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Modeling human regulation of momentum while interacting with the environment

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Modeling human regulation of momentum while interacting with the environment

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MODELING HUMAN REGULATION OF MOMENTUM
WHILE INTERACTING WITH THE ENVIRONMENT

by

Joseph Michael Munaretto

______________________________________________________

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
(BIOMEDICAL ENGINEERING)

May 2011

Copyright 2011 Joseph Michael Munaretto
ii
Acknowledgments

I would like to thank my advisor, Jill, for allowing me the flexibility in thought in ideas
and how this research has progressed into multiple projects, for always having time to
meet or talk, and for putting up with my stubbornness. I would like to thank Henryk for
sharing his expertise in modeling and mechanics over the years, and Korkut and
Shashank for putting up with me in the lab for 5 years. And of course I would like to
thank Rachel for being there for support.
iii
Table of Contents
Acknowledgments............................................................................................................... ii

List of Tables .......................................................................................................................v

List of Figures.................................................................................................................... vi

List of Equations............................................................................................................... xv

Abstract........................................................................................................................... xvii

Chapter 1: Introduction…………………………………………………………………..…….…1
Specific Aims and Research Hypotheses.........................................................................5

Chapter 2: Effect of Force Redirection on the Mechanical Demand in Imposed on
Upper Extremity during Manual Wheelchair Propulsion ................................10
Introduction....................................................................................................................10
Methods..........................................................................................................................12
Experimental..............................................................................................................12
Modeling....................................................................................................................13
Results............................................................................................................................18
Discussion......................................................................................................................27

Chapter 3: Sensitivity of Upper Extremity Mechanical Loading to the
Mediolateral Component of the Reaction Force during Manual
Wheelchair Propulsion.....................................................................................33
Introduction....................................................................................................................33
Methods..........................................................................................................................36
Experimental..............................................................................................................36
Modeling....................................................................................................................37
Results............................................................................................................................41
Discussion......................................................................................................................49

Chapter 4: Reconfiguration of the Upper Extremity Relative to the Pushrim
Affects Load Distribution during Wheelchair Propulsion...............................55
Introduction....................................................................................................................55
Methods..........................................................................................................................57
Experimental..............................................................................................................57
Modeling....................................................................................................................58
Results............................................................................................................................64
Discussion......................................................................................................................71

iv
Chapter 5: Effect of Landing Technique on Regulation of Momentum of the
Center of Mass .................................................................................................79
Introduction....................................................................................................................79
Methods..........................................................................................................................84
Overview....................................................................................................................84
Equations of Motion ..................................................................................................84
Experimentation.........................................................................................................86
Model Inputs ..............................................................................................................87
Foot / Surface Model .................................................................................................89
Validation...................................................................................................................90
Modified Simulations.................................................................................................93
Results............................................................................................................................97
Modifications at Contact............................................................................................97
Force Generation at Beginning of PIP .......................................................................98
Impulse Generation....................................................................................................99
Discussion....................................................................................................................104

Chapter 6: Effect of Modified Coordination on Momentum Generation in
Springboard Diving........................................................................................108
Introduction..................................................................................................................108
Methods........................................................................................................................111
Overview of Modeling Approach ............................................................................111
Equations of Motion ................................................................................................112
Experimentation.......................................................................................................114
Inputs........................................................................................................................115
Foot / Surface / Springboard Model.........................................................................115
Validation.................................................................................................................118
Modified Simulations...............................................................................................121
Results..........................................................................................................................126
Discussion....................................................................................................................135

Chapter 7: Summary ........................................................................................................140

Bibliography ....................................................................................................................149

v
List of Tables
Table 1: Kinetic measures (reaction force (RF) orientation, shoulder NJM,
elbow NJM, total NJM, and shoulder NJF) at time of peak RF for two
exemplar subjects across a range of different RF angles (90 =
tangential) for a self-selected graded manual WCP task. ................................19
Table 2: Average positional RMS error between simulated and experimental for
wrist, elbow, and shoulder endpoints...............................................................61
Table 3: Ankle, knee, and hip PD tracking coefficients ................................................89
Table 4: Final visco-elastic surface parameters used in simulation...............................91
Table 5: RMS error between simulated and experimental measures of ground
reaction force, CM velocity, shank and thigh angles, ankle vertical
position, and horizontal center of pressure excursion......................................93
Table 6: Stiffness and damping coefficients for PD controllers at the knee and
hip during modified simulations ......................................................................96
Table 7: Maximum flexor and extensor torques of ankle, knee, and hip used
during open loop simulation ............................................................................96
Table 8: Final visco-elastic surface parameters used in simulation.............................120
Table 9: RMS error between simulated and experimental measures of CM
linear acceleration, CM velocity, CM angular momentum, shank and
thigh angles, and ankle vertical position........................................................121
Table 10: List of diving simulations performed and corresponding results
(Figures 49-55, Table 10) ..............................................................................125
Table 11: CM vertical velocity, CM horizontal velocity, and angular momentum
at departure, and max knee extensor NJM across three knee
coordination strategies. The “straight” strategy reduces vertical and
angular momentum. The “two phase+” strategy increases vertical and
angular momentum, but incurs much higher maximum knee extensor
torque (NJM) since the knee is more flexed and the more horizontal
shank creates a larger moment arm for the reaction force. ............................133

vi
List of Figures
Figure 1: General model of interaction between human and environment........................2
Figure 2: Model development process...............................................................................3
Figure 3: Scope and flow of dissertation ...........................................................................9
Figure 4: Location of Vicon motion markers identified by solid circles. Two
markers on the posterior trunk are not shown in this figure. ...........................13
Figure 5: Joint reaction forces and moments applied to forearm and upper arm
segments...........................................................................................................15
Figure 6: The resultant reaction force direction θ
R
defined relative to the radial
direction at the location of the wrist. To vary over force directions, F
T

is kept constant while F
R
is varied. F
R
is modified to generate θ
R

between 10° and 90° ........................................................................................16
Figure 7: Elbow NJM, shoulder NJM, and total NJM at peak force across range
of RF directions θ
R
for subjects 1 and 2. Free body diagrams at peak
force for two force directions: Case 1: RF orientation more tangential
(red), Case 2: RF orientation more radial (blue). Change in force
direction relative to forearm alters direction and magnitude of elbow
NJM. Change in elbow NJM applied to upper arm plus change in
reaction force relative to upper arm affects direction and magnitude of
shoulder NJM...................................................................................................21
Figure 8: Between subject comparison (S1 vs S2) of joint kinetics (elbow NJM
(a), shoulder NJM (b), total NJM (sum of elbow and shoulder NJM
magnitudes) (c), and resultant shoulder NJF (d)), across time and
reaction force directions (relative to the radial direction passing
through wrist). Black dots indicate where the individual subject
operated in the experimental case. ...................................................................22

vii
Figure 9: Simulation results for subject 2 when keeping torque applied to the
wheel constant throughout the push phase. Mechanical demand
imposed on the upper extremity is represented by elbow NJM,
shoulder NJM, and total NJM and shoulder NJF during the contact
phase. By fixing reaction force magnitudes over time, these figures
give a sense of how potential loading varies between different
kinematic positions. Early in the phase, when the hand is behind TDC,
loading seems to be higher across force directions than later. Minimum
loading tends to occur near the end of the phase when the segments are
more aligned with the tangential direction of the pushrim ..............................25
Figure 10: Comparison of upper extremity joint kinetics early and late push phase.
Reaction force (RF) directions (red = tangential, blue = 30 deg from
radial) relative to the wheel are the same. Elbow is approximately at
the same angle in both cases, but orientation of the UE relative to the
pushrim and RF has changed. Early in the push phase, tangentially
directed force yields similar elbow flexor NJM than the more radially
directed force. Moments created by individual components of the net
joint forces about the upper arm CM tend to be larger in the radial case
which yields a higher shoulder NJM. Late in the push phase, the radial
force (blue) of the NJF contributes to the need for a larger elbow
extensor NJM which opposes the moment by the NJF on the upper
arm. ..................................................................................................................26
Figure 11: Reaction force (RF) at the hand/rim interface and net joint reaction
forces (NJF) and net joint moments (NJM) applied to forearm and
upper arm segments .........................................................................................38
Figure 12: The direction of the projected resultant reaction force (RF, green
vector) in the sagittal plane as applied to the body, θ
R
, is defined
relative to the radial line (dotted) passing through the wrist. The angle
φ defines the direction of the resultant RF relative to the sagittal plane
xy. Simulations involving variation in RF direction maintain the
magnitude of F
T
while varying the magnitude of F
R
and F
ML
. F
R
is
modified to generate θ
R
between 10° and 90° and F
ML
is modified to
generate φ between -30° and 30°. The orientation of the wrist on the
rim relative to the right horizontal passing through the wheel axis is
θ
W.
....................................................................................................................39
Figure 13: Time of peak reaction force expressed as % push phase .................................42

viii
Figure 14: Comparison of mechanical load distribution associated with reaction
force redirection for subject 1 and subject 2. Mechanical load is
expressed as elbow NJM, shoulder NJM, total NJM, and the axial
component of the shoulder NJF (parallel to the long longitudinal axis
of upper arm). Black dots indicate where the subject operated in the
experimental case.............................................................................................43
Figure 15: Frontal plane views of upper extremity segment free body diagrams for
subjects 1 and 2 at time of peak reaction force. Between subject
differences in reaction force/NJF orientation relative to each segment
(Subject 2 forearm is more horizontal and upper arm is more vertical
than those of Subject 1) affect mechanical load distribution across the
elbow and shoulder. Between subject differences in segment
orientation relative to pushrim illustrates how reaction force direction
relative to the segments and the adjacent joint NJM distributes load.
Similar lateral forces (green) across subjects yields larger elbow NJM
in subject 1, while similar medially directed forces (purple) yields
larger elbow NJM in subject 2. Variations in elbow NJM magnitude
and direction also affect magnitude of shoulder NJMs. ..................................44
Figure 16: Representative ML force slices projected onto one graph. Each slice
shows the effect of sagittal force direction on shoulder NJM would be
interpreted if operating at the specific ML force direction..............................46
Figure 17: Subject 1 and 2 elbow, shoulder, and total NJM at peak force across
sagittal force directions at different ML force directions (blue = EXP,
black = - 20 deg, green = 0 deg, cyan = 20 deg) as well as 2D model
distribution (pink). ...........................................................................................47
Figure 18: Simulation of force redirection in SEW plane. ML force direction
varies as a function of sagittal force direction. Plots show a) total NJM
distribution and the path of SEW plane force direction combinations b)
compares total NJM as a function of sagittal force angle between 2D
results and SEW plane results c) elbow NJM and d) shoulder NJM...............48
Figure 19: Coordinates describing position of upper extremity relative to the
pushrim. Simulations varied θ
W
and r
S
and results are reported in
relation joint angle (elbow angle θ
E
) and forearm angle (θ
F
) relative to
radial direction (dotted line passing from axle to wrist). When
modifying shoulder / axle position r
S
, the shoulder / axle angle is kept
constant and the elbow θ
E
and forearm θ
F
angles are constrained in
change (shoulder position translates along the dashed line)............................59

ix
Figure 20: When varying shoulder position and wrist angle, Law of Cosines
allows for calculation of elbow and forearm kinematics.................................60
Figure 21: Experimental (solid) vs simulated (dashed) elbow positional data..................61
Figure 22: The resultant reaction force direction θ
R
defined relative to the radial
direction at the location of the wrist. To vary over force directions, F
T

is kept constant while F
R
is varied. F
R
is modified to generate θ
R

between 20° and 90°.........................................................................................63
Figure 23: Elbow and shoulder NJM as a function of time and sagittal RF angle
θ
R
for experimental (top) vs modified wrist positions on the pushrim
(bottom). RF directions that minimize NJM of each joint change
between cases but also vary as a function of time. Different
combinations of forearm θ
F
and elbow θ
E
configurations at each point
in push phase may alter specific interpretations. Analysis at time of
peak RF is used but specific trends may vary at different points in
time. .................................................................................................................65
Figure 24: Elbow, shoulder, and total NJM and axial shoulder NJF as a function
of RF direction θ
R
and forearm angle θ
F
relative to pushrim at peak
force. Elbow angle θ
E
is kept constant. Effect of RF direction is
dependent on forearm angle. Larger forearm angles shift low moment
areas to more tangential RF directions. Black dot represents
experimental position.......................................................................................67
Figure 25: Elbow, shoulder, and total NJM, and axial shoulder NJF as a function
of RF direction θ
R
and elbow angle θ
E
at peak force. Forearm angle θ
F

relative to pushrim is kept constant. Effect of RF direction is
dependent on elbow angle. Larger elbow angles shift low shoulder
moment areas to more tangential RF directions. Black dot represents
experimental position.......................................................................................69
Figure 26: Total NJM at peak force as a function of forearm θ
F
and elbow θ
E

angles, under no constraint (top left) and a theoretical friction
constraint (top right). Relationship between shoulder distance r
S
(bottom left) & wrist angle θ
W
(bottom right) relative to forearm and
elbow angles are also illustrated ......................................................................71
Figure 27: Phases of Landing ............................................................................................80
Figure 28: Multi segment rigid body model including foot, forefoot, shank, thigh,
torso, arm, and head segments .........................................................................85
Figure 29: Visco-elastic model of foot/surface interaction................................................90
x
Figure 30: Match between simulated and measured reaction forces for normal
landing..............................................................................................................93
Figure 31: Tracking PD control was used in flight, standard PD control used
during impact phase, and open loop torques used during post impact
phase ................................................................................................................94
Figure 32: Flow Diagram depicting all potential simulation modifications. In
flight, initial orientation of the whole body (q3(0) ) may be altered 1
deg back or 2 deg forward. At the beginning of the impact phase, knee
and hip joint angles may be flexed / extended +/- 15 deg to create
softer and more rigid landings. Finally, open loop ankle / knee / hip
torques are varied to examine potential scenarios of impulse
generation.........................................................................................................95
Figure 33: Peak vertical force (Fy) and change in vertical velocity during the IP vs
amount of leg extension at contact. More flexed positions reduce
whole body rigidity and consequently lower the magnitude of the peak
vertical force during impact and the amount of reduction in downward
velocity of the center of mass during the IP. ...................................................98
Figure 34: Potential ground reaction force functional force space (FFS, green)
reflecting all possible force magnitudes and directions derived from all
ankle/knee/hip torque combinations for each landing condition (blue
segments) at 80 ms into the PIP. Segment configuration and velocities
were found to affect the ability to generate the reaction force
magnitude, direction, and the moment about the CM......................................99
Figure 35: Potential impulse generation after 80 ms, 160 ms, and 240 ms into PIP
for three land-and-stop tasks (8º less flexed (top graph), normal
(middle), and 8º more flexed (bottom)). Horizontal, vertical, and
angular impulse generation are described by changes in CM velocities
when scaled by bodyweight / inertia. The more upright segment
configuration at the beginning of the PIP (top, blue segment
configuration) can produce more impulse in a shorter time span,
whereas the more flexed position (bottom) can generate more impulse
with a longer time span. Changes in angular momentum during this
type of land-and-stop task are more dependent on the potential to
generate horizontal impulse than on vertical impulse....................................100

xi
Figure 36: Knee, hip, and ankle torques and change in angular momentum vs
change in CM horizontal and vertical velocity after 160 ms in PIP.
Extensor torques generate the largest combination of horizontal and
vertical changes in CM velocity. Positive angular momentum
generation is associated with reaction forces directed anterior to the
CM via less knee extensor torque, while negative angular momentum
is associated with forces directed posterior to the CM via less hip
extensor torque...............................................................................................101
Figure 37: Feasible combinations of absolute velocities after 80 ms, 120 ms, and
160 ms into PIP for three landings (8º less flexion, normal, 8º more
flexion) with a 2 degree forward tip. The forward tip shifts CM
horizontal velocity from 0 to 0.2 m/s, which must be reduced to zero in
addition to reducing vertical velocity to zero and keeping angular
momentum low. While all three configurations can reduce horizontal
velocity after 120 ms, the more flexion landing cannot yet reduce
vertical velocity to zero. After 160 ms, all three cases have reduced
linear momentum to zero. The direction of impulse generation
(arrows) needed to reduce moment changes across landing styles................103
Figure 38: Sum of absolute knee + hip torques at all feasible combinations of
horizontal and vertical velocity at 160 ms in PIP for three landings (8º
less flexion, normal, 8º more flexion). Line indicates zero vertical
velocity. In order to reduce vertical velocity at 160 ms, landings with
greater joint flexion have to use increasingly higher levels of knee and
hip torque. ......................................................................................................104
Figure 39: The take-off phase of a forward somersault performed from a
springboard. The diver initiates board contact (A) following the
hurdle with forward CM horizontal velocity and downward CM
vertical velocity. During board depression phase (B), the diver extends
the knee and hip to depress the board while maintaining CM over the
base of support (balance). During board recoil (C), the diver moves
upward while redirecting the reaction force (RF) posterior to the CM
to generate forward angular impulse required for successful
performance of a forward somersault dive. ...................................................110
Figure 40: Diagram of human model represented with generalized coordinates q
1
-
q
8.
....................................................................................................................113
Figure 41: Visco-elastic model of foot / springboard interaction....................................117

xii
Figure 42: Model of springboard uses a nonlinear torsion spring along with an
effective length that is shorter than the actual length of the
springboard. The effective length is shorter than the actual springboard
length to ensure that the orientation of the end of the rigid link is
representative of the end of the actual springboard that behaves more
nonlinearly. ....................................................................................................118
Figure 43: Model simulated and measured CM horizontal and vertical
accelerations...................................................................................................120
Figure 44: Model simulated and measured moment of the reaction force about the
CM. ................................................................................................................120
Figure 45: Exemplar modification in hip angle to simulate a deeper squat at
contact. Spline node of the experimental hip angle at minimum flexion
angle (~ at board contact) is shifted a desired number of degrees. From
a set point in flight until contact, the experimental curve is scaled to
reach the new minimum point. Similar scaling is then performed from
contact until the next node point at maximum hip flexion, which
occurs after the board begins to recoil. This method maps to SIM3
where minimum hip and knee angles decrease but orientation at time
of max hip flexion are the same as measured experimentally. For
SIM4, this node is shifted downwards an equal amount to the node at
contact to maintain the same angle excursion................................................123
Figure 46: Temporal relationship between board displacement and knee and hip
angular motion. Time of maximum hip angle (and time of pause in
knee extension) occurs slightly after the beginning of board recoil. .............123
Figure 47: Modification in knee and hip joint angle excursions during the board
recoil phase. Spline nodes located just after departure (max knee
angle) are varied and curves are scaled between here and time of
maximum hip angle........................................................................................124
Figure 48: Modification in knee angle coordination during contact with the
springboard. The subject extends the knee partially, pauses, then
continues to extend the knee as the board is recoiling. The “two phase”
modification (dotted line) simulates less initial extension followed by
rapid extension during recoil. The “straight” modification (open
circles) assumes the rate of knee extension is constant with time until
departure. .......................................................................................................125

xiii
Figure 49: Effect of change in initial shank orientation (SIM1) on changes in
maximum CM vertical velocity (A), CM horizontal velocity (B), and
angular momentum (C). Increasing forward tipping of the shank
decreases CM vertical velocity at departure but increases the other two
measures.........................................................................................................126
Figure 50: Effect of change in initial CM vertical velocity of the CM (SIM2) on
changes in maximum knee extensor NJM (top left), hip extensor NJM,
board depression (top right), CM vertical velocity (bottom left), CM
horizontal velocity, and angular momentum (bottom right). Increasing
downward CM velocity at contact increases all measures.............................127
Figure 51: Changes in board displacement, CM horizontal velocity, and CM
orientation at time of maximum board displacement with variations in
squat depth (SIM3). Increase in squat depth increases board
displacement, but reduces CM horizontal velocity and CM angle. The
latter two contribute to a forward tip of the CM, redirection of the
reaction force and generation of angular impulse in the BR phase. ..............128
Figure 52: Changes in board displacement, CM horizontal velocity, and CM
orientation at time of max board displacement. Increase in squat depth
(SIM4) increases board displacement, but reduces CM horizontal
velocity and CM angle. The latter two contribute to a forward tip of
the CM, redirection of the reaction force and generation of angular
impulse in the BR phase. ...............................................................................129
Figure 53: Effect of squat depth (SIM3) on kinematics and kinetics. X axis CM
horizontal velocity at departure, Y axis is CM vertical velocity at
departure. Plots show angular momentum at departure (A), minimum
knee angle (B), minimum hip angle (C), maximum knee extensor NJM
(D), maximum hip extensor NJM (E), and illustration of hip angle
modification to achieve deeper squat (F). Knee angle is modified in a
similar manner ...............................................................................................130
Figure 54: Effect of altering knee and hip angles at departure (SIM5) on pertinent
kinematics and kinetics. X axis CM horizontal velocity at departure, Y
axis is CM vertical velocity at departure. Plots show angular
momentum at departure (A), maximum knee angle (B), minimum hip
angle (C), maximum knee extensor NJM (D), maximum hip flexor
NJM (E), and illustration of hip angle modification to more hip flexion
(F)...................................................................................................................132

xiv
Figure 55: Effect of squat type on angular impulse, maximum knee angle, and
CM angle relative to the springboard at maximum board depression.
Both SIM7 (full extension) and SIM8 (partial extension) generate
more vertical impulse but less horizontal and angular impulse than the
normal squat (SIM5). Modified BR phase coordination can improve
angular impulse in all three. The more flexed configuration of SIM8
does not increase angular impulse relative to the other two conditions
although maximum knee angle achieved is similar (i.e. had larger knee
extension). SIM8 had the smallest CM angle at maximum board
depression making it more difficult to redirect the reaction force
posterior to the CM to generate forward angular impulse. ............................134

xv
List of Equations
Equation 1 ..........................................................................................................................14
Equation 2 ..........................................................................................................................14
Equation 3 ..........................................................................................................................16
Equation 4 ..........................................................................................................................16
Equation 5 ..........................................................................................................................17
Equation 6 ..........................................................................................................................17
Equation 7 ..........................................................................................................................17
Equation 8 ..........................................................................................................................37
Equation 9 ..........................................................................................................................37
Equation 10 ........................................................................................................................39
Equation 11 ........................................................................................................................39
Equation 12 ........................................................................................................................40
Equation 13 ........................................................................................................................40
Equation 14 ........................................................................................................................41
Equation 15 ........................................................................................................................60
Equation 16 ........................................................................................................................85
Equation 17 ........................................................................................................................88
Equation 18 ........................................................................................................................90
Equation 19: Generic cost function used to optimize foot – surface parameters
while minimizing error between chosen simulated and experimental
measures........................................................................................................91
Equation 20 ........................................................................................................................92
Equation 21 ........................................................................................................................96
xvi
Equation 22 ........................................................................................................................96
Equation 23 ......................................................................................................................113
Equation 24 ......................................................................................................................116
Equation 25 ......................................................................................................................117
Equation 26: Generic cost function used to optimize springboard parameters while
minimizing error between chosen simulated and experimental
measures......................................................................................................118
Equation 27 ......................................................................................................................119

xvii
Abstract
Many activities of daily life require continual interaction with the environment.
Improving understanding of how humans control interaction forces during goal-directed
tasks may aid in improving performance and reducing injury risk. Modeling allows us to
explore causal mechanisms and test hypotheses regarding control and dynamics of human
movement. In this thesis, experimentally validated dynamic models were used to study
how modifications in control affect performance and mechanical loading in different
contexts including wheelchair propulsion, landings, and springboard diving. In both 2D
and 3D models of wheelchair propulsion, redirection of the reaction force (RF) was found
to be an effective mechanism for redistributing load across the elbow and shoulder
without decrements in task performance. How RF affects load distribution was found to
be subject specific and dependent on time in push cycle and the configuration of the user
in the wheelchair. In land-and-stop tasks, increases in knee and hip joint flexion at contact
reduced peak impact force and impulse generated during the impact phase, increased
ability to generate impulse during the post impact phase (PIP), and increased either the
mechanical demand or time required to reduce CM momentum to zero during PIP.
Simulations of a forward somersault dive performed on a springboard revealed that
increasing forward tip of the body during flight decreased CM vertical velocity but
increased CM horizontal velocity and angular momentum at departure. Increase in
downward CM velocity at board contact increased all momenta at departure. Increased
squat depth at contact increased vertical velocity but decrease horizontal velocity and
angular momentum of the CM at departure. Increasing hip flexion and knee extension
xviii
excursions during board recoil increased angular impulse generation at departure.
Overall, we found that there exists multiple ways to achieve the mechanical objectives of
each task. Results show that modifications in strategy include regulation of RF and
segment kinematics of the upper / lower extremities, which alter the magnitude and
distribution of mechanical demand experienced. Subject specific, experimentally
validated models provide knowledge that may aid making decisions to improve
performance and reduce risk of injury in both clinical and athletic environments.
1
Chapter 1: Introduction

Research Focus
Many activities of daily living (ADL) involve ongoing interaction with the environment.
Successful performance of ADL requires satisfying task specific objectives without
injury. Task objectives often include multiple and often competing objectives at the whole
body and joint levels. Satisfying the mechanical objectives of the task often occurs over a
series of movement phases. For example, during high speed interaction with the
environment, large reaction forces are applied to the body at the point of contact. The
magnitude of the reaction forces are dependent on the initial conditions at contact (e.g.
total body momentum, endpoint velocity, and muscle activation prior to contact). If these
forces are not adequately controlled they may exceed the critical limits of bone or soft
tissues resulting in an acute injury. Understanding how individuals organize their
resources and regulate reaction forces during goal directed tasks is important in learning
how to better improve performance and reduce injury risk. The focus of this research is
to determine how humans regulate reaction forces and satisfy the mechanical objectives
of the task during contact with the environment.

Experimentally-based Modeling Approach
Human movement reflects the continual interaction between the nervous system, the
musculoskeletal system, and the environment (Figure 1). Simulations using
experimentally-validated dynamic models of the human body allow us to manipulate
individual variables that cannot be independently modified experimentally. In this series
2
of studies, hypotheses related to control and dynamics of goal directed movements will
be tested using experimentally validated dynamic models of the human body of sufficient
complexity to capture salient features of multijoint control and system dynamics
including tasks involving impact with the environment (large transient forces experienced
immediately after contact).

Figure 1: General model of interaction between human and environment
Understanding how an individual selectively distributes load within the musculoskeletal
system during goal directed tasks provides valuable insight regarding control logic and
dynamics at the whole body and segment levels. In addition, identification of
mechanisms individuals use to prepare for contact, distribute load within the
musculoskeletal system, and control total momentum in ways that satisfy task objectives
will enhance our ability to identify effective control strategies for regulating momentum
that reduce the risk of injury.
The process of model development, validation, and simulation incorporated in this body
of work is outlined in Figure 2. First, experiments were performed to determine the range
3
of control strategies individuals use to satisfy task objectives. Based on these
experimental results, model complexity was determined. The number of segments, 2D or
3D, and number of degrees of freedom should be chosen as to make the model as simple
as possible with sufficient complexity to test relevant research questions. Once the
dynamic model was created, the model validation was assessed by determining the
agreement between simulation results and experimental data. Refinement of model
complexity was pursued until agreement between simulation results and experimental
data was within observed trial-to-trial variability of comparable tasks performed by the
same individual.

Figure 2: Model development process.

Once a model of sufficient complexity was developed and validated, the model
incorporated experimental results to simulate modifications in control logic and system
4
dynamics during three different types of tasks: manual wheel chair propulsion by
individuals with spinal cord injures (involving hand/rim interaction using a rotating
instrumented wheel), landing performed by a recreational athlete (involving foot-first
interaction with a rigid surface (force plate), and take-off of a front somersault performed
by national level diver (involving first-foot interaction with a compliant surface (diving
springboard).
Wheelchair propulsion study was broken down into three parts, each with increasing
model complexity. The first study (Chapter 2) uses a 2D inverse dynamic model to
investigate the effects of sagittal plane force redirection on mechanical load distribution
across the shoulder and elbow. In chapter 2, 2D kinematics projected into the sagittal
plane and force direction was varied by modifying the radial force component. In chapter
3, 3D kinematics were used and 3D force direction was varied by modifying the radial
and mediolateral force components. In chapter 4, additional assumptions were added to
accommodate for modifications to the kinematic configuration of the forearm and upper
arm over time. This is done by assuming the shoulder is static and the wrist exactly
follows the curvature of the pushrim. Validation occurs by comparing measured vs
simulated wrist positions. Then the location of the wrist is allowed to shift, and upper
extremity kinematics are recalculated. Inverse dynamics as in chapter 2 is then applied
across different segment configurations.
Forward (torque driven) or inverse dynamic (motion driven) models were explored as
means for testing hypotheses about the control and dynamics of these types of tasks.
5
Costs and benefits were determined for each approach. If movement modification can be
made with a sufficient level of precision, motion driven modeling will likely behave
better than torque driven models (Gittoes et al., 2006, Wilson et al., 2006). Simulated
whole body motion can be unstable when driven by joint torques, so testing of
hypotheses regarding control logic or those involving optimization of movement patterns
were facilitated by using inverse dynamic simulations. While forward dynamics might be
inherently less stable, the torque driven approach was used to study how torques
combinations across multiple joints affect body accelerations. The modeling approach for
the landing and diving simulations used whole body dynamic models, while the manual
wheelchair propulsion simulations used a two segment dynamic model of the upper
extremity. The mechanical demand imposed on the musculoskeletal system was assessed
using joint torques and forces (net joint moments (NJM) and net joint forces (NJF) as
calculated using inverse dynamics). The rationale for each experiment and hypotheses to
be tested is provided in the background sections and introduction of each chapter.
Specific Aims and Research Hypotheses
The following are the specific aims and research hypotheses tested in each study. Each
study is presented as a stand alone chapter in a form consistent with a manuscript
submission to peer-reviewed journal and is comprised of introduction, methods, results,
and discussion sections.

6
Hand-first interaction with a rotating surface in the context of manual wheelchair
propulsion (WCP) as performed by individuals with spinal cord injury.
1. Determine the effect of reaction force (RF) redirection on the mechanical demand
imposed on the upper extremity in wheelchair propulsion using a 2D model
(Chapter 2)
a. Force redirection was hypothesized to affect net joint moment (NJM) and
net joint force (NJF) distribution between the shoulder and elbow joints
when performing the same graded manual wheelchair propulsion task.
b. Loading distribution was hypothesized to be subject specific and vary with
time during the contact phase.

2. Determine the sensitivity of UE mechanical loading to 3D rim RF redirection
during WCP in a graded task. The effect of increased model complexity
(incorporation of 3D reaction force and kinematics) was hypothesized to influence
the identification of strategies for distributing mechanical loading imposed on the
upper extremity (Chapter 3)
a. Inclusion of mediolateral (ML) forces (out of plane) was hypothesized to
alter the distribution of NJM and the NJF across the upper extremity
segments when using 3D kinematics

7
3. Determine how upper extremity segment configuration relative to the wheelchair
affects the distribution of mechanical demand across the upper extremity during
manual wheel chair propulsion (Chapter 4)
a. Altering the distance between the shoulder and the pushrim will change
the reaction force directions that minimize mechanical loading (NJM
shoulder, NJM elbow, NJF shoulder)
b. Changing the position of the wrist / hand on the pushrim will alter
direction of forces that minimize mechanical loading

Foot-first interaction with a rigid surface (force plate) in the context of a land-and-
stop task performed by a recreational athlete (Chapter 5)
4. Determine the effect of different experimentally observed landing strategies on
ability to regulate reaction force and momentum of the CM (mechanical
objective: reduce total body momentum at initial contact to zero at a time when
the whole body center of mass (CM) is over the base of support).
a. Changes in flight phase segment configurations at contact were
hypothesized to affect peak vertical force magnitude and the amount of
momentum reduced during the impact phase (IP)
b. Changes in flight phase segment kinematics at contact were hypothesized
to affect ability to generate force and impulse during the post impact phase
(PIP)
8
c. Change in flight phase segment configurations at contact were
hypothesized to affect mechanical demand (NJM) and ability to satisfy the
mechanical objectives of the task.

Foot-first interaction with a deformable energy-returning surface in the context of
forward somersault performed from a springboard by a national level diver
(Chapter 6)
5. Determine how modifications in multijoint coordination during the flight and
contact phases affect the ability to regulate reaction force relative to the CM.
a. Increasing initial body tip forward (CM relative to feet) is hypothesized to
reduce vertical velocity but increase angular momentum at departure
b. Larger downward CM vertical velocity and deeper squat positions at
initial board contact are hypothesized to result in greater board depression,
higher vertical velocities at board departure, and greater mechanical
demand imposed on muscles controlling knee and hip (NJM)
c. Utilization of residual lower extremity joint extension during board recoil
was hypothesized to increase the diver’s ability to redirect the reaction
force posterior to the CM thereby contributing to additional forward
angular momentum at board departure

9

Regulation of Momentum during
Human Interaction with Environment
Maintaining Linear
Momentum:
Wheelchair Propulsion
Effect of Force Redirection
on Mechanical Demand
Imposed on the Upper
Extremity during Manual
Wheelchair Propulsion
Chapter 2
Reconfiguration of the
Upper Extremity
Relative to the Pushrim
Affects Load
Distribution during
Wheelchair Propulsion
Chapter 4
Effect of Modified
Coordination on
Momentum Generation
in Springboard Diving
Chapter 6
Generating Linear and
Angular Momentum w/
Energy Returning System:
Dive Take-off
Reducing Linear and
Angular Momentum:
Land and Stop
Effect of Landing
Technique on
Regulation of Momentum
of the Center of Mass
Chapter 5
Sensitvity of Upper
Extremity Mechanical
Loading to the Mediolateral
Component of the Reaction
Force during Manual
Wheelchair Propulsion
Chapter 3
Regulation of Momentum during
Human Interaction with Environment
Maintaining Linear
Momentum:
Wheelchair Propulsion
Effect of Force Redirection
on Mechanical Demand
Imposed on the Upper
Extremity during Manual
Wheelchair Propulsion
Chapter 2
Reconfiguration of the
Upper Extremity
Relative to the Pushrim
Affects Load
Distribution during
Wheelchair Propulsion
Chapter 4
Effect of Modified
Coordination on
Momentum Generation
in Springboard Diving
Chapter 6
Generating Linear and
Angular Momentum w/
Energy Returning System:
Dive Take-off
Reducing Linear and
Angular Momentum:
Land and Stop
Effect of Landing
Technique on
Regulation of Momentum
of the Center of Mass
Chapter 5
Sensitvity of Upper
Extremity Mechanical
Loading to the Mediolateral
Component of the Reaction
Force during Manual
Wheelchair Propulsion
Chapter 3

Figure 3: Scope and flow of dissertation

10
Chapter 2: Effect of Force Redirection on the Mechanical
Demand in Imposed on Upper Extremity during Manual
Wheelchair Propulsion

Introduction
Manual wheelchair propulsion (WCP) is an effective form of wheeled mobility for
individuals with spinal cord or lower extremity injuries as it preserves independence and
participation in the community. Use of a manual wheelchair also preserves upper
extremity strength and embeds cardiovascular conditioning as part of activities of daily
life, in contrast to more costly powered wheelchairs. Manual propulsion of the user / WC
system requires sufficient tangential force applied at the hand/rim interface over a give
time to accelerate the mass and regulate the momentum of the total system (Boninger et
al., 1997). The repetitive nature of manual WCP exposes the upper extremity (UE) to
repetitive loading. The mechanical loading experienced during WCP can lead to acute
and overuse shoulder injuries that contribute to a loss of independence and a decrease in
quality of life (Ballinger et al., 2000, Mercer et al., 2006, Subbarao et al., 1995).
Experimental results indicate that there is more than one solution to satisfy the
mechanical objective of this propulsion task (Veeger et al., 1989, Masse et al., 1992, van
der Woude et al., 2001). Knowledge of the advantages and disadvantages of specific
WCP techniques is expected to assist clinicians in make decisions regarding
interventions.

11
Improvement in the interaction between the user and wheelchair during WCP is needed to
maintain performance without increasing the risk of injury. Maintaining the tangential
component of the rim force while redirecting the resultant force may provide a means for
redistribution of mechanical loading across the upper extremity without a decrement in
WCP task performance. Previous research with goal-directed tasks has found that
alteration of reaction force relative to segment orientation redistributes load across joints
(Mathiyakom et al., 2005, McNitt-Gray et al., 2001).
Proposed modifications in load distribution must consider an individual’s capacity to
generate force. Preservation of segment and joint kinematics while redirecting force
allows for WC users to coordinate and generate force at their preferred muscle lengths
and velocities. Since different subjects have various upper extremity segment properties
and are positioned differently in the wheelchair, observing inter-subject differences in
load distributions allows for potential decisions in technique modification to be subject-
specific. Simulations using an experimentally motivated dynamic multilink model can
explore causal relationships between force direction and load by preserving subject
specific kinematics and performance. Allowing only for radial force magnitude to change
yields results on potential load redistribution that are specific to each subject.
In this study, our aim was to determine the effect of reaction force redirection on the
mechanical demand imposed on the upper extremity in wheelchair propulsion using a 2D
model. Force redirection was hypothesized to affect net joint moments (NJM) and net
joint force (NJF) distribution between the shoulder and elbow joints when performing the
12
same manual wheelchair propulsion task. Loading distribution was hypothesized to be
subject specific and vary with time during the contact phase. To test these hypotheses,
force direction and magnitude were altered by changing the radial component of the
reaction force while experimental tangential force and WC user kinematics were
maintained. A 2D inverse dynamic model was used to determine NJM of the elbow and
shoulder as well as NJF of the shoulder. Solution spaces created through model
simulations provide a basis for assisting clinicians in identifying mechanical loading
implications of systematic variations in WCP technique specific to force direction, body
segment configuration, and key events in the propulsion phase. Knowledge of loading
consequences of specific WCP techniques is expected to aid clinicians prospectively plan
and implement effective rehabilitation interventions that aim to preserve UE function.

Methods
Experimental
Two wheelchair users with spinal cord injury (SCI) volunteered to participate in this
study in accordance with the Institutional Review Board at the Ranchos Los Amigos
National Rehabilitation Center, Downey, CA. The subjects performed wheelchair
propulsions on an ergometer providing resistance simulating movement up a graded slope
for 10 seconds. Reflective markers were used to monitor the 3D motion of the hand,
forearm, upper arm, and trunk segments. Three markers were also placed on the right
wheel to track wheel rotation (VICON, 50 Hz, Figure 4). Coordinates were rotated into a
(x,y,z) reference frame where x represented anterior/posterior position, y represented
13
superior / inferior position, and z represented mediolateral position. The sagittal plane xy
is oriented in global space to symmetrically bisect the user. The force applied to the
wheelchair during propulsion was measured using force transducers (SmartWheel 2500
Hz) in the radial, tangential, and mediolateral directions of the wheel. Force and
kinematics were then projected into the sagittal plane for use in the 2D model.

Figure 4: Location of Vicon motion markers identified by solid circles. Two markers on the posterior trunk are
not shown in this figure.
Modeling
The equations of motion used follow the generalized Newton-Euler ‘up the chain’ inverse
dynamics method. For both segments starting with the forearm:

14

-
-
x xCM
xP xCM xD
yP yCM yD
F ma
R ma R
R ma mg R
=
=
= +
∑

Equation 1

( ) ( ) ( ) ( ) - - . - . - . - - . -
z zCM zCM
zP zCM zCM zD xP P CoM yP CoM P xD CoM D yD D CoM
M = I
M I M R y y R x x R y y R x x
α
α = + +
∑

Equation 2

m = segment mass
xCM
a = segment acceleration in x direction
xP
R = reaction force acting on the proximal end of segment in x direction
yD
R = reaction force acting on the distal end of segment in the y direction
g = gravity constant
zCM
I = CM inertia about the z-axis
zCM
α = CM angular acceleration about the z-axis
zP
M = moment acting on the distal end of the segment about the z-axis
P
y = location of the proximal segment end in the y-direction
CoM
y = location of the segment CM in the y-direction

Starting with the reaction force acting at the wrist, the reaction forces at the elbow are
calculated, followed by the net joint moment at the elbow. These values are then applied
to the upper arm segment to calculate kinetics at the shoulder joint (Figure 5).

15

Figure 5: Joint reaction forces and moments applied to forearm and upper arm segments

Modifications in Force Direction
Radial forces do not directly contribute to torque generation about the wheel axis, and
can be varied as long as the tangential force is fixed (Figure 6).
16

Figure 6: The resultant reaction force direction θ
R
defined relative to the radial direction at the location of the
wrist. To vary over force directions, F
T
is kept constant while F
R
is varied. F
R
is modified to generate θ
R
between
10° ° ° ° and 90° ° ° °

The location of the wrist/pushrim reaction force is the same as the wrist angle and
calculated as
1
tan
W
W
W
y
x
θ
−
 
=
 
 

Equation 3
where x
w
and y
w
are the Cartesian coordinates of the wrist. The tangential force applied to
the wheel was calculated as
( ) ( ) cos ( ) ( )sin ( )
T y W x W
F t F t t F t t θ θ = −
Equation 4

θ
W

θ
R

F
T

F
R

17
where F
X
and F
Y
are the components of the reaction force in the global frame acting on
the wheel. The direction of the force acting on the WC user in the sagittal plane of the
global reference frame, θ
G
can be described as
G W R
θ θ θ = +

Equation 5

where θ
R
is the reaction force direction relative to the radial direction at the wrist /
pushrim interface. θ
G
, was allowed to vary to generate θ
R
between 10° and 90°. The angle
describing the medial-lateral component of the force, φ (toward body is positive), was set
to 0 for this study. At each instant in time, the resultant force magnitude needed to
generate the measured tangential force
( )
( )
sin( ( ) ) cos( )
T
mag
W G
F t
F t
t θ θ φ
=
− ×

Equation 6
From the computed resultant force and direction, [Fx Fy] components were computed for
each force (θ
G
) during simulation. For each force angle, inverse dynamics was performed
to determine NJM for the elbow and shoulder and the axial component of the shoulder
NJF. In addition, the sum of the magnitude of net joint moments (total NJM) at the elbow
and shoulder was computed.
| | | |
E S
J τ τ = +
Equation 7

18
Results
Reaction force (RF) direction was found to affect NJM and net joint force (NJF)
distribution between the shoulder and elbow joints when performing the same manual
wheelchair propulsion task. Load distribution was found to be subject specific and vary
with time during the contact phase. At the time of peak force, redirection of the RF at the
hand / pushrim interface resulted in subject-specific changes mechanical loading of the
upper extremity at peak force (Table 1, Figure 7). In general, NJM and NJF values were
highest in when the RF angle is small (radial direction). The NJM and NJFs then
decreased as is the RF angle increased and increased again when approaching RF angles
of 90º. In general, minimal elbow and shoulder NJM occur at different RF angles (Figure
7). For example, at the time of peak force, the minimum elbow NJM occurred when the
RF was at 90º and the minimum shoulder NJM occurred when the RF was at 53º for
subject 1. At very high and low RF angles, elbow and shoulder NJMs increase or
decrease together. When the RF is directed between these radial and tangential extremes,
there is a tradeoff between the magnitude and direction of the elbow and shoulder NJMs.
These trends are subject-specific. For example, the minimum elbow NJM occurred when
the RF was at 61º for subject 2 compared to 90º for subject 1 (Figure 7).

19
Tangential Force (N)
Push Phase % (0-1)
Tangential Force (N)
Push Phase % (0-1)
Force
Direction
Relative to
Radial (deg)
S1 S2 S1 S2 S1 S2 S1 S2 S1 S2
10 205.80 116.29 213.89 92.92 419.69 209.21 715.97 553.15 73.97 80.77
20 98.72 48.30 86.06 24.48 184.78 72.78 353.31 271.93 83.83 91.12
30 61.53 24.69 41.67 1.15 103.20 25.84 234.91 180.71 94.26 102.14
40 41.74 12.13 18.05 12.00 59.79 24.14 178.31 137.65 105.28 113.72
50 28.82 3.97 2.65 20.24 31.48 24.21 147.13 114.42 116.76 125.67
60 19.24 2.25 8.82 26.37 28.06 28.62 129.35 101.61 128.51 137.68
70 11.42 7.16 18.15 31.36 29.57 38.52 119.88 95.22 140.27 149.44
80 4.55 11.51 26.35 35.75 30.90 47.26 116.28 93.27 151.77 160.71
90 1.92 15.61 34.06 39.88 35.98 55.48 117.32 94.78 162.80 171.33
Angle Relative
to Humerus
(deg) Total NJM (Nm) Elbow NJM (Nm)
Shoulder NJM
(Nm)
Shoulder
Resultant NJF
(N)

Table 1: Kinetic measures (reaction force (RF) orientation, shoulder NJM, elbow NJM, total NJM, and shoulder
NJF) at time of peak RF for two exemplar subjects across a range of different RF angles (90 = tangential) for a
self-selected graded manual WCP task.

Loading of the upper extremity is altered because change in RF direction alters the
magnitude of the RF and moment arms relative to the forearm and upper arm (FBDs in
Figure 7). For example, in Case 1, the RF and elbow NJF acts to rotate the forearm
clockwise therefore requiring an elbow flexor NJM. In Case 2, the RF and elbow NJF
20
acts to rotate the forearm counterclockwise therefore requiring an elbow extensor NJM.
In Case 1, the elbow flexor NJM and the elbow and shoulder NJFs work together to
rotate the upper arm clockwise requiring a shoulder flexor NJM. In Case 2, the elbow and
shoulder NJFs are larger but more aligned with the upper arm to produce a small
clockwise moment while the elbow extensor NJM acts to rotate the upper arm counter-
clockwise. Thus a shoulder extensor NJM is needed.
Subject specific differences in the effect of r x RF are dependent on the orientation of the
UE relative to the pushrim at peak force. While at similar elbow flexion angles, the
direction of the shoulder / wrist vector (SW) is more tangential in subject 1 than subject
2. A tangentially directed force acting on subject 1 acts less posteriorly on the forearm
than it does in subject 2. A 30º RF acts more anteriorly on subject 1 than subject 2. This
changes the moment arm relative to the forearm and upper arm between the two subjects
and explains why the loading distribution changes between subjects.

21

Figure 7: Elbow NJM, shoulder NJM, and total NJM at peak force across range of RF directions θ
R
for subjects
1 and 2. Free body diagrams at peak force for two force directions: Case 1: RF orientation more tangential
(red), Case 2: RF orientation more radial (blue). Change in force direction relative to forearm alters direction
and magnitude of elbow NJM. Change in elbow NJM applied to upper arm plus change in reaction force
relative to upper arm affects direction and magnitude of shoulder NJM

The pattern of change in mechanical distribution due to force redirection is affected by
position on pushrim. From the middle to end of the push phase there is a clear trend in
location of minimum NJM values shifting from more radial RF to more tangential RF
directions (Figure 8). Locations of minimum NJM for subject 1 are found at more
tangential RF directions than subject 2 across time. Mechanical demand is lower in the
beginning and end than middle of the push phase since less propulsive force is generated.
22
S1
S2
θ
R
θ
R
Elbow NJM (Nm) Elbow NJM (Nm)
Shoulder NJM (Nm)
Shoulder NJM (Nm)
Total NJM (Nm)
Total NJM (Nm)
Axial Shoulder NJF (N)
Axial Shoulder NJF (N)
Time (s) Time (s)
Sagittal Force Angle (deg) Sagittal Force Angle (deg) Sagittal Force Angle (deg) Sagittal Force Angle (deg)
S1
S2
θ
R
θ
R
Elbow NJM (Nm) Elbow NJM (Nm)
Shoulder NJM (Nm)
Shoulder NJM (Nm)
Total NJM (Nm)
Total NJM (Nm)
Axial Shoulder NJF (N)
Axial Shoulder NJF (N)
Time (s) Time (s)
Sagittal Force Angle (deg) Sagittal Force Angle (deg) Sagittal Force Angle (deg) Sagittal Force Angle (deg)

Figure 8: Between subject comparison (S1 vs S2) of joint kinetics (elbow NJM (a), shoulder NJM (b), total NJM
(sum of elbow and shoulder NJM magnitudes) (c), and resultant shoulder NJF (d)), across time and reaction
force directions (relative to the radial direction passing through wrist). Black dots indicate where the individual
subject operated in the experimental case.
23
Changes in mechanical demand over time change with orientation of the RF and NJF
relative to the upper extremity segments (r x RF) and the adjacent joint NJM (elbow).
Since both segment configuration and measure tangential force magnitude change with
respect to time, the independent effect of each on the mechanical demand imposed on the
upper extremity is unclear. To control tangential force magnitude, the time-averaged
value was computed and used at all points in time in a quasi-static analysis for subject 2.
Radial force was still allowed to vary. Simulation results indicated that potential NJM and
NJF loading tends to be higher early in the push phase as compared to later in the push
phase (Figure 9). Minimum elbow, shoulder, and total NJM are located in more tangential
RF directions in the early push phase, then shift quickly to radial RF directions, and
finally trend back toward tangential RF directions by the end of the push phase. Total
NJM is highest across force directions at ~ 0.1 seconds then decreases with time.
Free body diagrams of early and late positions illustrate how orientation of RF relative to
UE segments changes throughout the push phase (Figure 10). When the wrist position on
the rim is posterior relative to top dead center (early phase), RF acts more posteriorly on
the upper extremity. As the push phase progresses, RFs increasingly act more anteriorly
to the CM of the forearm and upper arm segments. These shifts in proximal and distal
moments created by the RF and NJFs about the segment CM affect the magnitudes and
directions of the elbow and shoulder NJMs across positions.
Changes in RF direction relative to the upper extremity segments correspond with
changes in UE orientation relative to the pushrim. From early to late, the forearm changes
24
from a radial to tangential alignment with pushrim. Forearm reorientation changes
moment arm magnitudes relative to the RF which alters proximal and distal forces and
moments. For example, a tangentially directed RF creates a large moment about the
forearm CM in the early push phase and a low moment at the end of the push phase. At ~
0.07 s, the forearm is perpendicular to the pushrim so a RF applied in the tangential
direction will result in a maximal elbow NJM. From early to late, the SW vector changes
from almost directly opposing to perpendicular to almost directly in line with the
tangential direction of the pushrim. Shoulder NJM is largest in the tangential direction at
~0.17 s than any other time b/c the SW vector is almost perpendicular to the pushrim.

25
θ
R
θ
R
Elbow NJM (Nm) Shoulder NJM (Nm)
Total NJM (Nm) Axial Shoulder NJF (N)
Time (s) Time (s)
Sagittal Force Angle (deg)
Sagittal Force Angle (deg)
θ
R
θ
R
Elbow NJM (Nm) Shoulder NJM (Nm)
Total NJM (Nm) Axial Shoulder NJF (N)
Time (s) Time (s)
Sagittal Force Angle (deg)
Sagittal Force Angle (deg)

Figure 9: Simulation results for subject 2 when keeping torque applied to the wheel constant throughout the
push phase. Mechanical demand imposed on the upper extremity is represented by elbow NJM, shoulder NJM,
and total NJM and shoulder NJF during the contact phase. By fixing reaction force magnitudes over time, these
figures give a sense of how potential loading varies between different kinematic positions. Early in the phase,
when the hand is behind TDC, loading seems to be higher across force directions than later. Minimum loading
tends to occur near the end of the phase when the segments are more aligned with the tangential direction of the
pushrim

26

Figure 10: Comparison of upper extremity joint kinetics early and late push phase. Reaction force (RF)
directions (red = tangential, blue = 30 deg from radial) relative to the wheel are the same. Elbow is
approximately at the same angle in both cases, but orientation of the UE relative to the pushrim and RF has
changed. Early in the push phase, tangentially directed force yields similar elbow flexor NJM than the more
radially directed force. Moments created by individual components of the net joint forces about the upper arm
CM tend to be larger in the radial case which yields a higher shoulder NJM. Late in the push phase, the radial
force (blue) of the NJF contributes to the need for a larger elbow extensor NJM which opposes the moment by
the NJF on the upper arm.

27
Discussion
Repetitive loading during manual wheelchair propulsion contributes to overuse
associated with shoulder injury. Simulation results from this study indicate that
redirection of the hand / rim reaction force relative to the upper extremity segments
provides a means to redistribute mechanical load across joints and shift away from loads
associated with pain with out decrements in performance (same torque applied to wheel).
Model simulations using a 2D inverse dynamic model using subject-specific
experimental tangential force and kinematic data were used to determine upper extremity
NJMs and shoulder NJF when varying the magnitude of the radial component of the
reaction force. Load distribution trends were found to vary during the push phase and
were subject-specific. These simulation results provide a mechanical basis for clinical
decisions regarding interventions that aim to redistribute load as a means of avoiding
overuse injury.
The results in this study are consistent with other modeling and experimental studies that
have researched effective force direction. Simulation results indicate that as sagittal plane
reaction force direction varies the elbow, shoulder, and total NJM and shoulder axial NJF
change. Reaction forces oriented in radial directions contributed to especially high
magnitudes in all variables since the magnitude of the RF increased as the radial
component increased. Elbow, shoulder and total NJM and shoulder NJF reached
minimum magnitude at times the RF was directed in a non-tangential direction. This
finding is consistent with the modeling results by Rozendaal (Rozendaal and Veeger,
2000) that found the preferred force direction as defined by a cost / effect function is not
28
tangential. RFs in the tangential direction were associated with increases in the shoulder
NJM, as reported by others (Desroches et al., 2008, Bregman et al., 2008). While not
measuring energy expenditure directly, these simulation results also agree with the
experimental studies that have found higher energetic costs associated with trying to
direct the reaction force more tangentially (de Groot et al., 2002, Kotajarvi et al., 2006).
Interpretation of simulation results need to account for limitations in model complexity.
The model is 2D which assumes neglects out-of-plane mediolateral kinematics and
forces. In reality, both kinematics and force are 3D during WCP. The general trends in
loading distribution as a function of force direction are expected to be consistent although
more complex when moving to 3D. Future work will examine how 3D kinematics / force
affect potential distribution of mechanical loading (Chapter 3). Simulations in this study
assumed that the RF is applied directly to the wrist and therefore discounts the
contribution of grip as well as the wrist NJM on WCP mechanics. Variations in medial-
lateral forces may affect simulation results in that the mediolateral component of the RF
alters the moment arm between the RF and each segment’s CM. Simulation results are
expected to be especially sensitive when the RF is directed more radially in that the RF
tends to be higher and more sensitive to moment arms. Specific musculoskeletal loads
dependent on force / length / velocity and co-contraction are beyond the scope of this
study. However, we feel given these limitations the model is sufficient in complexity to
illustrate the sensitivity of joint kinetics (NJM & NJF) to reaction force redirection.
29
In WC propulsion, mechanical loading is affected by 1) reaction force direction 2)
relative orientations of the upper extremity segments (forearm and upper arm, i.e. elbow
flexion) and 3) orientation of the UE relative to the pushrim (i.e. shoulder / wrist axis
relative to tangential direction). All three mechanisms can alter NJM and NJF loading
across the elbow and shoulder joints. The implications of RF direction on load
distribution require consideration of the kinematic context in which the RF was generated
(as defined in #2 and #3) which is known to vary between subjects and with time (e.g.
throughout the push phase). As such, the effects of force direction are discussed in
relation to both local orientation (2) and global orientation (3).
Our results indicate that changing the orientation of the reaction force relative to upper
extremity segments changes the magnitudes and ratios of the elbow and shoulder NJMs
and NJFs. Changes in mechanical distribution have been found in other tasks such as
landings (McNitt-Gray et al., 2001), diving (Mathiyakom et al., 2007), and activities of
daily living (Mathiyakom et al., 2005). Force direction affects elbow NJM directly
through orientation of the force relative to the segment CM. A force directed posterior to
the forearm CM will require a flexor elbow NJM, while a force directed anterior will
require an extensor elbow NJM. Elbow flexor / extensor NJM created opposing extensor /
flexor moment acting at the distal end of the upper arm segment. The reaction forces
acting at the proximal and distal ends of the upper arm change in magnitude and direction
across force directions, and the interaction between these terms and the distal moment
(also changes with force direction) will determine the shoulder NJM. Given the same
force magnitude and direction relative to the forearm, shoulder NJM will change with
30
varying upper arm orientations (amount of elbow flexion). As upper arm shifts from
parallel (extended elbow) to perpendicular relative to the forearm, the force direction that
minimizes shoulder NJM shifts anteriorly away from the forearm. Therefore subject
specific and push phase differences in relative orientations of the upper extremity
segments alter loading distribution patterns. If subjects operate at different elbow flexion
angles at peak force, the effect of force redirection on load distribution may also be
different. Similarly, different elbow angles across the push phase could alter effect of
force direction on loading.
Loading distribution in WCP is affected not only by force direction relative to segment
orientation but also UE orientation relative to the pushrim. In whole body tasks, changes
in force direction and / or segment configuration must agree with whole body tasks
constraints of force direction relative to the center of mass (CM). A different constraint is
found in WC propulsion as force direction and magnitude must also align with having a
specific tangential force component relative to the pushrim. As force is directed more
radially, the magnitude must increase so that the tangential component remains the same
to maintain performance (Figure 10). How the arm is orientated relative to the tangential
and radial directions will alter both force magnitude and moment arms which will affect
loading distribution during WC propulsion. Forces directed close to radial will generally
create high loads regardless of moment arm magnitudes because force magnitude needs
to be extremely large in order to maintain the tangential component of the RF. The two
subjects used in this study had similar degrees of elbow flexion at peak force, but
different loading distributions because the orientation of the arm relative to the pushrim
31
was different (Figure 7). The loading effect of changing arm orientation relative to the
pushrim was also evident between early and late push phase instances for one subject
(Figure 10).
Changing upper local and global orientations of the upper arm collectively affect loading
distribution changes that occur across the propulsion phase. Potential loading (assuming
constant tangential force) would be highest in the start of the propulsion phase because
the upper arm is almost perpendicular to the forearm and UE orientation relative the
pushrim creates large moment arms across force directions. If “pulling” forces were
simulated, loading may be reduced but is not practical. At the end of the push phase,
upper arm and forearm segments are more parallel and aligned with the pushrim
tangential direction, so both moment arms and force magnitude are reduced. Force
direction, local UE orientation, and UE orientation relative to tangential direction all must
be considered when evaluating how a subject may redistribute load during WC
propulsion.
Using an experimentally motivated inverse dynamic model to perform force direction
sensitivity studies provides clinicians a method to assess current WCP techniques in the
context of mechanical loading (NJM and NJF) and association with pain / injury. The
solution spaces provide a template for making decisions on how to attempt to redistribute
load via force redirection. For example, at time of peak force, subject 1 was directing the
RF at about 80° from the radial (Figure 8). However, lower shoulder NJM could be
achieved if the RF was directed more radially to about 50° (Figure 7). Conversely, to
32
reduce the axial component of the shoulder NJF in subject 2, the RF should be directed
more tangentially from about 45° to 70°. Our results indicate that decisions on how to
shift an individual within a solution spaced must consider the kinematic context of force
generation. WCP kinematic used by individuals may appear different but the joint
kinetics indicate that they are experiencing comparable loading distribution conditions.
The solution spaces generated using simulation results also reflects that load distribution
will change at different wrist positions on the wheel even if the reaction force is kept in
the same direction relative to the pushrim. Together, these results provide better
understanding of how elbow and shoulder loads vary over different RF directions and
segment configurations in the push phase. These simulation results also provide
mechanically based information to guide clinical interventions that aim to maintain WCP
performance and redistribute load.

33
Chapter 3: Sensitivity of Upper Extremity Mechanical Loading
to the Mediolateral Component of the Reaction Force during
Manual Wheelchair Propulsion

Introduction
Individuals with spinal cord or lower extremity injury often rely on manual wheelchairs
to preserve independence and participation in the community. Manual wheelchair
propulsion (WCP) also serves as an effective means to preserve upper extremity strength
and embeds cardiovascular conditioning as part of activities of daily life, in contrast to
more costly powered wheelchairs. The mechanical objective of manual WCP is to
generate sufficient tangential force applied at the hand/rim interface over a give time to
regulate the momentum of the system (WC user and chair) (Boninger et al., 1997). The
repetitive nature of manual WCP exposes the upper extremity (UE) to repetitive loading
that can lead to acute and overuse shoulder injuries and a loss of independence (Ballinger
et al., 2000, Mercer et al., 2006, Subbarao et al., 1995). Experimental and modeling
simulation results indicate that there is more than one solution to satisfy the mechanical
objective of the propulsion task (Munaretto, 2011, Veeger et al., 1989, Masse et al., 1992,
van der Woude et al., 2001). Knowledge of the positive and negative consequences of
specific WCP techniques is expected to assist clinicians in fitting the user in the chair and
facilitating decisions regarding prospective interventions to avoid injury.
Improving the interaction between the user and wheelchair during WCP by redistributing
mechanical load across the UE is one way to maintain performance and potentially
34
reduce the risk of injury. Redirecting the resultant force (RF) applied to the rim while
maintaining the tangential component of the rim RF (F
T
) provides a means for
redistribution of mechanical loading across the upper extremity without a decrement in
WCP task performance (Munaretto, 2011). Previous research with goal-directed tasks has
found that alteration of reaction force direction relative to segment orientation
redistributes load across joints (Mathiyakom et al., 2005, McNitt-Gray et al., 2001).
Results from a 2D wheelchair model indicate that redirection of the RF in the sagittal
plane relative to the UE segment configuration redistributes the mechanical demand
imposed on the elbow and shoulder (Munaretto, 2011).
Proposed modifications in mechanical load distribution must consider an individual’s
capacity to generate force. Preservation of segment and joint kinematics while redirecting
force allows for WC users to coordinate and generate force at their preferred muscle
lengths and velocities. Since different WC users vary in their upper extremity segment
properties and their position in relation to the wheelchair, suggested technique
modification needs to be subject-specific. Simulations using an experimentally motivated
dynamic multilink model can explore causal relationships between force direction and
load by preserving subject specific kinematics and performance.
The effect of RF redirection in the context of kinematics outside the sagittal plane is
unclear. While the sensitivity of mechanical loading to RF redirection may be explored
via a simplified 2D model, the kinematics and RFs of WC users are in reality 3D.
Subject specific differences in the location of the shoulder relative to the pushrim in the
35
mediolateral (ML) direction as well as amount of shoulder internal rotation that moves
elbow laterally have been observed (Lin et al., 2009). The magnitude of the ML
component of the RF is considered negligible but exists. The relative magnitude of the
ML alters the orientation of the RF relative to the forearm and is likely to contribute to
the upper extremity kinematics and load distribution preferred by an individual WC user.
In this study, our aim was to determine the sensitivity of UE mechanical loading to 3D
rim RF redirection during WCP in a graded task. The effect of increased model
complexity (incorporation of 3D reaction force and kinematics) was hypothesized to
influence the identification of strategies for distributing mechanical load imposed on the
upper extremity. We tested this hypothesis by determining the mechanical loading
(shoulder and elbow net joint moments (NJM) and axial component of shoulder net joint
force (NJF)) under varied RF directions while maintaining experimental WC user
kinematics. The RF direction was varied by maintaining the tangential component of RF
and systematically varying the radial and ML components of RF. We expected that
simulations using a 3D RF with 3D kinematics would identify load distribution benefits
of out-of-sagittal plane force generation. A 3D inverse dynamic model was used to
determine NJM and NJF. Solution spaces characterizing mechanical loading of the upper
extremity under simulated conditions provide a comprehensive resource to assist
clinicians in identifying mechanical loading implications of WCP techniques specific to
reaction force direction and body segment configuration at key events in the propulsion
phase. A priori knowledge of loading consequences of specific WCP techniques under
36
realistic force generation conditions is expected to aid clinicians prospectively plan and
implement effective rehabilitation interventions that aim to preserve UE function.
Methods
Experimental
Two wheelchair users with spinal cord injury (SCI) volunteered to participate in this
study in accordance with the Institutional Review Board at the Ranchos Los Amigos
National Rehabilitation Center, Downey, CA. The subjects performed wheelchair
propulsions on an ergometer providing resistance simulating movement up a graded slope
for 10 seconds. Reflective markers were used to monitor the 3D motion of the hand,
forearm, upper arm, and trunk segments. Three markers were also placed on the right
wheel to track wheel rotation (VICON, 50 Hz). Coordinates were rotated into a (x,y,z)
reference frame where x represented anterior/posterior position, y represented superior /
inferior position, and z represented mediolateral position. The sagittal plane xy is oriented
in global space to symmetrically bisect the user. The force applied to the wheelchair
during propulsion was measured using force transducers (SmartWheel 2500 Hz) in the
radial, tangential, and ML directions of the wheel. The markers and upper extremity
model to estimate wrist, elbow, and shoulder joint centers followed methods described in
(Rao et al., 1996).
37
Modeling
Equations of Motion
The equations of motion used follow the generalized Newton-Euler ‘up the chain’ inverse
dynamics method. For both segments starting with the forearm:

-
-
x xCM
xP xCM xD
yP yCM yD
F ma
R ma R
R ma mg R
=
=
= +
∑

Equation 8

( ) ( ) ( ) ( ) - - . - . - . - - . -
z zCM zCM
zP zCM zCM zD xP P CoM yP CoM P xD CoM D yD D CoM
M = I
M I M R y y R x x R y y R x x
α
α = + +
∑

Equation 9

m = segment mass
xCM
a = segment acceleration in x direction
xP
R = reaction force acting on the proximal end of segment in x direction
yD
R = reaction force acting on the distal end of segment in the y direction
g = gravity constant
zCM
I = CM inertia about the z-axis
zCM
α = CM angular acceleration about the z-axis
zP
M = moment acting on the distal end of the segment about the z-axis
P
y = location of the proximal segment end in the y-direction
CoM
y = location of the segment CM in the y-direction

Similar equations are applied for full 3D analysis. Starting with the reaction force acting
at the wrist, the reaction forces at the elbow are calculated, followed by the net joint
moment at the elbow. These values are then applied to the upper arm segment to calculate
kinetics at the shoulder joint (Figure 5).

38

Figure 11: Reaction force (RF) at the hand/rim interface and net joint reaction forces (NJF) and net joint
moments (NJM) applied to forearm and upper arm segments

Modifications in Force Direction
Radial components of the RF (F
R
) do not directly contribute to torque generation about
the wheel axis and can be varied as long as the tangential component of the RF (F
T
) is
fixed (Figure 6).

39

Figure 12: The direction of the projected resultant reaction force (RF, green vector) in the sagittal plane as
applied to the body, θ
R
, is defined relative to the radial line (dotted) passing through the wrist. The angle φ
defines the direction of the resultant RF relative to the sagittal plane xy. Simulations involving variation in RF
direction maintain the magnitude of F
T
while varying the magnitude of F
R
and F
ML
. F
R
is modified to generate
θ
R
between 10° ° ° ° and 90° ° ° ° and F
ML
is modified to generate φ between -30° ° ° ° and 30° ° ° °. The orientation of the wrist on
the rim relative to the right horizontal passing through the wheel axis is θ
W.

The location of the reaction force is the same as the wrist angle and calculated as
1
tan
W
W
W
y
x
θ
−
 
=
 
 

Equation 10
where x
w
and y
w
are the Cartesian coordinates of the wrist. The F
T
applied to the wheel
was calculated as
( ) ( ) cos ( ) ( ) sin ( )
T y W x W
F t F t t F t t θ θ = −
Equation 11

θ
W

θ
R

F
T

F
R

φ
F
ML

2D
3D
Out of plane motion
F
T

40
where F
X
and F
Y
are the components of the reaction force in the global frame acting on
the wheel. The direction of the force acting on the WC user in the sagittal plane of the
global reference frame, θ
G
can be described as

G W R
θ θ θ = +
Equation 12

where θ
R
is the reaction force direction relative to the radial direction at the wrist /
pushrim interface. θ
G
, was allowed to vary to generate θ
R
between 10° and 90°. The angle
describing the medial-lateral component of the RF (F
ML
), φ was varied between -30° and
30°, where positive angles indicate a force directed laterally on the wrist and medially on
the pushrim. At each instant in time, the resultant force magnitude needed to generate the
measured F
T.

( )
( )
sin( ( ) ) cos( )
T
mag
W G
F t
F t
t θ θ φ
=
− ×

Equation 13
From the computed resultant force and direction, [Fx Fy,Fz] components were computed
for each force (θ
G
) during simulation. For each force angle, inverse dynamics was
performed to determine NJM for the elbow and shoulder and the axial component of the
shoulder NJF. In addition, the sum of the magnitude of net joint moments (total NJM) at
the elbow and shoulder was computed.

41
| | | |
E S
J τ τ = +

Equation 14

Results
Changes in both radial and ML components of the RF alter RF direction and distribution
of the NJM between the elbow and shoulder joints for both subjects at peak force (Figure
13 & Figure 14). As the RF direction in the sagittal plane moves from radial to tangential,
both shoulder and elbow NJMs decrease to a minimum at (S1 Elbow = 52°, Shoulder =
29°, S2 Elbow = 87°, Shoulder = 53°), then begin increasing again. Minimum shoulder
NJM occurs at a more radial RF direction than minimum elbow NJM. Locations of
minimum NJM occur in more tangential RF directions for subject 2 than subject 1. As the
RF direction moves from medial to lateral, both elbow and shoulder NJMs decrease to a
minimum (S1 Elbow = -1°, Shoulder = -17°, S2 Elbow = 10°, Shoulder = -15°), then
begin increasing again. Minimum shoulder NJM occurs at more medial RF directions
while minimum elbow NJM occurs in more lateral RF directions. Location of minimum
elbow NJM is subject specific (e.g. minimum elbow NJM for subject 2 occurs in more
lateral RF directions than for subject 1). Location of minimum shoulder NJM occurs at
similar ML RF directions for both subjects (e.g. minimum shoulder NJM for subject 1
occurs with a slightly more medial RF than subject 2). Collectively, total NJM varies as a
function of both radial and ML RF directions with lower magnitude (blue) regions
occurring as the RF direction changes from radial/medial to tangential/lateral. The axial
42
component of the shoulder NJF increases in compression as the RF shifts toward radial
and medial directions, but decreases in compression as RF shifts tangentially and laterally
and finally increases into tension.

Tangential Force (N)
Push Phase % (0-1)
Tangential Force (N)
Push Phase % (0-1)

Figure 13: Time of peak reaction force expressed as % push phase

43
S1
S2
Lateral
Medial
Lateral
Medial
Elbow NJM (Nm)
Shoulder NJM (Nm)
Total NJM (Nm)
Axial Shoulder NJF (N)
Elbow NJM (Nm)
Shoulder NJM (Nm)
Total NJM (Nm)
Axial Shoulder NJF (N)
Sagittal Force
Angle (deg)
Sagittal Force
Angle (deg)
ML Force Angle (deg)
ML Force Angle (deg) ML Force Angle (deg) ML Force Angle (deg)
S1
S2
Lateral
Medial
Lateral
Medial
Elbow NJM (Nm)
Shoulder NJM (Nm)
Total NJM (Nm)
Axial Shoulder NJF (N)
Elbow NJM (Nm)
Shoulder NJM (Nm)
Total NJM (Nm)
Axial Shoulder NJF (N)
Sagittal Force
Angle (deg)
Sagittal Force
Angle (deg)
ML Force Angle (deg)
ML Force Angle (deg) ML Force Angle (deg) ML Force Angle (deg)

Figure 14: Comparison of mechanical load distribution associated with reaction force redirection for subject 1
and subject 2. Mechanical load is expressed as elbow NJM, shoulder NJM, total NJM, and the axial component
of the shoulder NJF (parallel to the long longitudinal axis of upper arm). Black dots indicate where the subject
operated in the experimental case.
44
Changes in mechanical demand are associated with modifications in ML component of
the RF direction relative to each segment (Figure 15). A laterally directed RF will have a
small moment arm component relative to the forearm but a larger moment arm relative to
the upper arm resulting in a lower elbow NJM but higher shoulder NJM. As the RF is
directed more medially, the moment arm of the RF relative to the forearm CM increases
and elbow NJF relative to the upper arm CM decreases (r vector components from the
segment CM to the NJF). In addition, the elbow NJM opposes the moment created by r X
NJFs of the upper arm. As a result, elbow NJM increases while shoulder NJM decreases.

Figure 15: Frontal plane views of upper extremity segment free body diagrams for subjects 1 and 2 at time of
peak reaction force. Between subject differences in reaction force/NJF orientation relative to each segment
(Subject 2 forearm is more horizontal and upper arm is more vertical than those of Subject 1) affect mechanical
load distribution across the elbow and shoulder. Between subject differences in segment orientation relative to
pushrim illustrates how reaction force direction relative to the segments and the adjacent joint NJM distributes
load. Similar lateral forces (green) across subjects yields larger elbow NJM in subject 1, while similar medially
directed forces (purple) yields larger elbow NJM in subject 2. Variations in elbow NJM magnitude and direction
also affect magnitude of shoulder NJMs.

45
Subject specific differences in the effect of r x RF are dependent on the configuration and
orientation of the UE segments relative to the RF. The orientation of the forearm relative
to the pushrim is more vertical in subject 1 than subject 2. The more laterally directed
forearm in subject 2 will need a more laterally directed force to reduce elbow NJM. A
larger elbow angle in subject 1 orientates the upper arm slightly more vertically than the
upper arm of subject 2 relative to the pushrim. A larger elbow NJM acting at the distal
end of the upper arm in subject 2 is counteracted by slightly larger r x RF at the upper
arm, so shoulder NJM is of similar magnitude between subjects.
The effect of sagittal plane force direction on distribution of mechanical demand is
affected by the ML force direction (Figure 16 & Figure 17) when using 3D kinematics.
Potential redistribution of elbow and shoulder NJM may be attenuated when assuming a
fixed ML force direction. While in the 2D case shoulder NJM could potentially be
reduced close to zero, using 3D kinematics but assuming ML force is zero (green)
indicates shoulder NJM can only be reduced to 12 Nm in subject 1 and 10 Nm in subject
2. Using the experimental ML force (blue) direction further limits shoulder NJM
reduction. When ML force is directed 20 degrees medially (black), shoulder NJM can be
better redistributed. Conversely, potential elbow NJM reduction is limited with medial
forces but improved when using laterally directed forces.

46

Figure 16: Representative ML force slices projected onto one graph. Each slice shows the effect of sagittal force
direction on shoulder NJM would be interpreted if operating at the specific ML force direction

ML force direction also affects the sagittal force angles which are perceived to alter
loading when using 3D kinematics. In both subjects, as RF force is directed more
laterally, the location of apparent minimum shoulder NJM shifts tangentially. If one fixes
ML force direction to what was measured experimentally, sagittal force direction which
minimizes shoulder NJM may shift 10 degrees in the tangential direction (Figure 17).
47

Figure 17: Subject 1 and 2 elbow, shoulder, and total NJM at peak force across sagittal force directions at
different ML force directions (blue = EXP, black = - 20 deg, green = 0 deg, cyan = 20 deg) as well as 2D model
distribution (pink).

Combinations of sagittal and ML force angles which redirect force within the shoulder /
elbow / wrist (SEW) plane share the same shape, i.e. location of minimum elbow and

48
shoulder NJM occur in approximately the same force directions in both cases (Figure 10).
Elbow, shoulder, and total NJM distributions as a function of sagittal force angle are
slightly larger in magnitude than the 2D analysis. NJMs increase when forces are directed
away from this plane. Thus, consideration of force angle combinations that stay near the
SEW plane in 3D achieves similar results as a 2D analysis in terms of the sagittal force
direction which minimizes loading.

Figure 18: Simulation of force redirection in SEW plane. ML force direction varies as a function of sagittal force
direction. Plots show a) total NJM distribution and the path of SEW plane force direction combinations b)
compares total NJM as a function of sagittal force angle between 2D results and SEW plane results c) elbow
NJM and d) shoulder NJM

A B
C D

49
Discussion
Repetitive loading during manual wheelchair propulsion may lead to overuse associated
with shoulder injury. Redirection of the RF at the hand / rim interface relative to the
upper extremity segments provides a means to redistribute mechanical load across joints
to improve task performance or avoid overuse related injury. In this study, mechanical
demand imposed on the upper extremity (elbow and shoulder net joint moments and
shoulder net joint force) was simulated using a 3D inverse dynamic model and subject-
specific experimental tangential force and kinematic data while maintaining task
performance (torque applied to rotate the wheel remained constant). The reaction force
direction was systematically varied by modifying the radial and mediolateral components
of the reaction force while maintaining the tangential component as measured
experimentally. As hypothesized, the simulation results indicate that the distribution of
mechanical load changes with out-of-sagittal-plane reaction force redirection relative to
the 3D upper extremity segment kinematics. Minimum NJMs were found to occur at
times when the reaction force at the hand / rim interface was directed in non-tangential
directions. These results emphasize the need to consider how the reaction force applied to
the wheel influences the mechanical demand imposed on the upper extremity
musculoskeletal system. Solution spaces characterizing mechanical loading of the upper
extremity under conditions simulated in this study provide a comprehensive resource to
assist clinicians in identifying mechanical loading implications of WCP techniques.
Specifics regarding RF direction and body segment configuration at key events in the
propulsion phase provide the clinician with a mechanical basis to effectively design and
50
implement effective pre- and re-habilitation interventions that aim to preserve UE
function over time.
The model used to simulate mechanical load distribution under varying reaction force
conditions was found to be of sufficient complexity to illustrate the trade-offs between
NJM and NJF associated with reaction force redirection. Limitations of the study include
approximations associated with fixed point of reaction force application at the hand/rim
interface at the wrist rather than a moving center of pressure along the hand rim interface.
The authors also acknowledge the need to consider pros and cons of the mechanical
demand at the joints in the context of the individual WC users control capabilities as well
as the kinematic context for muscle force generation (length, velocity). These factors
must be considered together by the clinician prior to finalizing prospective decisions
regarding technique modifications.
Our results indicate that changing the alignment of the reaction force in the mediolateral
direction relative to upper extremity segment orientations changes the magnitudes and
ratios of NJM across the elbow and shoulder joints (Figure 14). Changes in mechanical
distribution via force redirection have been found in the sagittal plane (Munaretto, 2011)
as well as in other tasks such as landings (McNitt-Gray et al., 2001), diving (Mathiyakom
et al., 2007), and activities of daily living (Mathiyakom et al., 2005). ML force direction
affects elbow NJM directly through orientation of the force relative to the segment CM in
the frontal plane. Shoulder NJM demand is affected by both elbow NJM frontal plane
component as well as ML force direction relative to the upper arm segment (Figure 15).
51
If kinematics were purely 2D, then any ML force would increase moments across both
joints. However, shoulder position is generally medial to the pushrim (Boninger et al.,
2000) and so the force would have to direct medially to align with the UE and reduce
NJM across both joints. Contrarily, most subjects also exhibit shoulder internal rotation
which rotates the elbow laterally (Lin et al., 2009) and thus a lateral force would be
needed to pass through the forearm to keep elbow NJM low. The combination of these
two kinematic variables aligns the UE relative to the pushrim so that there is a tradeoff in
elbow and shoulder NJM as force direction shifts lateral to medial.
Simulation results in this study using 3D forces and 3D kinematics indicate that the
mechanical load distribution is sensitive to the ML component of the RF. Previous 2D
model simulation results indicate that redirection of the RF in the sagittal plane can alter
shoulder and elbow NJM and shoulder NJF (Munaretto, 2011). Fixing ML force direction
to zero or experimental, while varying the RF force direction in the sagittal (2D model
simulation), limits the ability to reduce shoulder and total NJM (Figure 17). In 2D
analysis (2D force, 2D kinematics), RFs acting 30 degrees from radial have high force
magnitudes but small moment arms relative to the shoulder joint (subject specific) and
may end up with small shoulder NJM. In 3D kinematics, the same sagittal force direction
has a larger moment arm relative to the shoulder because of the ML distance between the
wrist and shoulder. Unless the force is directed medially so that it can pass near the
shoulder joint, results would suggest the sagittal force would have a limited ability to
lower shoulder NJM. Conversely, if the reaction force is not directed laterally to pass
through the forearm, feasible variations in elbow NJM will not be observed. Thus, when
52
using 3D kinematics, one must consider ML force direction when attempting to identify
multijoint control strategies for redistributing mechanical load.
The combination of sagittal and ML force directions that pass near the UE plane
redistribute load similar to 2D analysis (Figure 10). Forces that go through the shoulder-
elbow-wrist (SEW) plane essentially reduce moment arms. If kinematics were 2D, then
adding a ML force direction would increase effective moments about both joints and
increase UE NJMs because overall force direction would be out of the SEW plane. As the
UE configuration changes relative to the pushrim, the SEW plane rotates to include ML
force components. The results in our study indicate that force redirection within the SEW
plane elicits similar changes in load distribution as our previous 2D analysis (Munaretto,
2011). NJM magnitudes are slightly higher but occur at similar sagittal force directions.
However, UE orientations of other subjects may exhibit larger out-of-plane kinematics
which may not have minimal loads in the SEW plane. As the degree of shoulder internal
rotation increases, the SEW plane rotates more perpendicularly to the tangential pushrim
direction. While the position vector “r” may be small, the RF term of the cross product (r
x RF) will significantly increase with larger rotations. The plane of force directions which
minimize total NJM load but redistribute across joints may not pass through the SEW
plane.
Using an experimentally motivated inverse dynamic model to perform force direction
sensitivity studies provides clinicians with a versatile method to assess current WCP
techniques in the context of mechanical loading (NJM and NJF) and association with
53
pain / injury. For example, if a change in shoulder NJM is desired to unload a painful
shoulder then subject 1 could explore redirection of the RF radially and medially from the
current force direction as a solution to alter shoulder NJM (Figure 14). If a reduction in
shoulder compression is desired, the opposite shift could be explored to reduce shoulder
NJF. These simulation results also provide a mechanical basis for identifying ways to
redistribute load across the upper extremity by considering shifts in locations within the
model-generated solution space. The WCP technique used by individuals may appear
different, but when considering the kinematic context of RF generation they may be
operating in similar loading distributions, and vice versa. Likewise, simulation results
also help account for variations in the effect of reaction force redirection on load
distribution as position varies within the push phase. Measurement of both kinematics
and reaction force can be utilized to explore feasible options before undertaking an
intervention. Shifts within the solution space also enable exploration of task performance
under more challenging environmental or control conditions (i.e. “what if” there is a need
to go faster using same multijoint control strategy). By coupling clinical assessment (e.g.
torque generating capacity at different muscle lengths and velocities) with the mechanical
demand imposed by different WCP techniques, the clinician can identify feasible
solutions for individual wheelchair users.
Future studies will determine how upper extremity segment configuration relative to the
wheelchair affects the distribution of mechanical demand across the elbow and shoulder
during manual wheel chair propulsion. Based on these simulation results, modifications
in the distance between the shoulder and the pushrim is expected to influence the reaction
54
force directions that minimize mechanical loading (NJM shoulder, NJM elbow, NJF
shoulder). In addition, altering the position of the wrist / hand on the pushrim is expected
to influence the reaction force directions that minimizes mechanical loading.
55
Chapter 4: Reconfiguration of the Upper Extremity Relative to
the Pushrim Affects Load Distribution during Wheelchair
Propulsion

Introduction
Individuals with lower extremity or spinal cord injury rely on manual wheelchair
propulsion (WCP) to maintain independence and community participation. Unlike more
expensive powered wheelchairs, manual wheelchair use promotes upper extremity
strength and cardiovascular conditioning as part of activities of daily life. Manual
propulsion of the user / WC system entails the generation of a tangential force at the hand
/ rim interface during hand contact to accelerate the mass and regulate the momentum of
the entire system (wheelchair user and chair) (Boninger et al., 1997). Chronic use of
manual WCP exposes the upper extremity (UE) to repetitive loading. Mechanical loading
experienced by the upper extremity during WCP has been associated with the high
incidence of acute and overuse shoulder injuries in manual wheelchair users. Disability,
secondary to the primary injury, contributes to a loss of autonomy and a decrement in
quality of life (Ballinger et al., 2000, Mercer et al., 2006, Subbarao et al., 1995).
Experimental results indicate that there is more than one solution to satisfy the
mechanical objective of this propulsion task (Munaretto, 2011, Raina, 2011, Veeger et al.,
1989, Masse et al., 1992, van der Woude et al., 2001).
Knowledge of the advantages and disadvantages of different WCP techniques can aid
clinicians in make decisions regarding pre- and re-habilitation interventions that aim to
maintain performance while reducing injury risk. Simulation studies indicate that
56
maintaining the tangential component of the RF and altering the radial component
provides multiple solutions for redistributing the mechanical loading across the upper
extremity without a decrement in performance (Munaretto, 2011). RF redirection
combined with alteration in upper extremity segment positions and configurations
provide additional solutions for load redistribution.
Modification in seat position alters shoulder and wrist position of the wheelchair user
relative to the wheel. Different seat positions have been reported to alter upper extremity
kinetics (van der Woude et al., 2009), however factors contributing to modified kinetics
have been difficult to systematically control in an experimental setting. Reconfiguration
of the upper extremity associated with different seat positions is expected to affect how
RF at the hand/rim interface is generated and how load is distributed during manual
WCP. Simulation studies provide an effective means for systematically modifying
variables that can not be controlled experimentally. Determining how individual
wheelchair users can maintain performance and effectively distribute load by redirecting
the RF during WCP, provides clinicians and wheelchair users with a priori knowledge of
feasible solutions in different kinematic contexts.
The aim of this study was to determine the sensitivity of RF redirection and load
distribution to upper extremity kinematic modifications during a WCP task. We
hypothesized that modifications in shoulder / wheel distance and wrist location relative to
the rim will affect how RF redirection distributes loading. To test this hypothesis,
simulations using a 2D inverse dynamic model estimating elbow and shoulder net joint
57
moments (NJM) and axial component of the net joint force (NJF) of the shoulder were
used to determine the sensitivity of load distribution to shoulder / wheel distance, wrist
location relative to the rim, and RF direction. Simulation results provide a means to
determine how changes in upper extremity kinematics (forearm relative to the pushrim
(global) and elbow angle (local)) affect force generation and load distribution.
Methods
Experimental
One wheelchair user with spinal cord injury (SCI) volunteered to participate in this study
in accordance with the Institutional Review Board at the Ranchos Los Amigos National
Rehabilitation Center, Downey, CA. The participant performed self-selected speed
wheelchair propulsions for 10 seconds. Reflective markers were used to monitor the 3D
motion of the hand, forearm, upper arm, and trunk segments. Three markers were also
placed on the right wheel to track wheel rotation (VICON, 50 Hz). Coordinates were
rotated into a (x,y,z) reference frame where x represented anterior/posterior position, y
represented superior / inferior position, and z represented mediolateral position. The
sagittal plane xy is oriented in global space to symmetrically bisect the user. The force
applied to the wheelchair during propulsion was measured using force transducers
(SmartWheel 2500 Hz) in the radial, tangential, and mediolateral directions of the wheel.
The markers and upper extremity model to estimate wrist, elbow, and shoulder joint
centers followed methods described in (Rao et al., 1996).
58
Modeling
We use a two segment, 2D model of the upper extremity. Experimental kinematics were
converted into the following coordinates that describe orientation of the UE relative to
the pushrim (Figure 19):
θ
W
(t): (wrist angle): Location of the wrist on the pushrim expressed as a rotation relative
to the right horizontal (i.e. top dead center = 90°). Simulations will modify this variable
θ
P:
(pushrim excursion): The range of pushrim excursion (ROM) for the push cycle. θ
P
=
initial θ
W
– final θ
W
. This is kept constant. Specifying a wrist angle for a given instant in
the push cycle will then determine wrist angles for the entire push cycle
θ
F
(t): (forearm angle): The angle of the forearm relative to the pushrim radial direction at
an instant.
θ
E
(t): (elbow angle): The angle of the upper arm relative to the forearm at an instant.
r
S:
(shoulder/axle distance): The distance of the shoulder relative to the wheel axle.
Simulations will modify this variable.

59

Figure 19: Coordinates describing position of upper extremity relative to the pushrim. Simulations varied θ
W

and r
S
and results are reported in relation joint angle (elbow angle θ
E
) and forearm angle (θ
F
) relative to radial
direction (dotted line passing from axle to wrist). When modifying shoulder / axle position r
S
, the shoulder / axle
angle is kept constant and the elbow θ
E
and forearm θ
F
angles are constrained in change (shoulder position
translates along the dashed line).
We assume the shoulder is in a constant position as determined by its average position
during the push cycle. Forearm and upper arm lengths are determined as averages of the
distances between elbow / wrist and shoulder / elbow centers of rotation in 3D over the
push phase. Then we restrict the model to 2D. Given the shoulder/axle distance and wrist
angle at time t, there is a unique orientation of the forearm and upper arm that are
realistic. We can determine the specific elbow position (law of Cosines) at time t that
agrees with the static constraints of forearm and upper arm segment length (Equation 15,
Figure 20). Iterating over experimental wrist angles θ
W
(t), UE kinematics are generated.
Comparison of experimental and simulated wrist positions (Figure 21) and average
θ
P

θ
W

θ
E

θ
F

r
S

60
positional errors of the wrist, elbow, and shoulder (Table 2) shows a strong match
between experimental and simulated upper extremity kinematics.

Figure 20: When varying shoulder position and wrist angle, Law of Cosines allows for calculation of elbow and
forearm kinematics

2 2 2
1
cos
2
SW U F
E
U F
L L L
L L
θ
−
− −
=
−

Equation 15

θ
W

L
U

L
F

(x
S
,y
S
)
(x
W
,y
W
)
L
SW

θ
E

61

Figure 21: Experimental (solid) vs simulated (dashed) elbow positional data

RMS error (m) X Y Z
Wrist 0.006 0.011 0.004
Elbow 0.013 0.006 0.013
Shoulder 0.008 0.002 0.003

Table 2: Average positional RMS error between simulated and experimental for wrist, elbow, and shoulder
endpoints

This process is then carried out across different shoulder distances r
S
and wrist angles θ
W
.
For each r
S
, there is a varying potential range of θ
W
at which the UE can operate. Lower
shoulder positions yield larger potential pushrim excursion angles θ
P
. θ
P
is determined by
finding all wrist angles θ
W
at which UE can connect with the wheel and avoiding 5
degrees of either full extension or flexion. Then this range is compared to the
experimental pushrim excursion (67°). We assume this range to be constant, but shifted
the location of this range through all feasible wrist positions. As r
S
increases, the feasible
62
pushrim excursion decreases until it exactly matches the experimental pushrim excursion.
Heights above this were not considered as they would involve reducing the pushrim
excursion or adding other assumptions.
Modifications in Force Direction
Radial and medial-lateral forces do not directly contribute to torque generation about the
wheel axis, and can be varied as long as the tangential force is fixed (Figure 22). The
location of the wrist/pushrim RF is the same as the wrist angle and calculated as
1
tan
W
W
W
y
x
θ
−
 
=
 
 
(1)
where x
w
and y
w
are the Cartesian coordinates of the wrist. The tangential force applied to
the wheel was calculated as
( ) ( ) cos ( ) ( ) sin ( )
T y W x W
F t F t t F t t θ θ = − (2)
where F
X
and F
Y
are the components of the reaction force in the global frame acting on
the wheel. The direction of the force acting on the WC user in the sagittal plane of the
global reference frame, θ
G
, was allowed to vary to generate θ
R
between 20° and 90°. The
angle describing the medial-lateral component of the force, φ (toward body is positive),
was set to 0 for this study. At each instant in time, the resultant force magnitude needed to
generate the measured tangential force
( )
( )
sin( ( ) ) cos( )
T
mag
W G
F t
F t
t θ θ φ
=
− ×
(3)
63
From the computed resultant force and direction, [Fx Fy] components were computed for
each force (θ
G
) during simulation. For each force angle, inverse dynamics was performed
to determine NJM for the elbow and shoulder and the axial component of the shoulder
NJF. In addition, the sum of the magnitude of net joint moments (total NJM) at the elbow
and shoulder was computed.
| | | |
E S
J τ τ = +
(4)

Figure 22: The resultant reaction force direction θ
R
defined relative to the radial direction at the
location of the wrist. To vary over force directions, F
T
is kept constant while F
R
is varied. F
R
is
modified to generate θ
R
between 20° ° ° ° and 90° ° ° °

θ
W

θ
R

F
T

F
R

64
Simulations
We simulated across all feasible pushrim excursions (0-100%) for a given shoulder
distance. Shoulder distances were varied from maximum feasible distance given pushrim
constraint to a minimum distance of a forearm’s length away from the pushrim.
Kinematics were recalculated for the entire push phase. Inverse dynamics with force
redirection was then performed at all positions and points in time. Results are expressed
as variations in angles of the forearm angle and elbow angle.
Results
Effect of force redirection on elbow and shoulder NJM loading depend on the specific
time interval within the push phase (Figure 23). At time of peak force (vertical line in
Figure 23), minimum elbow and shoulder NJMs occur in more radial RF directions when
comparing modified wrist positions (posterior on the pushrim relative to experimental
configuration). However, at earlier times in the push phase (time = 0.1 second), locations
of minimum shift to more tangential RF directions in the altered condition. Forearm and
elbow angles change with time in different manners.

65

Figure 23: Elbow and shoulder NJM as a function of time and sagittal RF angle θ
R
for experimental (top) vs
modified wrist positions on the pushrim (bottom). RF directions that minimize NJM of each joint change
between cases but also vary as a function of time. Different combinations of forearm θ
F
and elbow θ
E

configurations at each point in push phase may alter specific interpretations. Analysis at time of peak RF is
used but specific trends may vary at different points in time.

Change in forearm angle θ
F
relative to pushrim while keeping elbow angle constant
produces variations in both shoulder distance and wrist angle. At very small angles, the
forearm is more orientated with the radial direction and increases wrist angle (shifts
posteriorly). As forearm angle increases to moderate values, wrist angle decreases as the
wrist is brought more anterior and shoulder distance increases. Further increase in
forearm angle decreases wrist angle (more forward wrist) while shoulder distance begins
to decrease. As forearm angle increases while maintaining elbow angle, minimum elbow,
shoulder, and total NJM occur at increasingly tangential RF directions (Figure 24).
Minimum shoulder NJM remains at RF directions ~35° more radial than for elbow NJM.
Total NJM decreases as forearm angle increases if RF is directed more tangentially.
Shoulder axial NJF increases as elbow angle increases and RF direction shifts radially.

θ
R

θ
R

66
Changes in mechanical demand across RF angles occur because changing forearm angle
at peak force alters configuration of the UE relative to RF and pushrim. At low forearm
angles, RFs that keep moment arms small on the forearm and upper arm are more radially
directed which means larger force magnitudes, and r x F increases. As forearm angle
relative to pushrim increases, RF directions that keep UE moment arms small shift to
more tangential RF directions. Tangential RF directions have lower force magnitudes and
therefore total potential NJM of both joints may decrease.
67

Figure 24: Elbow, shoulder, and total NJM and axial shoulder NJF as a function of RF direction θ
R
and forearm
angle θ
F
relative to pushrim at peak force. Elbow angle θ
E
is kept constant. Effect of RF direction is dependent
on forearm angle. Larger forearm angles shift low moment areas to more tangential RF directions. Black dot
represents experimental position
Elbow angle was varied while forearm angle relative to the pushrim was fixed, and
results at peak force were analyzed. Change in elbow angle while keeping forearm angle
relative to pushrim constant produces variations in both shoulder distance and wrist
angle. Increasing elbow angle decreases wrist angle (more forward wrist) and increases
shoulder distance. As elbow angle increased, there was no change in effect of RF
redirection on elbow NJM while RF direction where minimum shoulder NJM is located
68
shifted from 15° to 40° from the radial direction (Figure 25). The difference in RF
directions which minimize elbow and shoulder NJM decreases with increasing elbow
angle. Total NJM increases then decreases as elbow angle increases. Shoulder axial NJF
increases as forearm angle increases and RF direction shifts radially.
Since forearm orientation relative to the pushrim did not change, there were no changes
in how r x RF alters elbow NJM. The relationship between RF magnitude and direction
relative to the forearm does not change. Elbow NJM distribution acting on the distal end
of the upper arm does not change as elbow angle changes and therefore changes in
shoulder NJM are due to changes in r x RF on the upper arm. Increasing elbow angle
rotates the upper arm into closer alignment with the forearm. RFs directed through or
close to the forearm will now have lower moment arms when acting on the upper arm.

69

Figure 25: Elbow, shoulder, and total NJM, and axial shoulder NJF as a function of RF direction θ
R
and elbow
angle θ
E
at peak force. Forearm angle θ
F
relative to pushrim is kept constant. Effect of RF direction is
dependent on elbow angle. Larger elbow angles shift low shoulder moment areas to more tangential RF
directions. Black dot represents experimental position

At peak force, assuming the subject chooses RF directions which minimize total NJM
loading, total NJM loading is dependent on the interaction between forearm and elbow
angles (Figure 10). As forearm angle increases and elbow angle increases, total NJM load
decreases. Positions that give lower total NJM seat the user lower in the wheelchair and
70
operate and smaller wrist angles. However, such configurations are not feasible with a
pushrim as subjects would have difficulty in grasping the pushrim. In addition, this
assumes the subject can generate a purely tangential RF, which is not feasible unless large
amount of grip force is used. Assuming an effective friction coefficient of μ=1, limit in
RF directions to 45° and lower alters the distribution of total NJM across configurations
(Figure 10). For forearm angles larger than 90-100°, total NJM begins increasing again.
Effect of UE configuration on total NJM at peak force shows that while increasing
forearm angle decreases total NJM, increasing elbow angle also reduces total NJM. When
adding the friction constraint, regions that initially predicted low total NJM now show
high load. The region that shows lowest total NJM post-constraint has forearm angles ~
80° from radial and more extended elbow angles.

71
1
X Y
F F μ
μ
=
=
Shoulder – Pushrim Distance (m)
1
X Y
F F μ
μ
=
=
Shoulder – Pushrim Distance (m) Shoulder – Pushrim Distance (m)

Figure 26: Total NJM at peak force as a function of forearm θ
F
and elbow θ
E
angles, under no constraint (top
left) and a theoretical friction constraint (top right). Relationship between shoulder distance r
S
(bottom left) &
wrist angle θ
W
(bottom right) relative to forearm and elbow angles are also illustrated

Discussion
Repetitive loading during manual wheelchair propulsion may lead to overuse associated
with shoulder injury. Redirection of the hand / rim RF relative to the upper extremity
segments may provide a means to redistribute mechanical load across joints and shift
away from loading associated with pain. Reconfiguration of the UE relative to the
pushrim may affect how RF redirection distributes load. In this study, a 2D inverse
dynamic model using subject-specific experimental tangential component of the RF and
kinematic data was used to perform a sensitivity analysis that varied shoulder / pushrim
72
distance and wrist placement. We calculated elbow NJM, shoulder NJM, and shoulder
axial NJF over a range of RF directions. We found that load distribution is dependent on
the configuration of the upper arm relative to the forearm and UE orientation relative to
the wheel. At peak force, lower shoulder / pushrim distances and more forward wrist
positions on the pushrim allow for more extended elbow positions and more UE /
pushrim alignment. If RF direction is constrained (due to friction, grip strength, etc.)
solutions for redistributing load shift within the solution space. These simulation results
provide mechanically based information to guide clinical interventions that aim to
maintain WCP performance and redistribute load by modifying RF direction, seat
configuration and hand/rim interaction. By advancing our understanding of how elbow
and shoulder loads vary over different RF directions and segment configurations in the
push phase, feasible clinical interventions can be identified and mechanically evaluated
prior to implementation.
Our previous research has shown that RF direction alters the distribution of mechanical
demand across joints and is subject specific and depends on location in the push phase
(Munaretto, 2011). This study takes an additional step to explore how those trends vary
across different configurations involving position of the wheelchair user relative to the
chair. Our results agree with studies that have intimated that optimal RF direction is not
tangential (Desroches et al., 2008, Rankin et al., 2010, Rozendaal and Veeger, 2000, de
Groot et al., 2002, Kotajarvi et al., 2006, Bregman et al., 2008) in many configurations if
we consider total NJM a loose indicator of cost. No other studies have used modeling to
study how RF redirection is affected by alteration in segment configuration. However, the
73
results found in this study can be extrapolated and compared to modeling and
experimental work in literature. Models of various complexity have been used to estimate
optimal RF direction (Lin et al., Rozendaal and Veeger, 2000), muscle forces (Rankin et
al., 2010), strength capacity (Guo et al., 2003), contact forces (Morrow et al., van
Drongelen et al., 2006, Dubowsky et al., 2008), and pushrim radius (Morrow et al.,
2003). Of particular relevance, Richter used a 2D model to study effects of seat height on
elbow and shoulder joint torques (Richter, 2001). His model assumed the RF direction to
be constant, and allowed scaling of force to spread out over different wrist angles. He
found that increasing seat height increased shoulder torque and decreases elbow torque.
Our results also show this when fixing RF direction that is initially more radial in
direction than the forearm. As shoulder height increases, the forearm will have to become
more radial and so its force moment arm will decrease. Higher shoulder will increase
effective moment arm about the upper arm.
Experimental studies looking at seat position have reported mixed findings. Many
variables are not controlled within and between studies, such as height adjustments
relative subject dimensions, weight distribution and wheelchair resistance, type of chair,
propulsion torque, and push frequency (van der Woude et al., 2009). General results
found over several studies include increased RF effectiveness (smaller radial force
component), decreased peak forces, and increased metabolic cost as seat height is
decreased from 100°-120° to 70°-90° (van der Woude et al., 2009, van der Woude et al.,
1989). Our results indicate that as shoulder / pushrim distance decreases (via decreasing
elbow angle and increasing forearm angle) that RF directions which minimize elbow and
74
shoulder NJM shift toward more tangential directions. This result is consistent with the
finding that increased force effectiveness tends to occur at lower positions. When
considering a frictional constraint, our results indicate total NJM to be minimal at
forearm angles slightly less than 90° and elbow angles 100°-120° when focusing on time
of peak force. While experimental findings indicate that lower shoulder positions are
associated with increases in energy consumption, it isn’t clear what the corresponding
load distribution was across seat heights.
Interpretation of this study must be taken carefully in light of the limitations and model
assumptions. The model is 2D which neglects out of plane kinematics and forces yet it
has sufficient complexity to illustrate the sensitivity of joint kinetics to RF direction and
segment configuration. In reality, both kinematics and RF are 3D during WCP. The
general trends in loading distribution as a function of RF direction are expected to be
consistent although more complex when moving to 3D. Future work will examine how
3D kinematics and 3D force affect the distribution of mechanical loading. The RF is
applied directly to the wrist and there may be a difference between the simulated and
actual location of force application. The RF directions at which loading is minimal for
each measure is expected to shift between conditions, yet the general trends represented
in solution space are expected to persist. Assessment of musculoskeletal loading at the
individual muscle level is beyond the scope of this study and is expected to be dependent
on force / length / velocity characteristics specific to each individual WC user. Based on
recent work by (Raina, 2011), the combination of smaller elbow angles and more
tangentially orientated forearm may not be feasible or optimal for particular wheelchair
75
user populations with deficits related to grasp (wheelchair users with tetraplegia). WC
users cannot generate pure tangential RFs without lots of grip strength, which may not be
available given a user’s capacity or at least could be accounted for in loading. Simulation
results incorporating a friction constraint illustrates how important subject specific
constraints need to be used in the interpretation and application of model simulation
results in clinical practice. Simulations without current WCP constraints do have some
benefit as they provide evidence for innovations in wheelchair design. For example, if a
level arm of same length as pushrim radius was used for WCP, the constraint of friction
and forearm angle would be removed and alternative control strategies become viable.
In WC propulsion, mechanical loading is affected by 1) RF direction, 2) relative
orientations of the upper extremity segments (forearm & upper arm, i.e. elbow flexion),
and 3) orientation of the UE relative to the pushrim (forearm relative to tangential
direction). All three mechanisms can alter loading across the elbow and shoulder joints.
In this study, we vary kinematic context #2 and #3 to study their effects on RF direction
and loading distribution. Our results indicate that changing the alignment of the upper
arm relative to the forearm while maintaining forearm angle does not alter NJM across
the elbow but changes how RF direction alters shoulder NJM. Minimal differences in
elbow NJM is to be expected, given how the two degrees of freedom are defined. For
example, if the forearm angle does not change relative to pushrim then for a given RF
direction relative to the pushrim, there will be no changes in elbow NJM since both
moment arm and RF magnitude stay the same. Since elbow NJM acts on the distal end of
the upper arm and is not changing across elbow angles, a change in shoulder NJM must
76
be due to changes in proximal/distal forces acting on the upper arm segment. At a 90°
elbow angle, a RF directed through the forearm will result in a large moments applied by
elbow and shoulder NJFs about the CM of the upper arm, likely requiring a relatively
large shoulder NJM to control the UE. As elbow angle moves closer to either 0° or 180°
in this configuration, the upper arm becomes more aligned with the elbow NJF and
proximal/distal moment arms of the elbow and shoulder NJFs are reduced. The effect of
RF direction on shoulder NJM will be similar as its effect on elbow NJM in these
extremes.
Changes in mechanical demand across RF angles occur because changing forearm angle
alters configuration of the UE relative to RF and pushrim. In WC propulsion the RF
direction and magnitude must generate a specific tangential force component relative to
the pushrim. RFs directed close to radial will generally create high loads regardless of
moment arm magnitudes because RF magnitude needs to be extremely large. At low
forearm angles, RFs that keep moment arms small on the forearm and upper arm are
more radially directed which means larger RF magnitudes, and r x RF increases.
However, if elbow angle is close to 0° or 180°, then moment arms for both forearm and
upper arm could be low enough to withstand the higher RF magnitude. As forearm angle
relative to pushrim increases, RF directions that keep UE moment arms small shift to
more tangential RF directions. Tangential RF directions have lower force magnitudes and
therefore total potential NJM of both joints may decrease, even when elbow angle is
moderate that allows either large moment arm about the forearm or upper arm. Thus,
77
when the UE is orientated more tangentially, a larger variance in elbow angles can be
allowed since the RF magnitude is lower.
When observing total NJM as a function of forearm and elbow configuration, results
agree with the concept that a larger forearm angle reduces loading when allowing the RF
direction to be freely chosen because of the reduction in RF magnitude. At peak force,
simulations indicate that further reduction is found as elbow angle increases. Our results
could only simulate up to 120° elbow angle as it was the maximum angle that would
allow the subject to generate the same range of motion on the pushrim – a constraint in
our simulation. If we allowed larger elbow angles by reducing the necessary ROM on the
pushrim, further reductions in total NJM would be expected. However, large average
elbow angles are unable to be kept across the entire push cycle given the constraints and
geometry of the pushrim. As shoulder distance from pushrim decreases, the elbow must
pass through a larger ROM than if the shoulder was further away. Low elbow angles will
be incurred with large elbow angles. Shorter push phases could remove the low elbow
angle portion of the phase and potentially further reduce total NJM but at the cost of
higher push frequency.
Using an experimentally motivated inverse dynamic model to perform RF direction
sensitivity studies provides clinicians a method to assess current WCP techniques in the
context of mechanical and association with pain / injury and allows for potential testing
of combinations of UE configuration and RF direction which may redistribute load in the
manner desired. For example, if it was desired to keep both shoulder NJM and shoulder
78
NJF at low magnitudes, one could reduce elbow angle and direct the RF in a more radial
direction (Figure 25). If one wanted to keep total NJM low, the subject could operate at
more extended elbow positions (Figure 10). Our results indicate that decisions on how to
shift an individual within a solution spaced must consider the kinematic context of force
generation. The effect of RF redirection on loading is dependent on UE configuration
relative to the pushrim. Experimentally motivated modeling allows us to explore the
“what if” a subject was reconfigured and/or wheelchair design was modified (i.e. level
arm instead of pushrim at same radius). Potential loads could be estimated and compared
to the individual’s torque generating capacity to see if the same strategy would work
across tasks.
79
Chapter 5: Effect of Landing Technique on Regulation of
Momentum of the Center of Mass

Introduction
Impact occurs during many weight bearing activities such as running, jumping, and stair
descent. During impact, the load applied to the body must be distributed so that the
critical limits of tissues are not exceeded and the task objectives are satisfied (e.g. control
of center of mass (CM) relative to the base of support). Satisfying task objectives at the
whole body level requires that linear and angular momentum be regulated during contact
with the environment. Regulation of linear and angular momentum is achieved by
generating linear and angular impulse during a series of phases (e.g. impact phase (IP)
and post-impact phase (PIP) of landing (Figure 27)). The initial conditions of one phase
reflect the interaction between control and dynamics of the body during previous phases
of the task. The nervous system signals the activation of muscles that control the
segments and system trajectory prior to and during interaction with the landing surface.
Understanding the relationship between neuromuscular control, system dynamics, and
loading of the musculoskeletal system is essential in the development of interventions
that aim to improve performance and reduce risk of musculoskeletal injury.

80

Figure 27: Phases of Landing

Successful land-and-stop tasks are achieved by reducing linear and angular momentum at
contact to zero at a time when the CM is within the base of support. To do so without
sustaining injury, experimental evidence indicates that humans and other organisms
prepare for the impending load imposed during the contact during flight phase and reduce
total body momentum over a series of phases. During foot first landings, flight phase
preparations include adjustments in the CM relative to the feet (McNitt-Gray et al.,
2001), segment orientations (McNitt-Gray, 1991), segment velocities (McNitt-Gray et al.,
2001), and coordinated muscle activation (McNitt-Gray et al., 2001, Dyhre-Poulsen et al.,
1991, Jones and Watt, 1971, Mizrahi and Susak, 1982). Landing strategies used by the
individual are thought to be dependent on the state of whole body CM linear and angular
momentum at touchdown, the properties of the surface, and the preferred distribution of
load across structures of the lower extremity. During the post impact phase (PIP), the
remainder of the momentum is reduced to zero and the center of mass (CM) trajectory is
controlled relative to the feet.
81
Landings are goal-directed tasks that involve reducing and/or redirecting the linear and
angular momentum of the body at contact. In some cases, as in athletics, the time
available to reduce or redirect momentum is often constrained. Waiting longer to initiate a
secondary task, as in a softer than normal landing delays the execution of the secondary
task (e.g. athletic land-and-go tasks) resulting in a significant reduction in performance
(McNitt-Gray, 1993, Devita and Skelly, 1992). While a reduction in the impact forces
associated with softer-than-normal landings has been presented as a positive feature in
landing mechanics (Cowling et al., 2003, McNair et al., 2000, Prapavessis et al., 2003,
Pflum et al., 2004, Myers and Hawkins), no causal relationship between peak vertical
force and lower extremity injury has been established nor has the consequence of softer
than normal landing on the post impact phase mechanics and secondary task performance
been fully investigated. From a mechanical perspective, reductions in the vertical reaction
force (RF) during the IP requires that more impulse be applied during the PIP to reduce
the same initial amount of momentum at contact. At the joint level, kinetic measures
reported for softer-than-normal landings can exceed those observed during normal
landings (Mills et al., 2009, Devita and Skelly, 1992, Zhang et al., 2000).
The ability of the individual to regulate reaction forces during contact is dependent on the
state of the body at contact (Schmidt et al., 2003, Hof, 2001). For instance, during a land-
and-stop task, the momentum of the body at contact must be reduced to zero at a time
when the CM is over the base of support. In order to control the CM trajectory and linear
and angular momentum that was not regulated during the IP, individuals must be able to
control the direction and magnitude of the RF during the PIP. Segment configurations at
82
the initiation of the PIP were expected to affect the ability of the individual to control the
RF relative to the CM. Specifically, differences in segment kinematics at the initiation of
the PIP were hypothesized to affect the ability of the individual to 1) regulate the CM
relative to the feet to maintain balance, particularly when encountering an unexpected
event and 2) reduce or redirect momentum during the performance of the secondary task.
Simulating landing mechanics over a range of segment configuration and momentum
conditions at the initiation of the PIP is expected to provide a better understanding of the
implications of control decisions made during the flight and impact phases of landing on
the ability to regulate momentum during the PIP.
Modeling how an individual prepares for and controls RF during landings allows us to
simulate hypothetical conditions and systematically modify variables that cannot be
manipulated experimentally. Dynamic models of varying complexity have been used to
study the behavior of the human body during landing. Previous models have represented
the human body as a point mass (Kingma et al., 1995), an inverted pendulum (Nakawaki,
1999), and a mass-spring-damper system (McMahon and Cheng, 1990, Farley and
González, 1996). Multi-segment models have also been developed (Gruber et al., 1998,
Mills et al., 2009, Pain and Challis, 2006, Wilson et al., 2006, Yeadon et al., 2006,
McNitt-Gray et al., 2006, Requejo et al., 2002, Requejo et al., 2004) to capture multijoint
movements. The foot-surface interaction during landing tasks has been modeled by
simply attaching the foot/ankle to the floor (Amirouche et al., 1990, Mochon and
McMahon, 1980, Yang et al., 1990, Chou et al., 1995), then by using a viscoelastic
elements with a few (Gerritsen et al., 1995, Gruber et al., 1998, Guler et al., 1998, Lo and
83
Ashton-Miller, 2008) to as many as 10 parameters (Gittoes et al., 2006, Wilson et al.,
2006). The difficulty in reproducing RFs with a validated foot surface model has led
many to incorporate passive wobbling masses in the shank, thigh, and torso segments to
reduce RFs (Alonso et al., 2007, Gittoes and Kerwin, 2009, Gruber et al., 1998, Mills et
al., 2009, Nigg and Liu, 1999, Pain and Challis, 2006, Wilson et al., 2006, Yeadon et al.,
2006, Zadpoor et al., 2007). To investigate how system dynamics and momentum control
change under a variety of conditions (see (McNitt-Gray, 2000) for a review), an
experimentally validated, torque driven model will be used to simulate impact and post
impact phases of landings.
The purpose of this study is to determine the effect of the kinematic conditions at contact
on the ability to regulate the reaction force and control linear and angular momentum of
the CM during the post impact phase. We hypothesize that change in segment orientation
at contact will 1) alter peak reaction forces (RF) and amount of impulse generated during
the impact phase (IP), 2) change ability to redirect the RF and generate impulse during
the post impact phase (PIP), and 3) alter the mechanical demand imposed on the lower
extremity (net joint moments (NJM)) and ability to satisfy mechanical objectives of the
task. Forward simulations, using an experimentally validated multi-link dynamic model,
will be used to test these hypotheses.
84
Methods
Overview
The modeling approach used to study modifications in landings will incorporate a 2D
whole body dynamic model that interacts with a visco-elastic foot / surface model. The
model will initially be driven with PD joint controllers tracking experimental joint angle
and angular velocity-time data, and validated by adjusting initial conditions and surface
parameters to get best agreement in a number of measures, including CM kinematics,
ankle displacement, and ground RF. After validation, modified simulations will occur by
altering initial conditions in the flight phase (shank angle, knee and hip angles) and
simulating over a span of ankle / knee / hip joint torques during the PIP.
Equations of Motion
The human body during contact with a rigid, flat surface is modeled using a seven
segment (foot, forefoot, shank, thigh, torso, arm, and head) 2D planar model with
revolute joints. The model is similar to that experimentally validated and developed by
Requejo (Requejo et al., 2004, Requejo, 2002) with the addition of a forefoot segment
(Gittoes et al., 2006, Wilson et al., 2006). The number of segments needed to adequately
represent the CM trajectory was based on sensitivity studies (Requejo et al., 2002) using
dynamic models varying in complexity. The inclusion of the head and arm segments
improves the kinematic data and provides sufficient complexity to determine the role of
the head and arm motion when preparing for contact and when regulating the CM
trajectory relative to the feet during contact. For this study, the addition of the forefoot
85
was found to significantly affect the ground reaction force during the IP and is need for
realistic impact forces (Yeadon et al., 2006).
The dynamic model was represented by generalized coordinates
1
q -
9
q . Coordinates
1
q -
3
q represented the ankle x position, ankle y position, and shank angle in global space,
respectively. The coordinates
4
q -
9
q .represented the relative joint angles between other
links as shown (Figure 28).

Figure 28: Multi segment rigid body model including foot, forefoot, shank, thigh, torso, arm, and head segments

Application Lagrange's formulation to the above model yields a set of nine second-order

differential equations in matrix form as follows:

∂  
+
 
∂
 
M(q)q + V(q,q) + G(q) = Q λ
q
&& &
T
f
P

Equation 16

86
where M(q) is an 9 x 9 mass matrix, V(q,q) & is an 9 x 1 vector representing centrifugal
and Coriolis terms, G(q) is an 9 x 1 vector of gravity terms, Q is a 9 x 1 vector of
generalized forces, λ is a 2x1 vector representing the reaction constraint force at the
foot/surface interface, and
∂  
 
∂
 
q
f
P
is a 2x9 matrix denotes the Jacobian of constraint
equation expressed with respect to the generalized coordinates. In our case ( )
f
P q is the
equation of the contact surface position in space.

Experimentation
One male recreational athlete (age = 27, height = 182 cm, mass = 84 kg) performed two
land-and-stop landings using their normal and their self-selected softer-than-normal
landing strategies. The participant provided informed consent in accordance with the
Institutional Review Board. The subject warmed up and practiced the experimental tasks
prior to data collection until they were familiar with the experimental set up. The subject
then initiated the landing tasks by stepping forward from a 0.5 m box and landed with
each foot fully supported by a rigid force plate. During the performance of each task,
sagittal plane kinematics (200 Hz, C
2
S) and reaction force (0.6 x 0.9 m
2
, 1200 Hz,
Kistler, Amhurst, MA, USA) were simultaneously collected and synchronized with the
kinematics data. The landing area was calibrated using a calibrated object with reflective
markers located one meter apart and video taped using a stationary camera (C
2
S, NAC
Visual Systems, Burbank, CA, USA). Body landmarks on the side of the body closer to
87
the camera were manually digitized (Peak Performance, Inc., Englewood, CO, USA).
Raw coordinate data were filtered using fifth order splines (Woltring, 1986) with a cutoff
frequency of 15 Hz for position data, 10 Hz for velocity data, and 5 Hz for acceleration
data. Coordinate data used for differentiation needed to be filtered with lower cutoff
frequencies to avoid reducing signal to noise ratio (Giakas and Baltzopoulos, 1997).
Body segment parameters based on an athletic population (de Leva, 1996) were
combined with the sagittal plane coordinate data and used to estimate segment and whole
body CM kinematics. Segment angles relative to horizontal were calculated using filtered
coordinate data and joint angles were calculated as the difference in segment angles (Fig
1). First and second derivatives of angle data were calculated from differentiation of
angle position splines.
Model Inputs
The seven segment forward dynamics model of the human body was constructed using
ADAMS (Mechanical Dynamics, Ann Arbor, Michigan, USA). Body segment
parameters, segment lengths, joint initial conditions (angular positions and velocities) and
joint acceleration time histories were input into the model (Fig 1). Simulations were
initiated 100 ms before contact. Simulations are terminated at 600 ms when experimental
CM velocity was reduced to zero. Simulations for validation were driven with
proportional / derivative (PD) controllers that produced torques in proportion to
simulated error in joint angles (
4
q -
8
q ) and angular velocities (
4
q & -
8
q & ) for each joint ‘j’
(Equation 17). The stiffness and damping constants were set high for the shoulder and
88
neck to match exactly with experimental, while the ankle, knee, and hip constants were
adjusted to track well but allow some give, especially for the impact phase (Table 3). The
final DOF, the metatarsal joint, was driven with a torsional spring with stiffness 1 Nm /
deg and damping 0.1 Nm / (deg/s).

( ) ( ) ( ) ( ) ( )
EXP EXP
j j j j j j j
t k t t b t t τ θ θ θ θ     = − + −
   
& &

Equation 17
89

Table 3: Ankle, knee, and hip PD tracking coefficients

Driving the simulation by PD tracking joint motions at this stage of model development
allowed us to quickly and simply simulate modifications in landing technique. This
simulation approach reduced the amount of computation time needed as the model was
more stable than if it had been driven with open loop torques. After validation, the
simulations in the PIP were switched to open loop torques to explore all potential
solutions.
Foot / Surface Model
The interaction between the foot/shoe and surface determined the behavior of the final
three degrees of freedom (q1-q3). The foot segment was represented as a rigid body in
the shape of a triangle with vertices acquired from the metatarsal, ankle, and heel
coordinates. The vertical foot/surface interaction was modeled using a nonlinear spring /
damper model (Gruber et al., 1998, Guler et al., 1998) and horizontal force using
Coloumb friction (Gerritsen et al., 1995). Three points of force application were located
at the heel, toe, and 5
th
metatarsal (Figure 29). The horizontal and vertical component of
the reaction force, Fx and Fy respectively, were computed as follows:

k (Nm / deg) b (Nm s / deg)
Ankle 1 2
Knee 10 2
Hip 10 2
90
2.5
-1
2
-
tan (100 )
x
y y f y f f
y f
F F
F C y D y y
x μ
π
=
= &
&

Equation 18

where
f
y is the vertical coordinate of each location on the foot,
f
x & and
f
y & are the
respective velocities, μ is Coulomb friction constant and set to 1, and C
y
and D
y
are the
vertical stiffness and damping constants (Equation 18). The inverse tangent function is
used as a continuous function proxy for determining the direction of the horizontal
velocity. These equations are implemented at the toe, metatarsal, and heel.
μ = Coulomb friction coefficient
C
y,
,D
y
=vertical stiffness, damping
-1
2
tan (100 )
x y f
F F x μ
π
= &
2.5
-
y y f y f f
F C y D y y
π
=
&
μ = Coulomb friction coefficient
C
y,
,D
y
=vertical stiffness, damping
-1
2
tan (100 )
x y f
F F x μ
π
= &
2.5
-
y y f y f f
F C y D y y
π
=
&

Figure 29: Visco-elastic model of foot/surface interaction
Validation
Dynamic Optimization Criteria
Experimental data acquired during both the normal and softer-than-normal landings
performed by the same participant were used in the validation process. First, the softer
landing was used in determination of the foot / surface properties. Initial values for C
y

91
and D
y
were set from literature (Gruber et al., 1998) but adjusted down an order of
magnitude to accommodate for athletic shoes worn by the participant. Next, simulations
were performed to optimize the following cost function:

ˆ | |
ˆ | |
i i
i
i
n
i i
i
x x
J
x
J w J
−
=
=
∑

Equation 19: Generic cost function used to optimize foot – surface parameters while minimizing error between
chosen simulated and experimental measures

where n is the number of variables in the cost function, J
i
is the normalized cost of an
individual variable,
i
x is the simulated variable, ˆ
i
x is the experimentally measured
variable, and w
i
is the weighting giving to each variable (Equation 19). Variables included
in the cost function are CM linear and angular momentum, segment orientations, and
ankle displacement. Optimization parameters were the initial linear velocities at the ankle
and shank angular velocity (
1
q & (0)-
3
q & (0)), and stiffness and damping parameters C
y
& D
y
.
Translational velocities were allowed to vary +/- 0.5 m/s and angular velocity was
allowed to vary +/- 30 deg/sec. All variances were within a reasonable range due to
segment and coordinate tracking error. Based on calculations using calibration
information, one pixel error gives 0 0055 . m ± and 1 105 . m s ± / at 200 Hz.

Viscoelastic Parameters
Vertical Stiffness (N/m^2.5) 4.34E+07
Vertical Damping (N s/m^2) 5.77E+05
mu 1

Table 4: Final visco-elastic surface parameters used in simulation

92
Evaluation
Visco-elastic parameters determined from optimization with the softer-than-normal
landing were then used in simulation with the normal landing trial (Table 4). Initial
conditions were optimized for the normal trial as the softer-than-normal landing trial
without variation in foot-surface parameters. RMS error was used to quantify the level of
agreement between simulated and experimental measures

[ ]
2
1
( ) ( )
n
SIM EXP
i
f i f i
Error
n
=
−
=
∑

Equation 20
(1)

where f is the given measure, ‘SIM’ is the model calculated result, ‘EXP’ is the measured
result, and n is the number of samples in the trial. Model validation procedures gives
reasonable match between the simulated and measured reaction forces (Figure 30) and
other pertinent measures (Table 5).

93

Figure 30: Match between simulated and measured reaction forces for normal landing

RMS Error Units
Fx 199.8 N
Fy 683.2 N
V CM X 0.14 m/s
V CM Y 0.18 m/s
Shank Angle 1.48 deg
Thigh Angle 11.63 deg
Ankle Y 3.4 N m s
CP X 0.04 m/s

Table 5: RMS error between simulated and experimental measures of ground reaction force, CM velocity,
shank and thigh angles, ankle vertical position, and horizontal center of pressure excursion

Modified Simulations
While validation simulations were driven with tracking PD controllers, modified
simulations use a series of different torque control (Figure 31). Tracking PD control
(PDT) was used in flight as in the validation simulations. Standard PD control (PDS) was
used during IP to allow for modified kinematics. Open loop (OL) torques were used
94
during PIP to explore a solution space sensitivity to different ankle / knee / hip torque
combinations.
Flight Impact Post Impact
PDT PDS
OL
Flight Impact Post Impact Flight Impact Post Impact
PDT PDS
OL

Figure 31: Tracking PD control was used in flight, standard PD control used during impact phase, and open
loop torques used during post impact phase

Modified Initial Conditions

Forward Tipping
Global initial conditions simulating slight off balance were created by altering q
3
(shank
angle) -2 degrees.

Modified Impact Phase Preparation
To simulate modified landings, changes in initial segment configuration were used.
Modified segment configuration was implemented by changing the knee and hip angles
just before contact. This was performed by modifying the experimental joint angle data
and using the PDT control in the flight phase. This method guarantees conservation of
CM linear and angular momentum across modifications before contact. Adjustments of
up to +/- 15 degrees were made to knee and hip angles. Knee and hip angles were
95
adjusted together so that horizontal CM velocity was kept approximately constant across
simulations at the end of the IP, while vertical CM velocity changes.
Flight Phase:
Modify Initial Orientation (Tip forward)
Impact Phase:
Modify Knee / Hip Position (Stiff / Soft Landing)
Post Impact Phase
Modify Ankle / Knee / Hip Torques
Flight Phase:
Modify Initial Orientation (Tip forward)
Impact Phase:
Modify Knee / Hip Position (Stiff / Soft Landing)
Post Impact Phase
Modify Ankle / Knee / Hip Torques
Flight Phase:
Modify Initial Orientation (Tip forward)
Impact Phase:
Modify Knee / Hip Position (Stiff / Soft Landing)
Post Impact Phase
Modify Ankle / Knee / Hip Torques

Figure 32: Flow Diagram depicting all potential simulation modifications. In flight, initial orientation of the
whole body (q3(0) ) may be altered 1 deg back or 2 deg forward. At the beginning of the impact phase, knee and
hip joint angles may be flexed / extended +/- 15 deg to create softer and more rigid landings. Finally, open loop
ankle / knee / hip torques are varied to examine potential scenarios of impulse generation

Modified Impact Phase
To simulate different IP dynamics, first we altered the torques from tracking (Equation
17) to standard PDS controller at the knee (Equation 21). The PDS controllers produced
torques as a proportion of error between simulated angles and angle at contact and
angular velocities relative to zero joint angular velocity. Instead of simply implementing
a similar controller at the hip, we incorporated experimental evidence of coordination
between the knee & hip. Experimental knee and hip angles indicate a 1:1 relationship in
angle changes. We assume that when landing more or less rigid, this coordination will be
essentially maintained. As such, we implemented a PD controller at the hip that
incorporates both knee and hip measures (Equation 22). Stiffness and damping
96
coefficients for the controllers were kept constant across all modified simulations (Table
6). Simulations then ran with the perturbed initial conditions in flight and PDS torques
until the beginning of the PIP. Here, PDS torques were turned off via a logistic function
that reaches 95% of maximum in 0.1 seconds.

( ) ( ( ) ( )) ( )
j j j j C j j
t k t t b t τ θ θ θ = − +
&

Equation 21

( ) ( ( ) ( )) ( ( ) ( ))
H H H K H H K
t k t t b t t τ θ θ θ θ = − + −
& &

Equation 22

Stiffness Damping
Knee 2 0.2
Hip 20 3

Table 6: Stiffness and damping coefficients for PD controllers at the knee and hip during modified simulations

PIP Torques
Open loop torques were then used for the PIP. Concurrent with the attenuation of the PDS
torques at the end of the IP, open loop torques were activated using a logistic function
that reaches 95% of the desired torque level in 0.1 seconds. Rise time to peak torque of
100 ms was used based Bobbert (Bobbert and Van Zandwijk, 1999). Maximal flexor /
extensor torques for ankle, knee, and hip were take from Anderson (Anderson et al.,
2007) with bodyweight of 84 kg and height of 1.82 m.

Table 7: Maximum flexor and extensor torques of ankle, knee, and hip used during open loop simulation
Max Torque Ankle Knee Hip
Flexor 49.2 129.8 168.5
Extensor 141.7 243.1 240.13
97
Simulations were performed across various combinations of ankle, knee, and hip torques.
Intervals were at 1/6 of the range between max flexor and extensor torque, to yield 7
possible torque values, and yield 343 possible combinations.
Post Processing
While all simulations were allowed to run for 400 ms, many will end up in unrealistic
configurations earlier. The following constraints were used to cut data 1) Force reduced
to 0 2) Rate of force production > 25000 N/s 3) Knee and hip angles greater than 170° or
less than 10° 4) Knee and hip angular velocities greater than 400 deg/s. Only data before
a constraint is reach are used.
Results
Modifications at Contact
Change in the amount of leg extension at contact alters peak vertical impact forces and
the amount of momentum reduced during the IP (Figure 33). As knee and hip joints are in
more flexed positions at contact, peak vertical force decreases and change in vertical
velocity during IP decreases.
98
Change in Vertical Velocity (m/s)
Peak Vertical Force vs Lower
Extremity Configuration
Change in Vertical Velocity of CM
vs Lower Extremity Configuration
Change in Vertical Velocity (m/s)
Peak Vertical Force vs Lower
Extremity Configuration
Change in Vertical Velocity of CM
vs Lower Extremity Configuration

Figure 33: Peak vertical force (Fy) and change in vertical velocity during the IP vs amount of leg extension at
contact. More flexed positions reduce whole body rigidity and consequently lower the magnitude of the peak
vertical force during impact and the amount of reduction in downward velocity of the center of mass during the
IP.
Force Generation at Beginning of PIP
Segment configuration at the beginning of the PIP (80 ms) affects the ability to generate
reaction forces during PIP (Figure 34). Higher vertical reaction forces can be generated
during the PIP from more extended joint positions than in more flexed joint positions.
More horizontal segments increase moment arms relative to vertical reaction forces and
net joint forces, so larger joint torques are needed to generate the same vertical force
magnitude than in a more upright position. As segments approach vertical alignment, the
ability to generate vertical reaction forces again decreases. While vertical force moment
arms decrease, upright segment orientations restrict further vertical acceleration. The
effect on horizontal force generation is less clear, as force generation in the horizontal
99
direction is dependent both on segment configuration / moment arms as well as vertical
force magnitude.

Figure 34: Potential ground reaction force functional force space (FFS, green) reflecting all possible force
magnitudes and directions derived from all ankle/knee/hip torque combinations for each landing condition (blue
segments) at 80 ms into the PIP. Segment configuration and velocities were found to affect the ability to generate
the reaction force magnitude, direction, and the moment about the CM.

Impulse Generation
Kinematic configuration at the beginning of the PIP also affects the ability to generate
linear and angular impulse during PIP (Figure 35). After 80 ms, more upright postures
generate more vertical, negative horizontal, and angular impulse than more flexed
landings. After 160 ms, impulse generation increases in all cases, with the normal flexion
landing now generate the most impulse. After 240 ms, the more flexed landing generates
the most impulse, especially in the horizontal direction. More flexed positions can
generate more impulse when more time is available.

100
Change in Angular Momentum (N m s)
80 ms 160 ms 240 ms
Change in CM Vertical Velocity (m/s)
Change in CM Horizontal Velocity (m/s)
Change in Angular Momentum (N m s)
80 ms 160 ms 240 ms
Change in CM Vertical Velocity (m/s)
Change in Angular Momentum (N m s)
80 ms 160 ms 240 ms
Change in CM Vertical Velocity (m/s)
Change in CM Horizontal Velocity (m/s)

Figure 35: Potential impulse generation after 80 ms, 160 ms, and 240 ms into PIP for three land-and-stop tasks
(8º less flexed (top graph), normal (middle), and 8º more flexed (bottom)). Horizontal, vertical, and angular
impulse generation are described by changes in CM velocities when scaled by bodyweight / inertia. The more
upright segment configuration at the beginning of the PIP (top, blue segment configuration) can produce more
impulse in a shorter time span, whereas the more flexed position (bottom) can generate more impulse with a
longer time span. Changes in angular momentum during this type of land-and-stop task are more dependent on
the potential to generate horizontal impulse than on vertical impulse.

101
Maximum vertical impulse is generated by the combination of maximum ankle, knee, and
hip extensor torques (Figure 36). Change in magnitudes of knee and hip torques changes
the direction of linear impulse generation as well as direction of angular impulse. Positive
angular momentum generation is associated with forces directed anterior to the CM via
less knee extensor torque, while negative angular momentum is associated with forces
directed posterior to the CM via less hip extensor torque.

Figure 36: Knee, hip, and ankle torques and change in angular momentum vs change in CM horizontal and
vertical velocity after 160 ms in PIP. Extensor torques generate the largest combination of horizontal and
vertical changes in CM velocity. Positive angular momentum generation is associated with reaction forces
directed anterior to the CM via less knee extensor torque, while negative angular momentum is associated with
forces directed posterior to the CM via less hip extensor torque.
(Nm)
(Nm) (Nm)
(kg m/s)
102
Time to reduction of linear momentum of the CM increases with landings with greater
joint flexion when body is tipped 2 degrees forward at contact (Figure 37). The forward
tip shifts horizontal velocity from zero to about 0.2 m/s at the beginning of the PIP. After
120 ms, both the most flexion and normal flexion configurations have the capability to
reduce both horizontal and vertical velocity components. The most flexed landing, due to
higher negative velocity at the start of the PIP takes until 160 ms to reduce momentum.
The direction of impulse generation needed to reduce CM momentum to zero also
changes across landing styles. Impulse generation must be directed more vertically as
landings become more flexed. Ability to generate horizontal impulse may be limited
when required to operate in the most vertical portions of the velocity space. In addition,
different torque sets may be required for different impulse directions. The more flexion
landing may use more equal contributions of hip and knee extensor torques, while less
flexion landings may use more knee extensor and possible hip flexors to reduce linear
momentum to zero (Figure 36). Mapping back onto the PIG curve (Figure 35), the
combination of more upright postures (bigger moment arm between CM and foot) and
directing impulse and forces more posterior (same horizontal but less vertical) may
increase angular impulse. Contrastingly, landings with greater joint flexion reduce
moment arm between CM and foot and also need to direct force / impulse less posterior
(same horizontal, more vertical) which could keep angular impulse generation lower.

103
160 ms
Absolute Angular Momentum (N m s)
80 ms
120 ms
Absolute Horizontal Velocity (m/s)
Absolute Angular Momentum (N m s)
Absolute Vertical Velocity (m/s)
160 ms
Absolute Angular Momentum (N m s)
80 ms
120 ms
Absolute Horizontal Velocity (m/s)
Absolute Angular Momentum (N m s)
Absolute Vertical Velocity (m/s)

Figure 37: Feasible combinations of absolute velocities after 80 ms, 120 ms, and 160 ms into PIP for three
landings (8º less flexion, normal, 8º more flexion) with a 2 degree forward tip. The forward tip shifts CM
horizontal velocity from 0 to 0.2 m/s, which must be reduced to zero in addition to reducing vertical velocity to
zero and keeping angular momentum low. While all three configurations can reduce horizontal velocity after
120 ms, the more flexion landing cannot yet reduce vertical velocity to zero. After 160 ms, all three cases have
reduced linear momentum to zero. The direction of impulse generation (arrows) needed to reduce moment
changes across landing styles

104
Landings that initiated the PIP with greater joint flexion required increases in mechanical
load (NJM) across the knee and hip in the PIP than landings with less joint flexion.
Assuming that task specifications require that time required to reduce the CM velocity to
zero remains the same, landings with greater joint flexion during the IP will require
greater knee and hip NJMs during the PIP to satisfy task objectives at the total body level
(Figure 38). The increase in mechanical demand imposed on the knee and hip during
landings involving more joint flexion reflects the need to generate more vertical impulse
when in more flexed joint positions (increase in moment arms of ankle, knee, and hip net
joint forces) during the PIP.

Absolute Horizontal Velocity (m/s)
Absolute Vertical Velocity (m/s)
Total Absolute Knee+Hip NJM (N)
Absolute Horizontal Velocity (m/s)
Absolute Vertical Velocity (m/s)
Total Absolute Knee+Hip NJM (N)
Absolute Horizontal Velocity (m/s)
Absolute Vertical Velocity (m/s)
Total Absolute Knee+Hip NJM (N)

Figure 38: Sum of absolute knee + hip torques at all feasible combinations of horizontal and vertical velocity at
160 ms in PIP for three landings (8º less flexion, normal, 8º more flexion). Line indicates zero vertical velocity. In
order to reduce vertical velocity at 160 ms, landings with greater joint flexion have to use increasingly higher
levels of knee and hip torque.

Discussion
Impact occurs in many weight bearing activities. How load is distributed during the
impact phase may affect ability to reach task goals in the post impact phase. In this study,
an experimentally-validated torque-driven multisegment model was developed to
105
determine how modifications in landing strategies affect reaction force regulation during
the impact phase and the potential for impulse generation and balance regulation during
the post impact phase. Simulation results indicate that more flexed configurations at
contact decrease peak force and amount of total body momentum reduced during IP,
increases joint flexion at beginning of PIP and ability to generate impulse, and increases
either time to reduce CM momentum or mechanical demand during PIP. Regulation of
horizontal and angular impulse generation via force redirection relative to the CM during
the post impact phase of landings involves multijoint coordination of the ankle/knee/hip
torques. Simulation results from this study provide quantitative evidence that control
implemented during flight and impact phases affects the ability of achieve task objectives
during the post-impact phase. The findings emphasize the need to consider the
implications of landing control strategies on the mechanical objectives in each phase of
the landing task.
Lower extremity segment configuration alters the ability to generate reaction forces. In
general, segments aligned with the RF and NJF reduce the magnitude of the proximal and
distal moments generated about the segment CM and often require relative small NJMs to
control segment motion. During landings that involve substantial vertical displacement of
the CM (softer-than-normal landings), deeper squat positions are achieved and
consequently the shank, thigh, and torso segments become more horizontal than in more
rigid landings. In these deeper squat positions, individuals often have difficulty
generating vertical reaction forces in this kinematic context (e.g. muscles at relatively
long lengths, proximal and distal moments generated by the NJFs are relatively large). In
106
contrast, in more upright segment configurations (e.g. segments essentially vertical) the
ability to generate vertical force is also compromised in that further vertical displacement
of the CM positions is limited. Effect of segment orientations on horizontal force
production is less clear, as horizontal force generation is partially dependent on
generating sufficient vertical force to avoid slipping at the foot/surface interface (friction
properties).
More flexed knee and hip joints increase impulse generation in longer durations but
decrease impulse generation in shorter time durations (Figure 35). More extended joints
allow for high forces to be generated immediately, while lower positions initially
generate lower force but have more time and distance to generate impulse. Lower
positions have been found to generate higher velocities in models optimizing squat
(Domire and Challis, 2007, Van Soest et al., 1994) and countermovement (Bobbert et al.,
1996) jump heights. This study differs from jumping studies in that landings require a
high amount of downward vertical velocity to be reduced at some point either during the
IP or PIP. More flexed landings generate less impulse during IP and have higher
downward velocities when starting the PIP. Larger downward velocities of the CM may
compromise an individual’s ability to generate sufficient impulse to slow down the CM
before undesirable segment configurations occur.
In this study, we found that landings with greater joint flexion increased time to reach
task goals or increased mechanical loading. Simulation results are consistent with
findings that landings with greater joint flexion have longer contact phases (i.e. require
107
more time to reduce vertical CM to zero (McNitt-Gray, 1993, Devita and Skelly, 1992)).
More flexed landings cannot generate velocity quickly and also have more residual
downward velocity to reduce. Conversely, if time to reduce momentum is constrained
then more flexed landings require larger moments because 1) more impulse is required
and 2) segments are more horizontal which increases moment arms. While landing more
flexed at contact may have benefits reducing peak forces during the impact phase, the
performance and loading effects in the post impact phase must also be considered.

108
Chapter 6: Effect of Modified Coordination on Momentum
Generation in Springboard Diving

Introduction
During weight bearing activities, the linear and angular momentum of the body are
regulated during a series of phases. The initial conditions of one phase reflect the ongoing
interaction between the nervous system, musculoskeletal system and the environment
during previous phases of the task. During foot first landing tasks, the nervous system
activates sets of muscles to control segment motion, system trajectory, and the reaction
force prior to and during contact with the landing surface. The transformation of these
neural commands into muscle forces depends on the state of the musculoskeletal system
including muscle length, velocity, and capacity to generate muscle force. The net effect of
these muscle forces ultimately results in a reaction force (RF) and whole body center of
mass (CM) trajectory that satisfies both the linear and angular impulse requirements of
the landing phase of the task (Bobbert and van Ingen Schenau, 1988, Hamill, 1985,
Ridderikhoff et al., 1999, Miller, 1990, Miller, 1989, Miller and Munro, 1984).
When interacting with a compliant landing surface, the duration of the contact phase
tends to increase allowing for multiple mechanical objectives to be achieved during
interaction with the surface. In the case of a forward somersault dive in springboard
diving, the vertical, horizontal, and angular momentum at departure are achieved during
board depression (BD) and board recoil (BR) portions of the contact phase (Figure 39).
At initial board contact following the hurdle, the diver initiates contact in a squat position
109
and depresses the board while maintaining their center of mass (CM) over the base of
support (feet). During board recoil, the diver regulates the reaction force relative to the
CM to generate the linear and angular momentum at board departure required to achieve
forward somersault during the subsequent flight phase. An increase in CM vertical
velocity at board departure provides the diver with more time to complete the forward
somersault and prepare for water entry. An increase in the angular momentum at board
departure allows the diver to complete the necessary somersaults with time to slow the
rate of body rotation and prepare for water entry. Experimental evidence indicates divers
have difficulty increasing vertical impulse generation without sacrificing angular impulse
generation, or vice versa (Miller, 2001).
Previous experimental research has identified several factors that may contribute to
improvement in overall dive performance (Miller and Munro, 1984, Miller, 2001).
During flight phase prior to initial board contact, the velocity of the CM, orientation of
the CM relative to the base of support, and the degree of lower extremity flexion (i.e.
how deep of a squat) are hypothesized to increase the diver’s ability to increase impulse
generation during board contact. Larger CM vertical velocity at initial board contact is
expected to contribute to added board depression and higher vertical velocities at board
departure. Maintaining the CM over the base of support as joints extend during board
deformation is expected to simplify control related to balance regulation. Utilization of
residual lower extremity joint extension during board recoil is expected increase the
diver’s ability to redirect the reaction force posterior to the CM thereby contributing to
additional forward angular momentum at board departure.
110

Figure 39: The take-off phase of a forward somersault performed from a springboard. The diver initiates board
contact (A) following the hurdle with forward CM horizontal velocity and downward CM vertical velocity.
During board depression phase (B), the diver extends the knee and hip to depress the board while maintaining
CM over the base of support (balance). During board recoil (C), the diver moves upward while redirecting the
reaction force (RF) posterior to the CM to generate forward angular impulse required for successful
performance of a forward somersault dive.

The benefits of proposed control modifications at contact, during board depression, and
board recoil on the generation of both linear and angular impulse in a forward
somersaulting task are difficult to determine experimentally. Previous research involving
simulation using dynamic models of the human body has been helpful in determining
optimal timing of lower extremity and shoulder torques during board contact (Cheng et
al., 2008, Cheng and Hubbard, 2005, Cheng and Hubbard, 2004, Miller, 2001, Yeadon et
al., 2006). The purpose of this study was to use model simulation results to determine
how modifications in multijoint control during the take-off phase of a forward somersault
affects the mechanical demand imposed on the knee and hip during board contact and the
V H ←
V V ↑
H
V H ←
V V ↓
H ~ 0
Flight
Board
Depression
Board
Recoil
Departure
111
ability of the diver to regulate the reaction force relative to the CM. Results from these
simulations were used to test the following hypotheses:
1. Increasing initial body tip forward (CM relative to feet) is hypothesized to reduce CM
vertical velocity but increase angular momentum at departure
2. Larger downward CM vertical velocity and deeper squat positions at initial board
contact are hypothesized to result in greater board depression, higher CM vertical
velocities at board departure, and greater mechanical demand imposed on muscles
controlling the knee and hip (net joint moments (NJM)).
3. Utilization of residual lower extremity joint extension during board recoil is
hypothesized to increase the diver’s ability to redirect the reaction force (RF) posterior to
the CM thereby contributing to additional forward angular momentum at board departure.
Methods
Overview of Modeling Approach
The modeling approach used to study modifications in springboard diving uses the same
human body model as in the landing model with the exception that the foot is modeled as
a single rigid segment. This representation of the foot during springboard diving is
consistent with the experimental kinematic data acquired during dive performance. A
model of the springboard is added as an additional component to represent the
deformable surface. Modifications in springboard coordination are achieved by
modifying spline knots of knee and hip joint motions. The model was validated by
112
adjusting initial conditions and springboard parameters to obtain the best agreement in a
number of measures, including CM kinematics and segment kinematics. Simulation
results using the validated model were obtained by systematically modifying initial
conditions at board contact as well as knee and hip joint motions throughout the flight,
BD, and BR phases.
Equations of Motion
The equations of motion are developed in the same formulation as in the landing
experiment. The human body during contact with a rigid, flat surface is modeled using a
six segment (foot, shank, thigh, torso, arm, and head) 2D planar model with revolute
joints. The model is similar to that developed by Requejo (Requejo et al., 2004). The
number of segments needed to adequately represent the CM trajectory was based on
sensitivity studies (Requejo et al., 2002) using dynamic models varying in complexity.
The inclusion of the head and arm segments improves the kinematic data and provides
sufficient complexity to determine the role of the head and arm motion when preparing
for contact and when regulating the CM trajectory relative to the feet during contact.
The dynamic model was represented by generalized coordinates
1
q -
8
q . Coordinates
1
q -
3
q represented the ankle x position, ankle y position, and shank angle in global space,
respectively. The coordinates
4
q -
8
q .represented the relative joint angles between other
links as shown (Figure 40).

113

Figure 40: Diagram of human model represented with generalized coordinates q
1
-q
8.

Application Lagrange's formulation to the above model yields a set of eight second-order
differential equations in matrix form as follows:
∂
 
+
 
∂
 
M(q)q + V(q,q) + G(q) = Q λ
q
&& &
T
f
P

Equation 23

where M(q) is an 8 x 8 mass matrix, V(q,q) & is an 8 x 1 vector representing centrifugal
and Coriolis terms, G(q) is an 8 x 1 vector of gravity terms, Q is a 8 x 1 vector of
generalized forces, λ is a 2x1 vector representing the reaction constraint force at the
foot/surface interface, and
∂  
 
∂
 
q
f
P
is a 2x8 matrix denotes the Jacobian of constraint
equation expressed with respect to the generalized coordinates. In our case ( )
f
P q is the
equation of the contact surface position in space.
114
Experimentation
One male Olympic level diver volunteered to participate and provided informed consent
in accordance with the Institutional Review Board. Prior to data collection, the diver
warmed up and practiced the experimental task until they were comfortable with the
experimental set up. The diver then performed three forward somersault dives and three
reverse somersault dives from a springboard and landed on a mat as regularly performed
during dry land practice. A calibrated object with reflective markers located one meter
apart was placed within the take-off area and video taped using a stationary camera (C
2
S,
NAC Visual Systems, Burbank, CA, USA). During the performance of each task, sagittal
plane kinematics were recorded (100 Hz, C
2
S). Body landmarks on the side of the body
closer to the camera were manually digitized (Peak Performance, Inc., Englewood, CO,
USA). Raw coordinate data was filtered using fifth order splines (Woltring, 1986) with a
cutoff frequency of 15 Hz for position data, 10 Hz for velocity data, and 5 Hz for
acceleration data. Coordinate data used for differentiation needed to be filtered with
lower cutoff frequencies to avoid reducing signal to noise ratio (Giakas and Baltzopoulos,
1997). Body segment parameters based on an athletic population (de Leva, 1996) were
combined with the sagittal plane coordinate data and used to estimate segment and whole
body CM kinematics. Segment angles relative to horizontal and joint angles were
calculated using filtered coordinate (Figure 40). First and second derivatives of angle data
were calculated from differentiation of angle position splines.
115
Inputs
The six segment inverse dynamics (ID) model of the human body was constructed using
ADAMS (Mechanical Dynamics, Ann Arbor, Michigan, USA). Body segment
parameters, segment lengths, joint initial conditions (angular positions and velocities) and
joint acceleration time histories were input into the model (Fig 1). Simulations were
initiated 120 ms prior to contact with the springboard. Simulations were terminated after
the foot looses contact with the board (departure). Specifically, the inputs consisted of
joint angle time histories (
4
( ) q t –
8
( ) q t ) as well as initial global position and orientation
(
1
q (0)-
3
q (0)) and initial global translational and angular velocities (
1
q & (0)-
3
q & (0)).
Rationale: Driving the simulation with joint motions allows us to simulate modifications
in dive technique quickly and simply. By driving with motion, we can reduce the amount
of computation time needed as the model will be more stable than it would if driven with
joint torques. Joint torques will be calculated as an output. The limitation to this method
is a lack of ability to simulate response to perturbations which is beyond the scope of this
particular study.
Foot / Surface / Springboard Model
Foot / Springboard Interface

The interaction between the foot & springboard was modeled similarly to the landing
simulations [see Chapter 5]. In this model, the foot segment is represented by one rigid
body but modeled as a triangle with endpoints of the 5
th
metatarsal, ankle, and heel
116
coordinates. The vertical interaction was modeled using a nonlinear spring / damper
model (Gruber et al., 1998, Guler et al., 1998) and horizontal force using Coloumb
friction (Gerritsen et al., 1995). There are two points of force application, at the heel and
5
th
metatarsal (Figure 29). The horizontal and vertical component of the reaction force,
Fx and Fy respectively, were computed as follows

2.5
-1
2
-
tan (100 )
x
y y f y f f
y f
F F
F C y D y y
x μ
π
=
= &
&

Equation 24

where
f
y is the vertical coordinate of each location on the foot,
f
x & and
f
y & are the
respective velocities, μ is Coulomb friction constant and set to 1, and C
y
= 4e
8
(N / m
2.5
)
and D
y
= 7e
5
(N s / m
2
) are the vertical stiffness and damping constants taken from
(Gruber et al., 1998) (Equation 18). The inverse tangent function is used as a continuous
function proxy for determining the direction of the horizontal velocity. These equations
are implemented at the metatarsal and heel.

117
μ = Coulomb friction coefficient
C
y,
,D
y
=vertical stiffness, damping
-1
2
tan (100 )
x y f
F F x μ
π
= &
2.5
-
y y f y f f
F C y D y y
π
= &
μ = Coulomb friction coefficient
C
y,
,D
y
=vertical stiffness, damping
-1
2
tan (100 )
x y f
F F x μ
π
= &
2.5
-
y y f y f f
F C y D y y
π
= &

Figure 41: Visco-elastic model of foot / springboard interaction
Springboard Model

Few models of the springboard have been developed. Sprigings created a lumped-mass
model with rotation as a function of displacement (Sprigings, 1989). Kooi and Kuipers
compared several models of varied complexity and determined that a rigid link with an
effective length and torsional spring adequately reproduced springboard characteristics
(Kooi, 1994) (Figure 42). The springboard / ground interface was modeled as a nonlinear
torsional spring following the equation:

board
k
α
τ θ =

Equation 25

where k is the stiffness constant, θ is the angle of displacement in radians, and α is a
constant of nonlinearity. The mass, equivalent length, and inertia are set from literature
(Kooi, 1994), but allowed to vary in the validation process.

118

Figure 42: Model of springboard uses a nonlinear torsion spring along with an effective length that is shorter
than the actual length of the springboard. The effective length is shorter than the actual springboard length to
ensure that the orientation of the end of the rigid link is representative of the end of the actual springboard that
behaves more nonlinearly.

Validation
Dynamic Optimization Criteria
Two different springboard dives initiated from a hurdle were used in the validation
process (Forward somersault = translate forward, rotate forward, Reverse somersault =
translate forward, rotate backwards). First, the reverse dive was used in determination of
the springboard model properties. Initial values for k
board
, board mass and length were set
from literature (Kooi, 1994) and α was set to 1. Next, simulations were performed to
optimize the following cost function:

ˆ | |
ˆ | |
i i
i
i
n
i i
i
x x
J
x
J w J
−
=
=
∑

Equation 26: Generic cost function used to optimize springboard parameters while minimizing error between
chosen simulated and experimental measures

where n is the number of variables in the cost function, J
i
is the normalized cost of an
individual variable,
i
x is the simulated variable, ˆ
i
x is the experimentally measured
variable, and w
i
is the weighting giving to each variable (Equation 19). Weightings are
119
chosen to approximately give equal weighting to the measures included. Variables
included in the cost function are CM linear and angular momentum and acceleration,
segment orientations, and ankle displacement. Optimization parameters were the initial
linear velocities at the ankle and shank angular velocity (
1
q & (0)-
3
q & (0)), shank orientation
3
q (0), board length, mass, k
board
, and α. Translational velocities were allowed to vary +/-
0.5 m/s, angles +/- 5 degrees, and angular velocity was allowed to vary +/- 30 deg/sec.
All variances were within a reasonable range due to segment and coordinate tracking
error. Based on calculations using calibration information, one pixel error gives
0 0055 . m ± and 1 105 . m s ± / at 100 Hz.

Evaluation
Springboard parameters determined from optimization with the reverse somersault dive
were then used in the simulation of the forward somersault trial (Table 8). Initial
conditions were optimized for the forward dive as done for the reverse dive without
variation in springboard parameters. RMS error was used to quantify the level of
agreement between simulated and experimental measures
[ ]
2
1
( ) ( )
n
SIM EXP
i
f i f i
Error
n
=
−
=
∑

Equation 27
(2)

where f is the given measure, ‘SIM’ is the model calculated result, ‘EXP’ is the measured
result, and n is the number of samples in the trial. Model validation procedures gives
120
reasonable match between the simulated and experimental based linear CM accelerations
(Figure 43), derivative of angular momentum (Figure 44), and other pertinent measures (
Table 9).

Springboard Parameters
Stiffness (N/rad^1.5) 6.89E+04
Alpha 1.51E+00
Mass (kg) 6.55
Length (m) 2.92

Table 8: Final visco-elastic surface parameters used in simulation

Figure 43: Model simulated and measured CM horizontal and vertical accelerations

Figure 44: Model simulated and measured moment of the reaction force about the CM.
121

RMS Error Units
CM
x &&
2.14 m/s
2

CM
y &&
4.08 m/s
2

CM
x &
0.078 m/s
CM
y &
0.19 m/s
CM
H
2.77 kg m/s
Shank Angle 4.37 deg
Thigh Angle 4.58 deg
Ankle Y Disp 0.0246 m

Table 9: RMS error between simulated and experimental measures of CM linear acceleration, CM velocity, CM
angular momentum, shank and thigh angles, and ankle vertical position

Modified Simulations
Once the model was validated, we used simulation results to test our hypotheses related
to the effect of modifications in multijoint control during the take-off phase of a forward
somersault on the mechanical demand imposed on the knee and hip during board contact
and the ability of the diver to regulation of the reaction force relative to the CM.

Modified CM kinematics at board contact (Flight Phase Control Modification)
Flight phase control modifications during the hurdle affect whole body orientation and
CM momentum at board contact. Both parameters were expected to affect the ability of
the diver to generate linear and angular impulse during contact with the springboard.
Whole body orientation (+/- 5°) was adjusted via shank angle (SIM1),
3
(0) q , and CM
initial CM vertical velocity (+/- 0.5 m/s) via
2
(0) q & while assuming joint kinematics
remain the same (SIM2).
122

Modified segment configuration at board contact (Deeper Squat)
Initial squat position at board contact was expected to affect the diver’s ability to generate
impulse during contact with the springboard. Experimental evidence indicates the
majority of divers tend to use all of their available ankle dorsiflexion during board
contact. As a result, experimental ankle angle trajectories were not modified as part of the
simulations. Simulations SIM3 and SIM4 modified initial knee and hip flexion angles at
contact. SIM3 modified joint excursion by returning the joints to their original values just
after max depression, while SIM4 maintained the measured range of motion. Splines of
the knee and hip angle/time curves were created and the node of the experimental angles
at minimum flexion angle (~ at contact) were shifted a desired number of degrees (Figure
45). From a set point in flight until contact, the experimental curves were scaled to reach
the new minimum points. Similar scaling was then performed from contact until the next
node point at maximum hip flexion, which occurs after the board begins to recoil (Figure
46). This method maps to SIM3 where minimum hip and knee angles were decreased but
orientation at time of max hip flexion were kept the same as measured experimentally.
For SIM4, this node was shifted downwards an equal amount to the node at contact to
maintain the same angle excursion. Minimum knee and hip angles were allowed to vary
+/- 23°. Only combinations which maintain foot placement similar to the validated
simulation were kept (average difference +/- 3° from experimental).

123

Figure 45: Exemplar modification in hip angle to simulate a deeper squat at contact. Spline node of the
experimental hip angle at minimum flexion angle (~ at board contact) is shifted a desired number of degrees.
From a set point in flight until contact, the experimental curve is scaled to reach the new minimum point.
Similar scaling is then performed from contact until the next node point at maximum hip flexion, which occurs
after the board begins to recoil. This method maps to SIM3 where minimum hip and knee angles decrease but
orientation at time of max hip flexion are the same as measured experimentally. For SIM4, this node is shifted
downwards an equal amount to the node at contact to maintain the same angle excursion.

Joint Angle (deg)
0
0.8
0.4
Board Displacement (m)
Time (s)
Joint Angle (deg)
0
0.8
0.4
Board Displacement (m)
Time (s)

Figure 46: Temporal relationship between board displacement and knee and hip angular motion. Time of
maximum hip angle (and time of pause in knee extension) occurs slightly after the beginning of board recoil.

Modified Board Recoil (Knee Extension / Hip Flexion multijoint coordination)

We hypothesized that more knee and hip flexion at the beginning of the board recoil
phase would provide residual joint flexion during board recoil and as such increase the
diver’s ability to redirection of the RF posterior to CM and increase angular impulse
generation. To test this hypothesis, we allow variance in the amount of excursion of knee
124
extension and hip flexion during the BR phase (SIM5). Similar to the modified squat
simulations, these modifications were scaled relative to experimental angle time curves
(Figure 47). The simulation scale knee and hip excursions between time of max hip angle
and board departure. Time of max hip extension coincides with a plateau in the knee
angle curve. The simulation uses normal knee and hip board depression technique so joint
angles at the beginning of the BR phase are the same as in the experimental case.
Knee
Hip
Time (s)
Angle (deg)
Knee
Hip
Time (s)
Angle (deg)

Figure 47: Modification in knee and hip joint angle excursions during the board recoil phase. Spline nodes
located just after departure (max knee angle) are varied and curves are scaled between here and time of
maximum hip angle.
Timing of knee joint extension may also have an effect on angular impulse generation
(SIM6). Assuming the same excursion from time of minimum knee angle to time of
maximum knee angle, two modifications were performed. The experimental data
naturally uses a “two phase” knee extension coordination, where the knee extends during
BD phase, then maintains a constant angle during the beginning of BR phase, then begins
extending rapidly until departure (Figure 48). We compared this to a simple constant rate
of knee extension. We also compared it to a modification resulting in even less knee
extension during BD phase, followed by a higher rate of knee extension during BR phase.
125

Figure 48: Modification in knee angle coordination during contact with the springboard. The subject extends
the knee partially, pauses, then continues to extend the knee as the board is recoiling. The “two phase”
modification (dotted line) simulates less initial extension followed by rapid extension during recoil. The
“straight” modification (open circles) assumes the rate of knee extension is constant with time until departure.

Interaction of Squat and Board Recoil Techniques

Final simulations will incorporate modification in board recoil technique (SIM5) applied
to the two squat modifications to result in two more simulations, SIM7 (from SIM3), and
SIM8 (from SIM4).

Variations by Phase Simulation Level
Flight BD BR
Figure
SIM1 Whole Tip Body Figure 49
SIM2 Whole Higher hurdle Figure 50
SIM3 Joint Deeper Squat More Extension Figure 51
Figure 53
SIM4 Joint Deeper Squat Same Extension Figure 52
SIM5 Joint Modify Knee / Hip Figure 54
SIM6 Joint Modify Knee
Table 11
SIM7 Joint Deeper Squat More Extension Modify Knee / Hip Figure 55
SIM8 Joint Deeper Squat Same Extension Modify Knee / Hip Figure 55

Table 10: List of diving simulations performed and corresponding results (Figures 49-55, Table 10)
126

Results

Initial global conditions in flight

Increasing shank angle at contact (SIM1) increases departure CM horizontal velocity and
angular momentum but decreases departure CM vertical velocity (Figure 49). Similar
tradeoffs can be found when altering initial shank angular velocity.

Figure 49: Effect of change in initial shank orientation (SIM1) on changes in maximum CM vertical velocity (A),
CM horizontal velocity (B), and angular momentum (C). Increasing forward tipping of the shank decreases CM
vertical velocity at departure but increases the other two measures

Increasing downward CM velocity at contact (SIM2) increases CM horizontal velocity,
CM vertical velocity, and total body angular momentum at departure (Figure 50).
Increase in CM vertical velocity at departure is less than the downward increase in initial
CM vertical velocity. Maximum knee and hip extensor torques (NJMs) and board
displacement also increases. Larger board displacements create higher reaction forces,
which can produce more impulse but necessitates larger NJM.
Back Forward
Horizontal Velocity vs Tip Angle Vertical Velocity Angular Momentum
Back Forward
127

Figure 50: Effect of change in initial CM vertical velocity of the CM (SIM2) on changes in maximum knee
extensor NJM (top left), hip extensor NJM, board depression (top right), CM vertical velocity (bottom left), CM
horizontal velocity, and angular momentum (bottom right). Increasing downward CM velocity at contact
increases all measures

Change in Squat Depth
Increases in squat depth at contact (SIM3) increases maximum board displacement,
reduces CM horizontal velocity at time of maximum board depression, and decreases the
CM angle at time of maximum board depression (Figure 51). Less board depression and
smaller CM horizontal velocities are found in SIM4 compared to SIM3 (Figure 52).
Max Hip NJM vs ΔV
Y
(0)
Max Knee NJM Max Board Depression
Faster Slower Faster Slower
Horizontal Velocity vs ΔV
Y
(0)
Vertical Velocity Angular Momentum
Faster Slower Faster Slower
128

Figure 51: Changes in board displacement, CM horizontal velocity, and CM orientation at time of maximum
board displacement with variations in squat depth (SIM3). Increase in squat depth increases board
displacement, but reduces CM horizontal velocity and CM angle. The latter two contribute to a forward tip of
the CM, redirection of the reaction force and generation of angular impulse in the BR phase.

129

Figure 52: Changes in board displacement, CM horizontal velocity, and CM orientation at time of max board
displacement. Increase in squat depth (SIM4) increases board displacement, but reduces CM horizontal velocity
and CM angle. The latter two contribute to a forward tip of the CM, redirection of the reaction force and
generation of angular impulse in the BR phase.

As knee and hip angles increase in flexion together at contact (SIM3), CM vertical
velocity at departure increases while CM horizontal velocity and angular momentum
magnitudes decrease (Figure 53). Maximum knee extensor NJM increases while
maximum hip extensor NJM is largely unaffected. Because ankle angle is constrained,
shift in knee and hip angles shift the CM onto the posterior portion of the base of support,
increasing the moment arm between the reaction force and knee joint. These changes in
CM and joint kinematics increase the knee NJM while allowing hip NJM to stay
130
relatively the same, redirects the force slightly posterior, and reduces horizontal impulse
generation.
F
E
D C
B A
CM Horizontal Velocity (m/s)
CM Horizontal Velocity (m/s)
CM Vertical Velocity (m/s)
CM Vertical Velocity (m/s)
CM Vertical Velocity (m/s)
Max Hip Extensor NJM (Nm)
Min Hip Angle (deg)
CM Angular Momentum (kg m/s)
Min Knee Angle (deg)
Max Knee Extensor NJM (Nm)
F
E
D C
B A
CM Horizontal Velocity (m/s)
CM Horizontal Velocity (m/s)
CM Vertical Velocity (m/s)
CM Vertical Velocity (m/s)
CM Vertical Velocity (m/s)
Max Hip Extensor NJM (Nm)
Min Hip Angle (deg)
CM Angular Momentum (kg m/s)
Min Knee Angle (deg)
Max Knee Extensor NJM (Nm)

Figure 53: Effect of squat depth (SIM3) on kinematics and kinetics. X axis CM horizontal velocity at departure,
Y axis is CM vertical velocity at departure. Plots show angular momentum at departure (A), minimum knee
angle (B), minimum hip angle (C), maximum knee extensor NJM (D), maximum hip extensor NJM (E), and
illustration of hip angle modification to achieve deeper squat (F). Knee angle is modified in a similar manner
131

Board Recoil Coordination – From Standard Position
Increasing both knee extension (Figure 54B) and hip flexion (Figure 54C) angles during
the BR phase (SIM5) increases angular momentum at departure but slightly decreases
horizontal and vertical momentum (Figure 54A). Maximum hip flexor and knee extensor
NJMs both increase with larger joint excursions. Increases in angular impulse are more
aligned with increases in hip flexion than knee extension. Additionally, some of the
maximum knee angles are not realistic as the human body is generally constrained to ~
180 degrees of knee extension. However, even while maintaining the same maximum
knee extension as experimentally measured, increases in hip flexion can increase with
angular impulse.

132
Knee
Hip
Time (s)
Angle (deg)
A
B
C
D
E
F
CM Horizontal Velocity (m/s)
CM Horizontal Velocity (m/s)
CM Vertical Velocity (m/s)
CM Vertical Velocity (m/s) CM Vertical Velocity (m/s)
CM Angular Momentum (kg m/s) Min Knee Angle (deg)
Min Hip Angle (deg)
Max Knee Extensor NJM (Nm)
Max Hip Flexor NJM (Nm)
Knee
Hip
Time (s)
Angle (deg)
Knee
Hip
Time (s)
Angle (deg)
A
B
C
D
E
F
CM Horizontal Velocity (m/s)
CM Horizontal Velocity (m/s)
CM Vertical Velocity (m/s)
CM Vertical Velocity (m/s) CM Vertical Velocity (m/s)
CM Angular Momentum (kg m/s) Min Knee Angle (deg)
Min Hip Angle (deg)
Max Knee Extensor NJM (Nm)
Max Hip Flexor NJM (Nm)

Figure 54: Effect of altering knee and hip angles at departure (SIM5) on pertinent kinematics and kinetics. X
axis CM horizontal velocity at departure, Y axis is CM vertical velocity at departure. Plots show angular
momentum at departure (A), maximum knee angle (B), minimum hip angle (C), maximum knee extensor NJM
(D), maximum hip flexor NJM (E), and illustration of hip angle modification to more hip flexion (F).

Constant rate of knee extension (SIM6) coordination reduces CM vertical velocity and
angular momentum at departure, but increases CM horizontal velocity (Table 11). Further
133
delayed knee extension (“two phase+”), slightly increases CM vertical velocity and
angular momentum at takeoff, but also reduces CM horizontal velocity as well as incurs a
much higher maximum knee extensor NJM.

Knee Coordination CM
y & (m/s)
CM
x & (m/s)
CM
H (N m s)
Max Knee Extensor NJM (N m)
Straight 4.43 -1.97 46.72 333
Exp 4.64 -1.37 53.12 358
Two Phase + 4.73 -0.83 54.7 686

Table 11: CM vertical velocity, CM horizontal velocity, and angular momentum at departure, and max knee
extensor NJM across three knee coordination strategies. The “straight” strategy reduces vertical and angular
momentum. The “two phase+” strategy increases vertical and angular momentum, but incurs much higher
maximum knee extensor torque (NJM) since the knee is more flexed and the more horizontal shank creates a
larger moment arm for the reaction force.

Interaction of Deeper Squat and Board Recoil Coordination

We were able to address the hypothesis that increased squat depth would increase vertical
impulse generation (Figure 51 & Figure 53). Separately, we were able to address the
hypothesis that increased knee extension and hip flexion excursion could increase angular
momentum (Figure 54). However, the interaction between the two has not been
addressed. We performed the same simulation across varying BR phase knee/hip
coordination for two squats. Both squats used increased knee and hip flexion angles 20
degrees from experimental. SIM7 extends back to original configuration just after max
board depression, while SIM8 performs the same amount of extension ROM as measured
experimentally and ends up in a more flexed position after the BD phase.
Ability to generate CM horizontal velocity is reduced in SIM7 and SIM8 simulations
compared to the standard simulation (Figure 55). Both modified squats had smaller CM
134
angles (CM / heel relative to springboard) compared to the normal squat (SIM5). While
SIM8 was more flexed at the beginning of the BR phase and able to use more knee
extension ROM to achieve similar max knee angles, it did not show the potential to
generate more angular impulse as hypothesized.

Figure 55: Effect of squat type on angular impulse, maximum knee angle, and CM angle relative to the
springboard at maximum board depression. Both SIM7 (full extension) and SIM8 (partial extension) generate
more vertical impulse but less horizontal and angular impulse than the normal squat (SIM5). Modified BR
phase coordination can improve angular impulse in all three. The more flexed configuration of SIM8 does not
increase angular impulse relative to the other two conditions although maximum knee angle achieved is similar
(i.e. had larger knee extension). SIM8 had the smallest CM angle at maximum board depression making it more
difficult to redirect the reaction force posterior to the CM to generate forward angular impulse.

135
Discussion
In springboard diving, regulation of momentum is accomplished through a series of
phases including flight, board depression, and board recoil. Modification of performance
in one phase affects performance in following phases. In this study, an experimentally
validated angle driven multisegment model was developed to test how modification of
control strategies affects generation of linear and angular impulse during contact with the
springboard. Simulation results indicate that vertical impulse generation during board
contact increases with increases in downward CM velocity at board contact as well as
increases in board depression from joint extension originating from a more flexed squat
position at board contact. Angular impulse generation was also found to increase with
greater force redirection relative to the center of mass. Redirection of the reaction force
originated from hip flexion and knee extension during the board recoil phase. Angular
impulse generation during board recoil was more difficult from deep squat positions at
the end of the board depression phase. Joint extension from a deeper squat decreases
horizontal impulse and shifts the location of the CM away from the edge of the board. In
general, the simulation results provide quantitative evidence of the trade-offs between
vertical, horizontal, and angular impulse generation associated with control modifications
in each of the board contact phases.
Impulse generation can be regulated by altering whole body kinematics at board contact.
The initial segment configuration and CM velocity at board contact are controlled in the
flight phase of the hurdle prior to board contact. Simulation results indicate that the trade-
offs between horizontal, vertical and angular impulse generation during board contact
136
could be modified by maintaining experimentally measured joint coordination and
altering the orientation of the body CM relative to the springboard. Tipping the body
backwards 5 degrees (SIM1) generates more vertical impulse but less horizontal and
angular impulse during board contact (Figure 49). Tipping back from the original position
allows the CM to stay over the feet longer during BD so that joint extension increases
maximum board depression. The reaction force is likely redirected backward with the
body which reduces the horizontal component and reduces horizontal impulse. The fact
that angular impulse decreases indicates that the reaction force did not redirect backwards
as much as the body, lowering its moment arm to CM. While the increased vertical
impulse provides additional time in the air, the reduction in horizontal impulse affects
board clearance in certain body positions during the flight phase of the dive. In contrast,
an increase in shank angle up to 5 degrees reduces vertical impulse but increased angular
and horizontal impulse. This may indicate why CM vertical velocity decreases but
angular momentum increases when performing dives requiring more demanding
somersaults (Miller, 2001).
We also found that when increasing the downward velocity of the CM in flight
(associated with a higher hurdle, SIM2), the magnitude of horizontal, vertical and angular
impulse increases with vertical impulse generation increasing the most (Figure 50). This
was expected as placing more potential energy into the springboard should elicit higher
energy returns during the BR phase (Miller and Munro, 1984). A more depressed board
will increase the peak force applied to the body in both horizontal and vertical directions
given the oblique board orientation during the BR phase. Larger forces allow more linear
137
impulse generation over time. Since horizontal force and impulse increases, the body CM
will shift more forward during the BR phase so that the reaction force can redirect further
posterior to the CM to increase angular impulse. The combination of body tipping (SIM1)
and increased downward CM velocity at initial board contact (SIM2) may provide
effective mechanisms to generate more impulse as well as redistribute impulse in the
vertical and both angular and horizontal directions.
Increased squat depth also adds ability to regulate impulse magnitude and direction. We
found that deeper squats at contact (SIM3) increased vertical impulse generation but
decreased angular and horizontal impulse at takeoff (Figure 51). The increase in CM
vertical velocity is consistent since a deeper squat depth slightly increases the downward
velocity at initial board contact and also allows more joint extension during BD to
increase maximum board deflection and reaction force magnitude. Decreases in angular
and horizontal impulse are likely due to the altered position of the CM relative to the feet
at varied squat depths (Figure 51, Figure 52). Since the ankle motion is expected to be the
same as observed experimentally, alterations in squat can only come from more knee and
hip flexion arising from modifications in thigh and trunk angles. With only 2 degrees of
freedom to modify and only 2 degrees of freedom output (CM X and Y positions), for a
given vertical CM position, horizontal CM location is prescribed. Modifications in knee
and hip angle excursions through the BD phase that keep the foot flat on the board shift
the CM back toward the heels of the feet. This has several consequences, including
increasing knee moment and decreasing the ability to redirect a force behind the CM as
needed in a forward somersaulting task (Figure 53).
138
Increased hip flexion and knee extension during the BR phase increases generation of
angular impulse, but slightly decreases vertical and horizontal impulse generation.
Increased extensor torque magnitudes at the knee and flexor torque at the hip further
contributes to reaction force redirection posterior to the CM as has been seen in other
studies involving angular impulse generation (Mathiyakom and McNitt-Gray, 2008,
Mathiyakom et al., 2006, Mathiyakom et al., 2007). A posteriorly directed force
contributes to a reduction in horizontal impulse. A reduction in vertical impulse occurs
since more hip flexion increasingly accelerates the trunk downward and reduces total CM
upward velocity (Figure 54). Increased knee extensor torque may cause the knee to
extend too far and run out of range of motion. Thus a more flexed knee would allow a
larger range of knee extension and larger knee moments to occur. Contrarily, a more
flexed hip at the start of the board recoil phase could reduce the range of motion of hip
flexion that can be generated to redirect the force. Thus, maintaining more flexed knees at
the beginning of the board recoil phase may only be of benefit to angular impulse
generation if the hip is still sufficiently extended.
Angular impulse generation can be increased during the BR phase with more flexed knee
positions provided that the CM trajectory is adequately regulated relative to the feet.
SIM8 found that horizontal and angular impulse generation were reduced when
performing a deeper squat and keeping both knee and hip joints more flexed than
experimentally measured (Figure 55). Although the additional knee extension and hip
flexion modification improves angular impulse compared to no change in BR phase joint
coordination, overall angular impulse was found to be lower from a deeper squat position
139
as compared to experimental. Thus, a flexed knee position during BR may increase
angular impulse generation, however the squat strategy used to achieve that position may
introduce limitations. However, if the diver modifies control in two phases (e.g. combines
the results from SIM1 (Figure 49) with SIM8) then it may be possible to achieve
increases in horizontal, vertical and angular impulse generation. These simulation results
provide quantitative evidence of the trade-offs between vertical, horizontal, and angular
impulse generation for a diver to consider when exploring control modifications in each
of the board contact phase.

140
Chapter 7: Summary

The goal of this body of work was to determine how humans regulate reaction forces and
distribute mechanical load during well-practiced goal directed tasks by using
experimentally motivated models of human interaction with the environment. Regulation
of reaction forces was studied at the joint torque level in several tasks involving upper
and lower extremity interaction with a variety of external surfaces. Foot-surface
interactions included foot contact with a rigid surface as in a landing and with a
deformable surface as in a springboard dive. Hand-surface interaction involved hand/rim
interaction during manual wheelchair propulsion. Task-specific objectives ranged from
maintaining performance as in the manual wheelchair task to improving performance of
tasks that require a decrease (landing) or increase (dive) in linear and angular momentum
generation. Model complexity and validation were based upon segment kinematics and
reaction force measures acquired during task performance. Subject-specific experimental
data was used to test hypotheses about how changes in segment configuration and
reaction force direction affect load distribution and task performance variables.
Simulation results, presented in the form of a solution space, indicate that there are
multiple ways of achieving the mechanical objectives of each task and illustrate how
shifts within the solution space alter load distribution.

141
Chapter 2
The repetitive nature and mechanical demand imposed on the upper extremity during
manual wheelchair propulsion is associated with overuse injuries of the shoulder.
Simulations exploring how wheelchair users can orientate the hand / pushrim reaction
force (RF) provide a means of determining how subjects with different capacities can
redistribute mechanical load. A two segment, 2D inverse dynamic model was used to
simulate mechanical load while varying the direction of the RF. Experimental data of a
graded propulsion task for two subjects was incorporated into the model. We
hypothesized that elbow and shoulder net joint moment (NJM) and shoulder axial net
joint force (NJF) could be redistributed across RF force directions. We found that load
distribution was affected by force redirection. Minimal shoulder NJM occurred at more
radial RF directions while minimal elbow NJM and shoulder NJF occurred in more
tangential RF directions. We found loading characteristics to be subject-specific in that
minimal NJM and NJF occurred with different RF directions (subject 2 RF more radial
than subject 1). We also found that the effect of RF direction was dependent on time and
location of the wrist on the pushrim. Direction of RF that minimizes NJM generally
shifted tangentially as the subject shifted the hand from posterior to anterior positions on
the pushrim. These results are explained by changes in the relative positioning of the
upper extremity segments relative to the RF (change in moment arms) as well as the
pushrim (change in force magnitude). The method used provides a template to potentially
modify subject-specific technique.

142
Chapter 3
Upper extremity (UE) pain and injury has been associated with manual wheelchair
propulsion (WCP). Both experiments and simulations using a 2D model indicate that
redirection of the reaction force (RF) at the hand/rim interface provides a means to
potentially redistribute mechanical loading across the upper extremity (UE). In this study,
simulations using a 3D dynamic model were used to determine if inclusion of the
mediolateral (ML) component of the reaction force and 3D segment kinematics in model
simulations influences the identification of multijoint control strategies that maintain
WCP performance and effectively distribute mechanical load across the upper extremity.
We hypothesized that loading distribution of elbow net joint moment (NJM), shoulder
NJM, and shoulder axial net joint force (NJF) using 3D kinematics would be dependent
on both radial and mediolateral force components. Simulation results indicate that
loading is affected by mediolateral (ML) force direction and magnitude. Elbow NJM and
shoulder axial NJF tended to decrease when the reaction force is directed laterally on the
UE and shoulder NJM tended to decrease when the reaction force is directed medially.
Results were subject-specific and depended on UE segment configuration relative to the
pushrim. Lack of inclusion of ML force variation when using 3D kinematics was shown
to significantly alter conclusions about ability to reduce shoulder NJM via force
redirection. This a prioi knowledge provided by experimentally validated model
simulation results is expected to facilitate clinical decision making when facilitating the
skill acquisition process and when considering intervention to avoid over use injury
during WCP.
143
Chapter 4
Repetitive loading during manual wheelchair propulsion (WCP) contributes to overuse
associated with upper extremity (UE) injury. Redirection of the hand / rim reaction force
(RF) relative to the upper extremity segments provides a means to redistribute
mechanical load across joints and shift load away from areas at risk. Reconfiguration of
the UE relative to the pushrim was hypothesized to influence how redirection of the RF
redistributes load. In this study, 2D inverse dynamic model using subject-specific
experimental tangential component of the RF and 3D kinematic data was used to perform
a sensitivity analysis that varied shoulder/pushrim distance and wrist placement. Elbow
net joint moment (NJM), shoulder NJM, and shoulder axial net joint force (NJF) were
calculated over a range of RF directions. RF direction was systematically varied by
maintaining the tangential component of the RF and varying the magnitude of the radial
component. Simulation results indicate that load distribution depends on configuration of
the upper arm relative to the forearm and UE orientation relative to the wheel. At peak
force, lower shoulder / pushrim distances and more forward wrist positions on the
pushrim allow for more extended elbow positions and improved UE / pushrim alignment.
If RF direction is constrained (due to friction, grip strength, etc.) solutions for
redistributing load shift within the solution space. These simulation results provide
mechanically based information to guide clinical interventions that aim to maintain WCP
performance and redistribute load by modifying RF direction, seat configuration and
hand/rim interaction.

144
Chapter 5
This study determines the effect of multijoint control strategies utilized during landing on
mechanical loading and impulse generation during foot contact. Changes in segment
configuration at contact were hypothesized to affect a) the impulse generated during the
impact phase (IP) and b) the mechanical demand and linear and angular impulse
regulation during the post impact phase (PIP) of a land-and-stop task. An experimentally
validated torque driven multisegment model of the body was used to determine how
modifications in segment configuration at contact affect PIP momentum regulation and
lower extremity load distribution during landing. Simulation results indicate that more
joint flexion at touchdown decreases the amount of vertical momentum reduced during
the IP and the resulting segment configuration at the end of the IP affects the ability to
generate linear and angular impulse during the PIP. The greater the vertical impulse
generated during the IP, the less the vertical momentum to be reduced during the PIP.
Landings initiated with more joint flexion require greater extensor torque magnitudes
during PIP to reduce momentum to zero and generate less unwanted angular impulse
when regulating horizontal momentum than landing initiated with less joint flexion.
Shifts within the simulation generated solution space illustrate how choices made during
the flight and impact phases alter load distribution within the lower extremity and the
ability to satisfy task objectives during the post-impact phase. When considering
modifications in landing strategies that aim to reduce the reaction force during the IP, one
also needs to consider performance consequences in the post impact phase.

145
Chapter 6
In springboard diving, regulation of momentum is accomplished through a series of
phases including flight, board depression, and board recoil. Modification of performance
in one phase affects performance in following phases. In this study, an experimentally
validated angle driven multisegment model was developed to test how modification of
control strategies affects generation of linear and angular impulse during contact with the
springboard. Simulation results indicate that vertical impulse generation during board
contact increases with increased downward velocity at board contact as well as increased
board depression from joint extension originating from a more flexed squat position at
board contact. Angular impulse generation also increased with greater force redirection
relative to the center of mass originating from hip flexion and knee extension during the
board recoil phase. Angular impulse generation during board return was more difficult
from deep squat positions at the end of the board depression phase. Joint extension from a
deeper squat decreased horizontal impulse and shifted the location of the CM away from
the end of the board. In general, the simulation results provide quantitative evidence of
the trade-offs between vertical, horizontal, and angular impulse generation associated
with control modifications in each of the board contact phases.

Conclusions
In all cases, achieving the mechanical objectives of each task involves regulation of the
reaction force (RF) in relation to the system center of mass trajectory (CM). Load
distribution among the muscles controlling the upper or lower extremity, as represented
146
by net joint moments (NJM) and net joint force (NJF), was found to be dependent on the
reaction force orientation relative to segments as well as the adjacent joint NJM. The
results indicate that in wheelchair propulsion (WCP), the RF direction and upper
extremity segment configuration relative to the push rim can be changed to alter
mechanical load distribution of the upper extremity without a decrement in task
performance (same propulsive torque applied to the wheel by the tangential component of
the RF). Configuration of the upper extremity relative to the pushrim could also be
changed to alter the mechanical load at any specified force direction, while still
successively accomplishing the task goal of propulsion. 3D representation of segment
configuration and reaction force generation was used to account for individual differences
in segment configuration and position within the wheelchair. Simulation results indicate
that 2D modeling was found to effectively represent load distribution trade-offs between
multijoint control solutions in the plane defined by the wrist, elbow and shoulder.
In landing, simulation results show how different multijoint control strategies utilized
during impact phase affect loading and impulse generation during the post-impact phase.
In a land-and-stop task, the mechanical objective of reducing the momentum of the body
at contact to zero at a time when the CM is over the base of support can be accomplished
from different segment configurations and initial CM kinematics. Simulation results
indicate that there are multiple ways of achieving this mechanical objective and illustrate
how shifts within the solution space alter load distribution within the lower extremity as
well as task performance. Likewise, in springboard diving, generation of linear and
angular impulse required for dive performance can be achieved via different strategies in
147
flight, board depression, and board recoil phases. Simulation results of a front dive
performed from a hurdle illustrate how shifts within the solution space during each phase
of the dive alters load distribution within the lower extremity and overall task
performance.
In each case, the mechanical objective of each task was achieved using more than one
strategy. Simulation results indicate that modifications in strategy involve alteration in
reaction forces and segment kinematics the extremity. Changes in the orientation of the
RF relative to the segments of the upper or lower extremity alter the distribution of the
mechanical load across the joints. Alignment of the RF with the distal segment may
reduce the net joint moments required to control the distal segment. This reduction in the
NJM required to control the distal segment may contribute to an increase in the proximal
NJMs and NJFs involved in the control of the proximal segment, depending on the
orientation of the net joint force relative to the proximal segment. These results
emphasize that modifications in control strategies involve control of more than one joint.
Aligning segments with the reaction force can reduce some loading associated with
control of segment rotation (NJM) but correspondingly increase control of segment
translation (NJF). These observed trade-offs between NJM and NJF were previously
discussed by Prliutsky and Zatsiorsky in different types of landings (more or less rigid)
(Zatsiorsky, 1987). From a performance perspective, segment alignment with the reaction
force can reduce the range of motion available to perform work and control CM
trajectory, as evidenced in landing and diving strategies. Upright postures may be
beneficial for reducing NJM and muscular demand, but may allow less opportunity for
148
linear and angular impulse generation. Although this was not studied specifically in
wheelchair propulsion, the same concept applies.
Overall, activities in daily life involve ongoing interaction with the environment.
Suggestions to improve performance and load distribution must consider task objectives
at the whole body, subsystem (extremity), and joint levels in each phase of the task. True
benefit will only come when these multiple objectives are considered, satisfied, and
enhanced. The simulation results in this series of studies provide a quantitative basis for
clinicians to make informed decisions regarding the mechanical and control implications
of technique modifications and clinical interventions. If technique modification is
required (e.g. need to unload the should NJF), the simulation results provide a means to
assess the benefits and consequences of specific technique modifications under
consideration (i.e. force redirection, segment configuration, position of end user relative
to mechanical device (e.g. wheelchair, springboard). This a prioi knowledge provided by
experimentally validated model simulation results is expected to facilitate clinical
decision making when considering interventions as well as the skill acquisition process.

149
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Asset Metadata

Creator Munaretto, Joseph Michael (author)

Core Title Modeling human regulation of momentum while interacting with the environment

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Biomedical Engineering

Publication Date 03/01/2011

Defense Date 01/27/2011

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag biomechanics,impact,Landing,Modeling,OAI-PMH Harvest,simulation,wheelchair propulsion

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor McNitt-Gray, Jill L. (committee chair), Flashner, Henryk (committee member), Khoo, Michael C.K. (committee member)

Creator Email jmunaretto@gmail.com,munaretto@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m3668

Unique identifier UC1423633

Identifier etd-Munaretto-4323 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-432711 (legacy record id),usctheses-m3668 (legacy record id)

Legacy Identifier etd-Munaretto-4323.pdf

Dmrecord 432711

Document Type Dissertation

Rights Munaretto, Joseph Michael

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Repository Name Libraries, University of Southern California

Repository Location Los Angeles, California

Repository Email cisadmin@lib.usc.edu