haydon, D. S., Pinder, R. A., Grimshaw, P. N., & Robertson, W. S. P. (2018). Test design and
individual analysis in wheelchair rugby. Journal of Science and Medicine in Sport, 21(12),
1262–1267. http://doi.org/10.1016/j.jsams.2018.04.001
Haydon, D. S., Pinder, R. A., Grimshaw, P. N., & Robertson, W. S. P. (2019). Wheelchair Rugby
chair configurations: an individual, Robust design approach. Sports Biomechanics, 1–16.
http://doi.org/10.1080/14763141.2019.1649451
143

Hayes, D. (1987). Body Segment Contributions to Free Throw Shooting in Basketball (p. 7).
Horst, F., Janssen, D., Beckmann, H., & Schöllhorn, W. I. (2020). Can Individual Movement
Characteristics Across Different Throwing Disciplines Be Identified in High-
Performance Decathletes? Frontiers in Psychology, 11, 2262.
http://doi.org/10.3389/fpsyg.2020.02262
Hughes, J., Weimar, W. H., Sheth, P. N., & Brubaker, E. (1992). Biomechanics of Wheelchair
Propulsion as a Function of Seat Position and User-to-Chair Interface, 7.
Kanko, R. M., Laende, E. K., Davis, E. M., Selbie, W. S., & Deluzio, K. J. (2021). Concurrent
assessment of gait kinematics using marker-based and markerless motion capture.
Journal of Biomechanics, 127, 110665. http://doi.org/10.1016/j.jbiomech.2021.110665
Kanko, R. M., Laende, E. K., Strutzenberger, G., Brown, M., Selbie, W. S., DePaul, V., … Deluzio,
K. J. (2021). Assessment of spatiotemporal gait parameters using a deep learning
algorithm-based markerless motion capture system. Journal of Biomechanics, 122,
110414. http://doi.org/10.1016/j.jbiomech.2021.110414
Kanko, R. M., Laende, E., Selbie, W. S., & Deluzio, K. J. (2021). Inter-session repeatability of
markerless motion capture gait kinematics. Journal of Biomechanics, 121, 110422.
http://doi.org/10.1016/j.jbiomech.2021.110422
Le Meur, Y. T. R., & Torres-Ronda, L. (2019). 10 challenges facing today’s applied sport
scientist. Sport Performance & Science Reports, 1(57). Retrieved from
https://sportperfsci.com/10-challenges-facing-todays-applied-sport-scientist/
Liu, B. J. (2019). Performance Tracking: A Multimedia Informatics System to Improve
Decision Support in Movement Analysis. In J. M. Pallis, J. L. McNitt-Gray, & G. K. Hung
(Eds.), (pp. 43–54). Cham: Springer International Publishing.
http://doi.org/10.1007/978-3-030-13467-9_3
Liu, J., Stewart, H., Wiens, C., Mcnitt-Gray, J., & Liu, B. (2022). Development of an integrated
biomechanics informatics system with knowledge discovery and decision support tools
for research of injury prevention and performance enhancement. Computers in Biology
and Medicine, 141, 105062. http://doi.org/10.1016/j.compbiomed.2021.105062
Majaess, G. G., Kirby, R. L., Ackroyd-Stolarz, S. A., & Charlebois, P. B. (1993). Influence of seat
position on the static and dynamic forward and rear stability of occupied wheelchairs.
Archives of Physical Medicine and Rehabilitation, 74(9), 977–982.
http://doi.org/10.5555/uri:pii:000399939390278I
Malone, L. A., Gervais, P. L., & Steadward, R. D. (2002). Shooting mechanics related to player
classification and free throw success in wheelchair basketball. Journal of Rehabilitation
Research and Development, 39(6), 701–709.
Masse, L. C., Lamontagne, M., & O’Riain, M. D. (1992). Biomechanical analysis of wheelchair
propulsion for various seating positions. The Journal of Rehabilitation Research and
Development, 29(3), 12. http://doi.org/10.1682/JRRD.1992.07.0012
144

Mathis, A., Mamidanna, P., Cury, K. M., Abe, T., Murthy, V. N., Mathis, M. W., & Bethge, M.
(2018). DeepLabCut: markerless pose estimation of user-defined body parts with deep
learning. Nature Neuroscience, 21(9), 1281–1289. http://doi.org/10.1038/s41593-018-
0209-y
McNitt-Gray, J., Requejo, P., Flashner, H., & Held, L. (2004). Modeling the musculoskeletal
behavior of gymnasts during landings on gymnastics mats. The Engineering of Sport, 5.
Miller, S., & Bartlett, R. (1996). The relationship between basketball shooting kinematics,
distance and playing position. Journal of Sports Sciences, 14(3), 243–253.
http://doi.org/10.1080/02640419608727708
Miller, S., & Bartlett, R. M. (1993). The effects of increased shooting distance in the
basketball jump shot. Journal of Sports Sciences, 11(4), 285–293.
http://doi.org/10.1080/02640419308729998
Mortimer, E. M. (1951). Basketball Shooting. Research Quarterly. American Association for
Health, Physical Education and Recreation, 22(2), 234–243.
http://doi.org/10.1080/10671188.1951.10761944
Mulroy, S. J., Newsam, C. J., Gutierrez, D., Requejo, P., Gronley, J. K., Lighthall Haubert, L., &
Perry, J. (2005). Effect of Fore-Aft Seat Position on Shoulder Demands During
Wheelchair Propulsion: Part 1. A Kinetic Analysis. The Journal of Spinal Cord Medicine,
28(3), 214–221. http://doi.org/10.1080/10790268.2005.11753815
Munaretto, J. M., McNitt-Gray, J. L., Flashner, H., & Requejo, P. S. (2012). Simulated effect of
reaction force redirection on the upper extremity mechanical demand imposed during
manual wheelchair propulsion. Clinical Biomechanics, 27(3), 255–262.
http://doi.org/10.1016/j.clinbiomech.2011.10.001
Munaretto, J. M., McNitt-Gray, J. L., Flashner, H., & Requejo, P. S. (2013). Reconfiguration of
the upper extremity relative to the pushrim affects load distribution during wheelchair
propulsion. Medical Engineering & Physics, 35(8), 1141–1149.
http://doi.org/10.1016/j.medengphy.2012.12.002
Nakano, N., Fukashiro, S., & Yoshioka, S. (2020). The effect of increased shooting distance
on energy flow in basketball jump shot. Sports Biomechanics, 19(3), 366–381.
http://doi.org/10.1080/14763141.2018.1480728
Nakano, N., Inaba, Y., Fukashiro, S., & Yoshioka, S. (2020). Basketball players minimize the
effect of motor noise by using near-minimum release speed in free-throw shooting.
Human Movement Science, 70, 102583. http://doi.org/10.1016/j.humov.2020.102583
Nath, T., Mathis, A., Chen, A. C., Patel, A., Bethge, M., & Mathis, M. W. (2019). Using
DeepLabCut for 3D markerless pose estimation across species and behaviors. Nature
Protocols, 14(7), 2152–2176. http://doi.org/10.1038/s41596-019-0176-0
145

National spinal cord injury statistical center, facts and figures at a glance. (2019). Retrieved
from https://www.nscisc.uab.edu/Public/Facts%20and%20Figures%202019%20-
%20Final.pdf
Nunome, H., Doyo, W., Sakurai, S., Ikegmai, Y., & Yabe, K. (2002). A kinematic study of the
upper-limb motion of wheelchair basketball shooting in tetraplegic adults. Journal of
Rehabilitation Research and Development, 39(1), 63–71.
Okazaki, V. H. A., & Rodacki, A. L. F. (2012). Increased distance of shooting on basketball
jump shot, 11(2), 231–237.
Okubo, H., & Hubbard, M. (2015). Kinematics of Arm Joint Motions in Basketball Shooting.
Procedia Engineering, 112, 443–448. http://doi.org/10.1016/j.proeng.2015.07.222
Okubo, H., & Hubbard, M. (2016). Comparison of Shooting Arm Motions in Basketball.
Procedia Engineering, 147, 133–138. http://doi.org/10.1016/j.proeng.2016.06.202
Papp, M., Russell, I., Requejo, P. S., Furumasu, J., & McNitt-Gray, J. L. (2019). Reaction Force
Generation and Mechanical Demand Imposed on the Shoulder When Initiating Manual
Wheelchair Propulsion and at Self-Selected Fast Speeds. Journal of Biomechanical
Engineering, 141(12), 124505. http://doi.org/10.1115/1.4045492
Preservation of Upper Limb Function Following Spinal Cord Injury: A Clinical Practice
Guideline for Health-Care Professionals. (2005). The Journal of Spinal Cord Medicine,
28(5), 434–470. http://doi.org/10.1080/10790268.2005.11753844
Requejo, P. S., McNitt-Gray, J. L., & Flashner, H. (2004). Modification of landing conditions at
contact via flight. Biological Cybernetics, 90(5), 327–336.
http://doi.org/10.1007/s00422-004-0473-7
Rojas, F. J., Cepero, M., Ona, A., & Gutierrez, M. (2000). Kinematic adjustments in the
basketball jump shot against an opponent. Ergonomics, 43(10), 1651–1660.
http://doi.org/10.1080/001401300750004069
Russell, Ian M. (2018). Upper Extremity Control and Dynamics during Manual Wheelchair
Propulsion at Different Speeds and Wheelchair Configurations (PhD thesis).
Russell, Ian M., Raina, S., Requejo, P. S., Wilcox, R. R., Mulroy, S., & McNitt-Gray, J. L. (2015).
Modifications in Wheelchair Propulsion Technique with Speed. Frontiers in
Bioengineering and Biotechnology, 3. http://doi.org/10.3389/fbioe.2015.00171
Schwark, B. N., Mackenzie, S. J., & Sprigings, E. J. (2004). Optimizing the Release Conditions
for a Free Throw in Wheelchair Basketball. Journal of Applied Biomechanics, 20(2), 153–
166. http://doi.org/10.1123/jab.20.2.153
Tran, C. M., & Silverberg, L. M. (2008). Optimal release conditions for the free throw in
men’s basketball. Journal of Sports Sciences, 26(11), 1147–1155.
http://doi.org/10.1080/02640410802004948
146

van der Woude, L., Bouw, A., van Wegen, J., van As, H., Veeger, D., & de Groot, S. (2009). Seat
height: Effects on submaximal hand rim wheelchair performance during spinal cord
injury rehabilitation. Journal of Rehabilitation Medicine, 41(3), 143–149.
http://doi.org/10.2340/16501977-0296
van der Woude, L. H., Veeger, D. J., Rozendal, R. H., & Sargean, T. J. (1989). Seat height in
handrim wheelchair propulsion. Journal of Rehabilitation Research and developmentJ
Rehabil Res Dev, 26(4), 31–50.
Verma, S. K. (2019). A Medical Imaging Informatics Based Human Performance Analytics
System (PhD thesis). Retrieved from https://digitallibrary.usc.edu/asset-
management/2A3BF1W2YITO
Vincent, J., Stergiou, P., & Katz, L. (2009). The Role of Databases in Sport Science: Current
Practice and Future Potential. International Journal of Computer Science in Sport, 8, 17.
Wagner, E. (2018). Using nonlinear feedback control to model human landing mechanics.pdf
(PhD thesis). Retrieved from https://doi.org/10.25549/usctheses-c40-472327
Walters, M., Hudson, J., & Bird, M. (1990). Kinematic adjustments in basketball shooting at
three distances.
Wiens, C., & McNitt-Gray, J. L. (2020). The contribution of body center of mass velocity to
basketball ball release velocity across shot distances.
Wilcox, R. (2017). Modern Statistics for the Social and Behavioral Sciences: A Practical
Introduction, Second Edition. CRC Press.
Wilcox, R. R., & Schönbrodt, F. D. (2021). The WRS package for robust statistics in r (version
0.38.1). Retrieved from https://github.com/nicebread/WRS

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Creator Wiens, Casey (author)

Core Title Using biomechanics to understand how an individual accomplishes a task in a variety of contexts

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Degree Conferral Date 2022-12

Publication Date 10/03/2022

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Type texts

Source 20221017-usctheses-batch-986 (), University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright. The original signature page accompanying the original submission of the work to the USC Libraries is retained by the USC Libraries and a copy of it may be obtained by authorized requesters contacting the repository e-mail address given.

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA

Repository Email cisadmin@lib.usc.edu