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Control and dynamics of turning tasks with different rotation and translation requirements

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Control and dynamics of turning tasks with different rotation and translation requirements

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Content CONTROL AND DYNAMICS OF TURNING TASKS WITH
DIFFERENT ROTATION AND TRANSLATION
REQUIREMENTS

By
Antonia Zaferiou

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)

December 2015

Copyright 2015 Antonia Zaferiou
i

Dedication
To     
Acknowledgements
I am grateful for the love and support my family has shared with me throughout my life. My family
supported my interests as I grew from a mini ballerina into a mechanical engineer. Special thanks must be
given to my cousins Evan and Kendra (“The Cousins California”) who have been very helpful and tolerant
as my roommates during the last two years.
As an undergraduate student, I was lucky enough to meet Matias. He always brings out the best in me and
my biggest smiles. By supporting each other, we have grown and continue to grow together through
academic, personal, and professional endeavors. Matias, thank you!
While studying at Cooper Union, Matias and I took a trip to the American Society of Biomechanics annual
conference in hopes that I would find interesting graduate programs. Little did we know that I would find
the perfect job opportunity flyer: “Performing Arts Biomechanics PhD studentship in sunny Southern
California”. This flyer was the starting point of my studentship with Dr. Jill McNitt-Gray.
I would like to thank Jill for her dedication to my personal and academic development. She has helped me
structure a dissertation that advances our understanding of how people control their bodies to complete
challenging tasks. She has also supported and helped develop my interest in teaching, despite the time
commitment that was involved. Above all, she has treated her lab as family to support our teamwork and
foster our growth. Thank you Travis, Ian, Ed, Chris, Joe, Shashank, Laura, and Korkut for the teamwork and
happy lab atmosphere. I am also grateful for the high school and undergraduate research assistants who
were crucially helpful during data collection and pre-processing.
I would like to thank Dr. Henryk Flashner, Dr. Kornelia Kulig, and Dr. Philip Requejo for their time and
invaluable perspectives as members of my dissertation committee.
I acknowledge financial support for this work from the USC Endowed Myronis Fellowship, Biomechanics
Research Laboratory, and Body Engineering Los Angeles GK-12 (NSF Grant DGE 1045595 & USC's Viterbi
School of Engineering).
Finally, thank you dance students, teachers, and professionals for participating in my research.

ii

Table of Contents
Dedication .................................................................................................................................................. i
Acknowledgements .................................................................................................................................... i
Table of Contents ...................................................................................................................................... ii
Abstract ..................................................................................................................................................... 1
Modification of Impulse Generation during Piqué Turns with Increased Rotational Demands ........... 2
Modification of Impulse Generation during Pirouette Turns with Increased Rotational Demands ..... 2
Whole-Body Balance Regulation during the Turn Phase of Pi qué and Pirouette Turns ................... 3
Lower Extremity Control during Turns Initiated with and without Hip External Rotation ................... 3
Chapter 1. Introduction ................................................................................................................................ 5
Overview ................................................................................................................................................... 5
Mechanics of a Turn .................................................................................................................................. 6
Impulse Generation Mechanisms during Turns .................................................................................... 6
Maintaining Balance during the Turn Phase and Reducing Rotation during the Termination Phase .. 8
Experimental Approach and Application of Findings ................................................................................ 9
Systematic Comparisons of Achieving Mechanical Objectives during Turn Performance ................... 9
References .............................................................................................................................................. 11
Chapter 2. Specific Aims and Hypotheses ................................................................................................... 15
I. Modification of Impulse Generation during piqué turns with increased rotational demands............ 15
II. Modification of Impulse Generation during pirouette turns with increased rotational demands .... 15
III. Balance Regulation during the Turn Phase of Piqué and Pirouette Turns ......................................... 16
IV. Comparison of Impulse Generation between pirouettes initiated with and without hip external
rotation ................................................................................................................................................... 16
Chapter 3. Experimental Design ................................................................................................................. 17
Experimental Procedures ........................................................................................................................ 17
Inclusion Criteria ................................................................................................................................. 17
Exclusion Criteria ................................................................................................................................. 17
Questionnaire ..................................................................................................................................... 17
Overview of Participant tasks ............................................................................................................. 18
Data collection ........................................................................................................................................ 19
Kinematics ........................................................................................................................................... 19
Kinetics ................................................................................................................................................ 21
Muscle Recruitment ............................................................................................................................ 22
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Data processing and Analysis .................................................................................................................. 22
Kinematics ........................................................................................................................................... 22
Kinetics ................................................................................................................................................ 24
Joint Kinetics ....................................................................................................................................... 24
Muscle Recruitment ............................................................................................................................ 26
Statistics .............................................................................................................................................. 26
References .............................................................................................................................................. 27
Chapter 4. Modification of Impulse Generation during Piqué Turns with Increased Rotational Demands
.................................................................................................................................................................... 29
Introduction ............................................................................................................................................ 29
Methods .................................................................................................................................................. 31
Results ..................................................................................................................................................... 32
Discussion................................................................................................................................................ 38
References .............................................................................................................................................. 39
Chapter 5. Modification of Impulse Generation during Pirouette Turns with Increased Rotational
Demands ..................................................................................................................................................... 42
Introduction ............................................................................................................................................ 42
Methods .................................................................................................................................................. 43
Results ..................................................................................................................................................... 45
Discussion................................................................................................................................................ 50
References .............................................................................................................................................. 51
Chapter 6. Whole-Body Balance Regulation during the Turn Phase of Piqué and Pirouette Turns ........... 54
Introduction ............................................................................................................................................ 54
Methods .................................................................................................................................................. 56
Results ..................................................................................................................................................... 57
Discussion................................................................................................................................................ 63
References .............................................................................................................................................. 66
Chapter 7. Lower Extremity Control during Turns Initiated with and without Hip External Rotation ....... 68
Introduction ............................................................................................................................................ 68
Methods .................................................................................................................................................. 70
Results ..................................................................................................................................................... 71
Discussion................................................................................................................................................ 79
References .............................................................................................................................................. 82
1

Abstract
Turning is fundamental to locomotion, yet, not fully understood from a control and dynamics perspective.
Without advances in our current understanding, clinical populations may continue to struggle to change
direction while walking and bipedal robots will fail to execute turns as performed by humans. This work
focused on identifying the mechanical strategies dancers used to satisfy multiple mechanical objectives
during fundamental dance turns. The overarching goal of this research was to understand how dancers
effectively control their bodies to interact with their environment during turns requiring varied amounts
of rotation and translation. With this knowledge, training procedures for dancers can be improved
through more specific cuing from dance teachers or through development of interactive technology to
provide feedback. While there may be fundamental differences in the capabilities of clinical populations
compared to skilled ballet and contemporary dancers, by studying solutions experts use under
progressively more challenging conditions, insight is gained regarding control priorities that can be
mapped to help other populations.
During turns, each leg plays a distinct role in generating the reaction forces required to control both linear
and angular momentum of the body. The reaction force regulation over time, generates linear and angular
impulse needed for the desired movement. However, angular impulse about the body's center of mass
involves reaction force components that are not aligned with the desired center of mass trajectory, which
imposes conflicts in control priorities. Through coordination of each leg’s reaction force generation, the
aforementioned conflicts can be appeased.
Turns performed by dancers provided a unique opportunity to understand how skilled individuals
successfully satisfy multiple mechanical objectives. Specifically, “piqué” and “pirouette” turns with
inherent variations of rotation and translation were studied to determine how dancers satisfy linear and
angular momentum requirements, while maintaining balance. Each turn serves as a well-practiced task
that can be performed with increased rotational requirements (e.g. single, double). Additionally, both
turns impose a specific postural challenge during the turn phase: the dancer must spin while supported
by a single leg (extended knee and plantarflexed ankle) and a very small base (the forefoot). The
differences in how pirouette and piqué turns are terminated also provided a systematic comparison
between balance maintenance during a translating turn (piqué) and a “turn-and-stop” displacement turn
(pirouette). By using a within-subject experimental design, control preferences of an individual across
tasks were identified, which may be used in the design of personalized feedback to improve performance.
In this series of studies, skilled dancers performed single and double piqué and pirouette turns while each
leg was supported by a forceplate. During each turn, reaction forces were measured using dual forceplates
(1200 Hz) while three dimensional kinematics were simultaneously captured (100 Hz). At the whole-body
level, linear and angular impulse generated by the push and turn legs during turn initiation and
contributing factors to impulse generation (resultant horizontal reaction force, sinθ, position vector
magnitude) were quantified and compared across the group and within a dancer (α = .05). During the turn
phase, balance regulation was compared between piqué and pirouette turns and between single and
double turns across the group and within a dancer. At the segment-level, the contributions at the ankle,
knee, and hip during impulse generation were compared between pirouette turns initiated with and
without hip external rotation.

2

Modification of Impulse Generation during Piqué Turns with Increased Rotational Demands
The purpose of this study was to determine how skilled dancers (n=10) used the push and turn leg to
regulate angular and linear impulse generated during the initiation phase of piqué turns performed with
increased rotational demands. During the initiation of a piqué turn, a dancer interacts with the
environment to generate lateral and angular impulse in order to satisfy the lateral and rotational
momentum requirements. The piqué turn is initiated with single leg support from the “push leg” and the
turn phase occurs with single leg support from the “turn leg”. The turn initiation phase ends as the push
leg departs the ground, shortly after the turn leg makes initial contact with the ground.
Results indicate that in order to increase the amount of body rotation from the performance of a single
piqué turn to a double piqué turn, dancers tended to increase the net angular impulse generated and
decrease the mean lateral impulse generated. The push leg contributed more angular and lateral impulse
compared to the turn leg in both single and double turns. However, all dancers studied increased angular
impulse generated by the turn leg, despite its contact with an extended knee, plantarflexed ankle, and
contact only with the forefoot during a short duration (~0.2 s). As number of turns performed increased,
dancers increased the push leg’s mean anterior impulse generation and the turn leg’s mean posterior
impulse generation, consistent with mechanisms to increase angular impulse. The push leg tended to
increase the mean moment applied about the center of mass via redirecting the reaction force, whereas
the turn leg used combinations of modulation of the reaction force (magnitude and direction) and
increased position vector length (either via decreased center of mass velocity towards the turn leg, and/or
by contacting the ground earlier with the turn leg as the center of mass was approaching the turn leg’s
ground contact). Control strategies used by dancers during progressively more challenging turning tasks
tended to be subject-specific. By coordinating the generation of reaction forces between legs, the net
horizontal impulse in the anterior/posterior direction remained minimal, despite impulse regulation used
to achieve increased rotational demands.
Modification of Impulse Generation during Pirouette Turns with Increased Rotational Demands
The purpose of this study was to determine how skilled dancers (n=11) used the push and turn leg to
regulate angular and linear impulse generated during the initiation phase of pirouette turns performed
with increased rotational demands. During the initiation of a pirouette turn, a dancer generates linear and
angular impulse in order to satisfy the linear center of mass displacement and angular momentum
requirements. The pirouette turn is initiated with double leg support from both the push leg and turn leg.
The turn initiation phase ended as the push leg departed from the ground.
Results indicate that as rotational demands increased from performance of a single pirouette turn to a
double pirouette turn, dancers increased the mean net angular impulse generated and maintained
minimal linear impulse generated towards the turn leg’s base of support. The contribution of each leg to
net angular impulse in both single and double pirouettes was linked with stance configuration strategies.
While the center of mass horizontal position resides somewhere within the base of support initially,
stylistic differences between schools of ballet provided context for some range across subjects regarding
the initial center of mass positioning closer to the turn leg or to the push leg. Dancers who initiated the
turn with a larger position vector between the center of mass and the turn leg’s base of support generated
more mean angular impulse with the turn leg during both single and double pirouettes. Conversely,
dancers who initiated the turn with the center of mass closer to the turn leg, generated more angular
impulse with the push leg in both single and double turns. However, all dancers studied generated more
3

linear impulse in the direction of the turn leg’s base of support with the push leg than they did with the
turn leg. Overall, dancers increased the horizontal reaction force magnitude at one or both legs in order
to increase the moment applied about the center of mass. The push leg also tended to increase the mean
moment applied about the center of mass via redirecting the reaction force. As was the case during piqué
turn initiation, by coordinating the generation of reaction forces between legs, changes in the mean net
horizontal impulse perpendicular to the desired center of mass trajectory remained minimal, despite
impulse regulation at each leg used to achieve increased rotational demands.
Whole-Body Balance Regulation during the Turn Phase of Pi qué and Pirouette Turns
The purpose of this study was to compare balance regulation strategies used by skilled dancers (n=10)
during the turn phase between piqué and pirouette turns and between single and double turns. After the
initiation of both piqué and pirouette turns, the turn phase required whole body rotation while
maintaining balance in a challenging kinematic context. However, differences in how the pirouette and
piqué turn is terminated provided a systematic comparison between balance maintenance during a
translating turn (piqué) and a “turn-and-stop” or minimal displacement turn (pirouette). As rotational
demands increase, it was expected that turns with multiple rotations impose a need to position the CM
over the base of support for longer periods of time. Maintaining the CM position over the base of support
for a longer period was expected to require more corrective actions that involve regulation of the reaction
forces relative to the center of mass.
Comparisons between the piqué and pirouette, for both single and double turns, revealed that the center
of mass during the pirouette was more vertically aligned than was the center of mass during the piqué
turn. Throughout the turn phase of a pirouette, the dancers’ center of mass was aligned within 15° from
vertical (the mean alignment for both single and double pirouettes was less than 5° for all subjects, n=10).
As rotational demand increased in both turns, the ground reaction forces were regulated relative to the
CM. By controlling the braking force and moment applied about the CM the potential for the CM to
overshoot the horizontal positon of the base of support in the primary direction of travel was limited.
Lower Extremity Control during Turns Initiated with and without Hip External Rotation
The purpose of this study was to compare impulse generation strategies used by skilled dancers (n=5) at
each leg and the associated muscle recruitment strategies during the turn initiation phase of pirouettes
performed with and without hip external rotation. Classical ballet turns are typically initiated and
performed with the hips externally rotated, whereas, more modern choreography requires dancers to
also be proficient in performing tasks with neutral hip alignment. This provided an opportunity to
investigate how dancers satisfy the same mechanical objectives at the total body level when generating
ground reaction forces using different leg kinematics. In addition to comparing impulse generation
strategies, activation of superficial hip muscles were monitored using surface electromyography (1200 Hz)
and joint kinetics during turn initiation were determined for both legs using measured ground reaction
forces, 3D segment kinematics, and body segment parameters.
Results indicate that differences in impulse generation between turn conditions were consistent with
initial stance configuration. Despite differences in ground reaction force orientations between turn
conditions, on average, at least 90% of the ground reaction force was aligned with the respective leg plane
for both turn conditions. In addition, a majority of the net joint moment at the ankle, knee, and hip acted
about an axis perpendicular to the leg plane. However, differences in tibia segment alignment relative to
the leg plane affected the distribution of the knee net joint moment when represented with respect to
4

the tibia versus the thigh reference system. During both turn types, most participants used primarily
extensor moments at the ankle and knee, flexor and abductor moment at the push leg’s hip, and extensor
and abductor moments at the turn leg’s hip. While muscle recruitment patterns were subject-specific,
they were consistent with the knee and hip joint moments across turn conditions.

The technique-related findings of this series of studies indicated that dancers coordinated both legs to
regulate the reaction forces during the initiation and turn phases of piqué and pirouette turns. Dancers
used subject-specific mechanisms to increase angular impulse generated during turn initiation. However,
at the segment-level, during the initiation of pirouettes with varied initial hip kinematics, dancers tended
to align their lower extremities with each reaction force in a way that simplified control at the hip across
tasks. These whole-body and segment-level results can be used to inform the design of customized
feedback technologies that aim to facilitate skill acquisition and improve dance performance.
5

Chapter 1. Introduction
Overview
Turning is a challenging and fundamental activity that we all perform in the course of our daily lives. To
navigate our environment, we must often turn our bodies to circumvent obstacles while maintaining our
balance and a functional pace. The performance of these turning tasks reflects the ongoing interaction
between the nervous system, musculoskeletal system, and reaction forces generated at the foot-surface
interface during foot contact (Figure 1-1) [1]. Turns requiring varied rotation and translation demands
often involve satisfying multiple, and often, competing mechanical objectives at the whole body and
segment levels. At the whole body level, the ground reaction forces (RF) generated by each leg must be
regulated in relation to the center of mass (center of mass) trajectory during foot contact so that the net
linear and angular impulse
1
requirements, specific to the turning task, are satisfied. At the segment level,
the RF generated must be coordinated in relation to segment motion to facilitate multi-joint control
without increasing risk of injury. Failure to simultaneously satisfy these mechanical objectives at the
whole-body and segment levels can result in poor outcomes (e.g., falls, injury, etc.). Studying how the
same individual satisfies the mechanical objectives of comparable tasks with varied linear and rotational
demands has been effective in elucidating subject-specific control preferences in goal-directed
movements [2]–[7]. Knowledge of the control and dynamics used by an individual to initiate and perform
turns under a variety of conditions can inform development of intervention tools that facilitate skill
acquisition for individuals with varied physical capacities [8].

Figure 1-1: Diagram representing the ongoing interaction between nervous system, musculoskeletal system, and reaction forces
generated at foot-surface interface [1]
This series of studies determined how linear and angular impulse generation and balance requirements
were met during two fundamental dance turns with different rotation and translation demands.
Furthermore, the within-subject experimental design assisted in identifying an individual’s control
preferences across tasks. This information is needed when designing interactive-media learning
environments that aim to improve an individual’s performance of balance and turning tasks.

1
Impulse: integral of force or moment (torque) over time
6

Mechanics of a Turn
A turn is comprised of three phases: initiation, turning, and termination. Each phase has distinct
mechanical objectives. During the initiation phase of a turn, the performer generates the linear and
angular impulse required during the turn phase. During the turn phase, the mechanical objective is to
rotate while maintaining balance by controlling the center of mass (CM) above the base of support. Finally,
during the termination phase, whole-body rotation is terminated whereas the trajectory of the center of
mass can either terminate or continue in the desired direction of travel.
Impulse Generation Mechanisms during Turns
To change the angular momentum of the body, a net angular impulse must be generated. Angular impulse
is generated by controlling the RF relative to the center of mass over time. Explicitly, angular impulse is
the compounding effect (the integral) of a RF applying a moment about the center of mass over a period
of time. During a turn, the moment applied about a vertical axis through the center of mass by the
resultant horizontal reaction force (RFh) is determined by the cross product of the position vector (r CM)
from the center of mass to the point of RFh application and the RFh (Figure 1-2). If the angle θ, between
the RFh and r CM is known, the moment can also be computed by multiplying the magnitudes of the RFh
and r CM vectors with sinθ. Therefore, RFhs acting through the center of mass do not contribute to angular
impulse.

Figure 1-2: Diagram representation of how to calculate moment about a vertical axis through the center of mass.
Reaction forces involved in the generation of angular impulse also contribute to linear impulse generation,
which is equivalent to a change in linear momentum. Horizontal impulse is the compounding effect (the
integral) of RFh applied to the body over a period of time. In order to satisfy both the translation and
rotation requirements of the turning tasks, RFs generated by each leg need to be coordinated.
For example, in turning tasks like the golf swing, the linear and angular impulse generation by the legs is
coordinated so that the linear impulse generated is primarily toward the target [9] (Figure 1-3A). During
the transition and early downswing phases, the anterior and posterior components of the rear and target
leg RFs contribute to the angular impulse generated about the center of mass [9]. The generation of these
RFhs needs to be coordinated between legs so that the net linear impulse generated in the anterior/
posterior direction remains minimal.
In turning while walking, the rotation and translation requirements are satisfied by coordinating the RFs
generated by each leg using sequential foot contacts[10]–[15]. Each leg subsystem is loaded uniquely
through preparation, redirection, and termination during at least three foot contacts [11]–[13], [16],
7

[17].For example, to change heading direction from anterior to the right, a step turn strategy [12] can be
used to apply a net horizontal impulse towards the right (Figure 1-3B). Additionally, a moment about the
center of mass is applied by at least one of the RFs to rotate the body towards the desired heading
direction [11]. For successful performance, the impulse generated during each foot contact must be
coordinated over time to satisfy both the linear and angular rotation requirements. The sequential use of
each foot contact to satisfy net impulse requirements relate to the findings that pre-planning turning
maneuvers is important to task success [18]–[21].

Figure 1-3: Example leg coordination strategies to control RFh to accomplish translation and rotation requirements
during (A) the golf swing (B) turning while walking using a “step turn” strategy.
As rotational demands of a turn increase, the angular impulse generated by the legs can increase in
multiple ways. These ways include increasing RFh magnitude, changing RFh direction, increasing the
distance from RF point of application and center of mass (r CM), and/or increasing the duration the moment
is applied about the center of mass (Figure 1-4). Previous work with elite golfers found that angular impulse
generated in association with shot distance regulation was increased by scaling the RFh magnitude with
minimal changes in RFh direction [9]. These increases in RFh magnitude also introduced increases in
magnitude of the anterior or posterior components of the RFh at each leg. These increases in RFh
magnitude, however, were coordinated so that anterior and posterior directed impulses were neutralized
and translation of the center of mass during the golf swing remained minimal. Further investigation of the
motor control revealed that generation of RFhs in a specific direction was associated with activation of
certain sets of muscles. For instance, when the RFh was directed anteriorly, posterior leg muscles (such
as hamstrings) were activated. As RFh direction changed, the set of muscles activated shifted. These
results suggest that increases in RFh magnitude will correspond with increases in selective muscle
activation whereas RF redirection is likely to involve a shift in the set of muscles activated. Scaling of RFh
magnitude may prove to be a more simple solution from a neuromuscular perspective [22]. Additionally,
using RFh magnitude modulation to increase angular impulse generated may simplify control because it
would not drastically change the joint moments imposed on the lower extremity, as would changing RFh
orientation relative to the lower extremity [23].
8

Figure 1-4: Schematic demonstrating many ways to increase angular impulse generated with corresponding
consequences.
Maintaining Balance during the Turn Phase and Reducing Rotation during the Termination Phase
The primary goal of the turn phase of ambulatory and classical dance turns is to rotate while maintaining
balance. Static balance requires the center of mass positioned above and within the base of support (base
of support) so that the net vertical and horizontal forces acting on the body are of zero magnitude. Vertical
alignment of the center of mass relative to the base of support can be achieved by redirecting the reaction
force (RF), and/or by reconfiguring segments to reposition the center of mass or the base of support.
Previous experimentally-validated model simulation studies have shown that ability to redirect RFhs
relative to the center of mass increases when the lower extremity is flexed [24] In the case of dance turns
(e.g, pirouette turns), the single support leg during the turn phase is often extended at the knee and the
forefoot (ground contact surface) is sliding while spinning, and as a result, does not facilitate RFh
redirection. In a previous study of balance during the turn phase of pirouettes, Lott and Laws found that
gyro-dynamic effects such as precession were not applicable to pirouettes, implying that balance
maintenance requirements during the turn phase can be treated as they are during static balancing [25].
Additionally, they concluded that a dancer would topple out of a multiple-revolution turn based on initial
COM-base of support alignment at the beginning of the turn phase without corrective segment
reconfigurations during the turn [25]. In the termination phase of the turn, whole-body rotation is reduced
whereas the center of mass trajectory will depend on the final goal of the task. For instance, during turning
while walking and piqué turns, the step taken during termination maintains center of mass trajectory in
the final heading direction [12]. In a turn and stop task, like the pirouette, the center of mass velocity
would come to rest at a time when the center of mass is vertically aligned with the base of support [26].
9

Experimental Approach and Application of Findings
This body of work determined how individuals satisfy the linear and angular impulse generation and
balance requirements of two fundamental dance turns with different rotation and translation
requirements (Figure 1-5). The within-subject experimental design assisted in identifying an individual’s
control preferences across tasks, which can be used in the design of interactive-media learning
environments that aim to improve an individual’s performance of balance and turning tasks.

Figure 1-5: Turns selected (piqué and pirouette turns) differ in rotation, translation, and balance requirements.
By identifying control strategies preferred by an individual, we can personalize augmented feedback to
improve performance. Emerging interactive media technologies offer exciting opportunities for the
development of training tools geared towards improving maneuverability using real-time biofeedback
[27]–[33]. In the context of turns, audible cues represent a promising form of biofeedback conveyed
through the sonification
*
of reaction forces (RF) in relation to body segments or center of mass trajectory.
Sonified feedback for skill acquisition is a relatively new medium, but has the potential to augment clinical
practice, in-field training, and at-home rehabilitation game design [33].
Sonification is especially suited for turning tasks. Visual feedback is the typical real-time feedback
developed by biomechanists and clinicians [34]–[36]. However, forcing the visual system to focus on
visual feedback during turning tasks could overtax the visual processing required during turning [18],
[19], [37]–[41]. Results of the following proposed studies will deliver the content needed to personalize
this type of skill acquisition tool for a variety of end-users (e.g., novice dancer, older adult faller, patient
with motor deficits, etc.).
Systematic Comparisons of Achieving Mechanical Objectives during Turn Performance
Turns performed by dancers provide a unique opportunity to understand how skilled individuals
successfully satisfy different impulse generation and balance requirements during turns. Piqué and
Pirouette turns are two fundamental turns regularly performed by beginning dancers as well as

*
Sonification: an interactive-media design that conveys data through selected sound
10

professional dancers (Figure 1-6) [42]. Each serves as a well-practiced turn task that can be performed with
increased rotational requirements (e.g. single, double). The piqué turn is performed while translating
laterally, whereas the pirouette involves minimal translation of the center of mass and termination in a
stationary position (e.g. “fifth position”) (Figure 1-6). These differences in termination phase objectives are
likely to affect maintenance of balance during the turn phase. Additionally, both turns impose a
challenging constraint during the turn phase: the dancer must spin with single-limb support on an
extended leg (extended knee and plantarflexed ankle), while supported by a very small base of support
(the forefoot) [43], [44].

Figure 1-6: Specific mechanical goals for each turn by phase.
In ballet, these turns are performed with hip external rotation, whereas, in contemporary and modern
choreography, these turns can be performed with a neutral hip alignment. Initiating turns with different
degrees of hip rotation, may alter the orientation of the RFh relative to the lower extremity segments.
These differences could contribute to differences in lower extremity joint kinetics during turn initiation
[22]. In addition, the differences in degree of hip external rotation may change the relative lengths of
muscle-tendon-units crossing the hip and subsequently, alter muscle recruitment [45].
The aforementioned differences between the turns selected inherently modify the impulse generation
and balance requirements. As we compared performance of these turns, one overarching hypothesis was
that when an individual chooses a way to increase angular impulse to complete more rotations within a
turn phase, there will likely be a consequence to meet the other mechanical demands (translational or
balance) that will be assuaged through leg coordination. For instance, if angular impulse generated
increases by increasing components of the RFh perpendicular to the desired direction of center of mass
travel, both legs must work together to preserve desired net linear impulse. Another working hypothesis
is that the center of mass must be maintained within a certain degree of vertical alignment during turns,
and turns of increased rotation may have less tolerance for malalignment relative to vertical. Finally, we
11

expected that if degree of hip external rotation is changed during the initiation of the turn, different sets
of muscles would be activated because the kinematic context and force-generation capacity of muscles
had been modified [22].
References
[1] H. Flashner, A. Beuter, and A. Arabyan, “Fitting mathematical functions to joint kinematics during
stepping: implications for motor control,” Biol. Cybern., vol. 58, pp. 91–99, 1988.
[2] J. L. McNitt-Gray, D. M. Hester, W. Mathiyakom, and B. a Munkasy, “Mechanical demand and
multijoint control during landing depend on orientation of the body segments relative to the
reaction force.,” J. Biomech., vol. 34, no. 11, pp. 1471–82, Nov. 2001.
[3] W. Mathiyakom, J. L. McNitt-Gray, and R. R. Wilcox, “Regulation of angular impulse during two
forward translating tasks.,” J. Appl. Biomech., vol. 23, no. 2, pp. 149–61, May 2007.
[4] W. Mathiyakom, J. L. McNitt-Gray, and R. Wilcox, “Lower extremity control and dynamics during
backward angular impulse generation in forward translating tasks.,” J. Biomech., vol. 39, no. 6,
pp. 990–1000, Jan. 2006.
[5] W. Mathiyakom, J. L. McNitt-Gray, P. Requejo, and K. Costa, “Modifying center of mass trajectory
during sit-to-stand tasks redistributes the mechanical demand across the lower extremity
joints.,” Clin. Biomech. (Bristol, Avon), vol. 20, no. 1, pp. 105–11, Jan. 2005.
[6] W. Mathiyakom, J. L. McNitt-Gray, and R. Wilcox, “Lower extremity control and dynamics during
backward angular impulse generation in backward translating tasks.,” Exp. brain Res., vol. 169,
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15

Chapter 2. Specific Aims and Hypotheses

Figure 2-1: Overview schematic of comparisons made for each specific aim (SA1-4)
I. Modification of Impulse Generation during piqué turns with increased rotational
demands
Aim: To determine how individuals use the push and turn leg (Figure 1-6) to regulate angular and linear
impulse generated during initiation of laterally translating turning tasks with increased rotational
demands.
Hypotheses: During the turn initiation phase,
 Hypothesis 1: as rotation demands of the turn increase, individuals will increase net angular impulse
and maintain net lateral impulse generated.
 Hypothesis 2: the push leg will generate more angular and linear impulse than will the turn leg for
both single and double turns.
 Hypothesis 4: as rotation demands of the turn increase, individuals will increase net angular impulse
by increasing resultant horizontal reaction force (RFh) magnitude at each leg.
 Hypothesis 5: individuals will coordinate the generation of anterior/ posterior impulse generated by
each leg during the turn initiation phase to satisfy the center of mass trajectory requirements.
These hypotheses were tested by comparing how dancers generate linear and angular impulse while
performing single and double piqué turns. A piqué turn requires lateral center of mass trajectory while
rotating during the turn phase.
II. Modification of Impulse Generation during pirouette turns with increased rotational
demands
Aim: To determine how individuals use the push and turn leg (Figure 1-6) to regulate angular and linear
impulse generated during initiation of pirouette turns with increased rotational demands.
Hypotheses: During the turn initiation phase,
SA3
SA4
16

 Hypothesis 1: as rotation demands of the turn increase, individuals will increase net angular impulse
and maintain net linear impulse generated.
 Hypothesis 2: the push leg will generate more angular and linear impulse than will the turn leg for
both single and double turns.
 Hypothesis 3: as rotation demands of the turn increase, individuals will increase net angular impulse
by increasing resultant horizontal reaction force (RFh) magnitude at each leg.
These hypotheses were tested by comparing how dancers generate linear and angular impulse while
performing single and double pirouette turns. A pirouette turn requires minimal center of mass
displacement toward the turn phase stance leg and rotation during the turn phase without center of
mass translation.
III. Balance Regulation during the Turn Phase of Piqué and Pirouette Turns
Aim: To compare balance regulation during the turn phase between piqué and pirouette turns and of
increased rotational demand.
Hypotheses: During the turn phase,
 Hypothesis 1: the initial center of mass velocity during the piqué turn would be greater than that
during the pirouette in the direction of the turn leg’s base of support,
 Hypothesis 2: the average angle between the base of support – center of mass and vertical during a
pirouette would be smaller than the average angle during a piqué turn,
 Hypothesis 3: as the rotational demands increase, the reaction force will be regulated relative to the
center of mass to maintain base of support and center of mass vertical alignment.
These hypotheses were tested by comparing how balance is regulated at the whole-body level (center of
mass vs. base of support vs. RF) and local-level (trunk-leg coordination) during the turn phase of
pirouette and piqué turns.
IV. Comparison of Impulse Generation between pirouettes initiated with and without hip
external rotation
Aim: To compare impulse generation strategies of each leg and associated muscle recruitment strategies
during the turn initiation phase of pirouettes performed with and without hip external rotation.
Hypotheses:
 Hypothesis 1: The net linear and net angular impulse generated during the turn initiation phase will
remain the same for pirouette turns initiated with and without external hip rotation.
 Hypothesis 2: Turns initiated with and without external hip rotation will involve different joint kinetics
and muscle activation patterns.
 Hypothesis 3: As the angular impulse requirements of the pirouette increases, the muscle sets used
during turns of increasing rotation will correspond with alterations in lower extremity joint kinetics
These hypotheses were tested by comparing how impulse is generated by each leg and which muscles
are activated during the initiation phase of pirouettes initiated with and without hip external rotation.

17

Chapter 3. Experimental Design
Experimental Procedures
Female professional and pre-professional dancers were recruited (n≥10; based on similar published
studies using within-subject designs) in the Southern California area for this study. Each subject was
informed and asked to consent to serve as a subject in accordance with the USC Institutional Review Board
for Human Subjects. Prior to data collection, a dancer had the opportunity to review and practice
experimental conditions by visiting a website with sample videos of experimental conditions, as
performed in the lab space. Prior to performance during data collection, dancers were able to acclimate
to the lab space by practicing turns on the dance flooring surface of the forceplates. All dancers had ample
time to prepare their bodies (i.e., stretching, performing a self-selected warmup, etc.) and customize
frictional characteristics as they would for a performance (which may have included selecting preferred
footwear and rosin was provided if preferred, as is customary in dance studios).
Inclusion Criteria
Dancers volunteering to participate in Protocol 1 self-reported ability to successfully perform seven of ten
triple pirouette turns that terminate with the center of mass above base of support, in “fifth position”. To
participate in Protocol 2, dancers additionally self-reported ability to be able to successfully perform seven
of ten triple pirouette turns using neutral hip alignment, landing in “sixth position”. All participants were
medically cleared to participate in dance activities and were free of lower extremity injury that required
medical attention in the previous 6 months.
Exclusion Criteria
Dancers who do not meet the inclusion criteria.
Questionnaire
All subjects were asked to fill out a questionnaire detailing their previous and current dance training and
experience. These data were used to approximate average time spent in dance and physical activity during
the past year.

Name:
Date of Birth:
Current Activity
Dance Classes Hours/week
Rehearsal Hours/week
Performance Hours/week
Teaching Hours/week
Other: What kind of
activity?

How many
hrs/week

Dance History and Preferences
18

Training history (start
age, Russian/Balanchine
ballet, type of modern,
pointe shoe history, etc.)

Age starting pointe NA
Age ending pointe NA
Circle which best
describes your dance
expertise
Only ballet Ballet and Contemporary Only Contemporary
Ballet and Modern Only Modern
Ballet, Contemporary, and Modern
How much time do you
spend in “turnout”?

Circle one: about 0%, 25%, 50%, 75%, 100% of the time dancing.
Do you feel more
comfortable performing
tasks with turnout?
Yes No
Do you have any pain or
current injuries in the
lower extremity?
Yes No

Overview of Participant tasks
Calibration tasks
Calibration tasks included a static trial used to measure bodyweight and establish the mathematical
relationship between anatomical and tracking retroreflective markers (anatomical markers were removed
prior to experimental task performance). Other calibration tasks included functional joint movement tasks
to calculate functional joint axes and centers of the ankle, knee, and hip [1], [2]. Portions of each ankle,
knee, and hip joint center calibration motion used unloaded joint flexion, which is used to calculate
functional joint axes. If muscle recruitment was monitored by electromyography, isometric manual
muscle tests were measured as a basis for muscle recruitment normalization [3].
Experimental tasks
There are two sets of data collection protocols based on a participant’s expertise (Figure 3-1). Specific
Aims I.-III. were investigated using the data collection Protocol 1. Specific Aim IV. was investigated using
the data collection Protocol 2.
19

Figure 3-1: Flowchart of experimental conditions for Protocol 1 and Protocol 2.
The choice between participation in Protocol 1 or Protocol 2 was based on if a participant met the inclusion
criteria for each protocol.
Each participant of Protocol 1 was asked to perform pirouette and piqué turns of increasing rotational
demand (single and double), while each participant of Protocol 2 was asked to perform pirouettes with
modified hip alignment (neutral hip alignment vs. hip external rotation) instead of piqué turns (Figure
3-1). The performer was reminded to perform these turns as he/she would normally perform them, and
chose a preferred turn direction (if applicable). A metronome or music with a constant tempo (80-82bpm)
was used to control turn initiation phase timing, just as a dancer would normally adhere to tempo
requirements in choreography. In pilot work, 80-82 beats per minute was been found to be a reasonable
tempo for the timing of the turn initiation phase leading to successful performance of triple piqué turns.
For example, the examiner cued the dancer with “start balanced, and perform a piqué turn to the beat of
the music/metronome (so that the turn initiation is complete within one beat), continue with a single
piqué following the line towards a target pole, and finish by walking towards the target pole”. For the
performance of pirouettes, the examiner cued the dancer with “perform a pirouette en dehours from
static fourth position and landing in fifth position” (or landing in sixth position, if performing pirouettes
with neutral hip alignment).
Data collection
Kinematics
Recorded motion
Body segment kinematics were captured simultaneously in the frontal, sagittal, and transverse planes
(60Hz Panasonic, Secaucus, NY & 300Hz Casio, Dover, NJ) and were used to verify successful completion
of tasks.
Coordinate data
3D segment kinematics were captured using a retro reflective 16-camera motion capture system (100Hz,
Natural Point, Optitrak, Corvallis, OR). Three-dimensional kinematics were recorded at 100 Hz using
Natural Point cameras (n=16) and Acquire3D software (C-Motion, Germantown, MD). The laboratory
20

environment was calibrated prior to the participant’s arrival. During recording, cameras sent an external
sync pulse to the force and electromyography data acquisition hardware via a BNC cable such that the
kinematics, kinetics, and muscle recruitment data were synchronized. During calibration of the lab using
the 16 camera setup, point residuals were estimated by the software below 0.56mm for each data
collection.

Markerset

Figure 3-2: Markerset including anatomic and tracking retroreflective markers.
A custom markerset including anatomic and tracking retroreflective markers (1.2 cm diameter, B&L
Engineering) were applied to the participant using an adhesive Velcro-system, skin adhesive spray, and
coban tape. The markerset allowed for use of segment properties presented by DeLeva [4], [5]. Markers
were applied and checked by the same experienced experimenter and lab assistants for all collections to
avoid inter-tester differences in landmark locations or application procedures.
Anatomic Markers
Retroreflective markers were applied directly to the skin over the palpated body landmarks. After a
calibration trial was collected, anatomic markers were removed prior to movement trials. Any markers
that did not interfere with movement were left on and used as tracking markers, if necessary.
Tracking Markers
21

Locations of at least three, non-collinear markers affixed to a segment must be known in order to
completely define the orientation of a segment in space over time. These tracking markers were attached
to the shank and thigh segments using methods defined in the literature and previously tested in our lab
by using rigid cuffs. Tracking marker attachment protocol was designed to minimize error due to
movement of the markers relative to the body segment. Sources of error are marker vibrations on impact,
soft tissue movement, and marker cuff slippage.
Prior to collection, four retroreflective markers were affixed to each cuff in a configuration determined by
the suggestions presented by Cappello et al.: four markers per segment were used with a mean cluster
radius (average of the distance between each marker and the center of cluster) greater than ten times
the standard deviation of expected experimental errors (determined in pilot studies) [6]. The markers
were oriented with the longest principal axis along the longitudinal axis of the segment. The rigid shells
were securely fastened to the segment by using coban tape. In some cases, the cuffs were placed over
EMG electrodes. In pilot studies in our lab, it has been determined that this set-up does not interfere with
EMG signals. Foot, pelvis, and upper extremity tracking markers will be applied directly to the skin,
compression shorts, leotard, or footwear (without cuffs). All tracking markers were placed in locations
that allowed for natural kinematics used by dancers to transition between positions used in the piqué and
pirouette turns.
Though there were at least four tracking markers per segment, the three tracking markers used to define
the orientation of a segment were selected based on an automatic detection algorithm that selected the
three markers with the least gaps in raw marker data of the trial and phase of interest (if gaps were
applicable). The reference system was then created such that reference system axes used the two longest
vectors between the three markers, which made the orientation measurement more robust (smaller
vector orientation difference in a longer vector, given the same displacement of a vector’s endpoint
associated with marker residuals/measurement error).
Kinetics
Ground Reaction Forces
Ground reaction forces were measured using two forceplates (0.6 x 0.9 m
2
, 1200 Hz, Kistler, Amhurst, MA,
USA), amplified, and digitized (National Instruments A/D board; custom data collection software).
Forceplates were covered with dance flooring (Mezzafloor, Bolo Productions, Lancaster, CA) to preserve
the frictional characteristics that dancers are accustomed to performing with (Figure 3-3). These covers
were isolated so that they do not transfer force between forceplates or surrounding flooring. Material
properties of the flooring were chosen so that there was 1:1 correspondence between measured force
and force applied to the surface of the dance flooring without any elastic deformation of the surface.

Figure 3-3: Individual forceplate covers for dance floor friction characteristics. Markers for calibrating motion capture are also
shown here, screwed into tapped holes in each forceplate for alignment between force coordinate system and motion capture
coordinate system.
22

Lab setup and lab coordinate systems
The lab’s reference system is based on the forceplate coordinate systems (Figure 3-4). Calibration markers
were screwed into machined holes in the forceplate’s surface to ensure alignment between kinetic and
kinematic measurements.

Figure 3-4: Forceplate-based reference system is used when collecting 3D segment coordinate data from 16 cameras
mounted on ceiling beams or tripods.
Muscle Recruitment
Activation of superficial hip muscles were monitored using surface electromyography (Konigsberg,
1200Hz), amplified, and digitized (National Instruments A/D board; custom data collection software) so
that it was synchronized with ground reaction force data. Skin over the belly of each muscle of interest
was shaved and cleaned prior to the application of surface electrodes [7]. Dual electrodes with an inter-
electrode distance of 1 cm were placed over the muscle belly, parallel to the muscle fibers (Noraxon,
Scottsdale, AZ).
Monitored muscles:
 Right and Left Biceps Femoris
 Right and Left Gluteus Maximus
 Right and Left Gluteus Medius
 Right and Left Rectus Femoris
Data processing and Analysis
Kinematics
The processing of 3D kinematics required multiple steps through programs and custom Matlab software.
After marker data were measured using Aquire3D and identified using AMASS (C-Motion), C3D files were
imported into Visual3D (C-Motion) to export marker data as a “.txt” file for subsequent processing in
Matlab. Upon importing kinematic data, gaps in data (if applicable) were filled using a cubic spline
smoothing Matlab function (“CSAPS”) with a user-input smoothness factor “p” based on Jackson et al. [8].
Functional joint centers during joint calibration movements of the hip, knee, and ankle were calculated
using custom Matlab code following the calculation method of Schwartz and Rozumalski to find
instantaneous center of rotation between two rigid bodies[9], [10]. This also used estimates of functional
23

joint centers from anatomic markers as an initial location (needed for the post-hoc mathematical selection
of an average/mode intersection of the instantaneous axes of rotation). For calculation of the functional
joint centers of the knee and ankle (2 degree of freedom joints), the calculated center of rotation was
projected onto a plane bisecting the medial and lateral condyle and malleoli markers, respectively.
Using the static calibration trial, functional joint centers defined the endpoints of each segment. Equal
segment lengths throughout experimental tasks were achieved by using the shank as a basis segment for
the lower extremity. A mapping between anatomic reference systems and tracking reference systems for
each segment was calculated (rotation matrix) during the static trial (Figure 3-5).

Figure 3-5: Mapping between tracking and anatomic markers
This allowed for calculation of anatomic landmarks and representation of joint kinetics about anatomic
segment axes even if some anatomical markers were taken off during experimental tasks or are occluded
within a trial. In pilot work, the difference between calculated (via rotation matrices) and measured
anatomical markers ranged from 2-7mm. The corresponding segment orientation error ranged between
3°-6°.
Using estimates of segment parameters, segment center of masses and total body center of mass (CM)
were calculated for analysis of whole-body dynamics [5]. These measures were used to provide kinematic
context for analysis of kinetics (whole-body and subsystem) and muscle recruitment patterns. Segment
center of masses enabled comparisons of segment configuration throughout the movement. Pilot work
suggested tracking markers were more likely to move relative to the thigh segment than the markers on
the shank, due to thigh muscle structure and motion. By using the shank as a basis segment, the error in
hip joint center position as calculated by the thigh tracking markers was mitigated. In pilot work, the
difference between total body center of mass position calculated with and without basis segments was
on the order of 2mm.
𝑥 𝑇𝐵𝐶𝑀 =
(∑𝑚 𝑖 𝑥 𝑐𝑚 ,𝑖 )
𝑏𝑜𝑑𝑦 𝑚𝑎𝑠𝑠 (𝑓𝑜𝑟 𝑖 = 1 𝑡𝑜 𝑛 𝑏𝑜𝑑𝑦 𝑠𝑒𝑔𝑚𝑒𝑛𝑡𝑠 )
24

𝑦 𝑇𝐵𝐶𝑀 =
(∑𝑚 𝑖 𝑦 𝑐𝑚 ,𝑖 )
𝑏𝑜𝑑𝑦 𝑚𝑎𝑠𝑠 (𝑓𝑜𝑟 𝑖 = 1 𝑡𝑜 𝑛 𝑏𝑜𝑑𝑦 𝑠𝑒𝑔𝑚𝑒𝑛𝑡𝑠 )
Kinetics
Reaction forces (RF) in x (RFx) and y (RFy) directions were used to calculate the resultant horizontal RF:
𝑅𝐹 ℎ = √𝑅𝐹
𝑥 2
+ 𝑅𝐹
𝑦 2

and linear impulses in each direction:
∫ RFy dt
𝑡𝑓
𝑡𝑖
, ∫ RFx dt
𝑡𝑓
𝑡𝑖

Net horizontal impulse is the sum of the linear impulse generated by each leg.
Center of pressures were calculated as described by Kistler forceplate documentation [11]. By using linear
impulse in each direction and the initial CM position (from kinematics), the CM trajectory was calculated.
This CM trajectory was found to be well-aligned with the CM calculated using markerset data and
estimated body segment parameters [4] in static and motion trials. This was a preferred method because
measurement error of reaction forces was less than that of kinematic calculations.
By knowing the CM horizontal position and the center of pressure (the point of force application), the
vector was defined from the CM to the COP as 𝑟 𝑐𝑚
⃗⃗⃗⃗⃗⃗ , and used to calculate the moment applied about a
vertical axis through the CM from each leg’s RFh:
𝑀𝑜𝑚𝑒𝑛𝑡 = 𝑟 𝑐𝑚
⃗⃗⃗⃗⃗⃗ × 𝑅𝐹
ℎ
⃗⃗⃗⃗⃗⃗⃗
= |𝑟 𝑐𝑚
⃗⃗⃗⃗⃗⃗ |sin𝜃 |𝑅𝐹
ℎ
⃗⃗⃗⃗⃗⃗⃗
|.
The free moment (Tz, torque applied about a vertical axis) contributed to net moment from each leg’s
interaction with the forceplate [11]. Angular Impulse generated at each leg was calculated using moment
calculated and the free Moment. Net angular impulse is the sum of the angular impulse generated by each
leg.
Net Angular Impulse= ∫ Net Moment dt = ∫ (𝑇 𝑧 ⃗⃗⃗
+ 𝑟 𝑐𝑚
⃗⃗⃗⃗⃗⃗ × 𝑅𝐹
ℎ
⃗⃗⃗⃗⃗⃗⃗
)
leg1
+ (𝑇𝑧
⃗⃗⃗⃗
+ 𝑟 𝑐𝑚
⃗⃗⃗⃗⃗⃗ × 𝑅𝐹
ℎ
⃗⃗⃗⃗⃗⃗⃗
)
leg2
dt
𝑡𝑓
𝑡𝑖

𝑡𝑓
𝑡𝑖

To compare how the angular impulse was generated by a performer, the alternative representation of the
cross product (𝑀 ⃗ ⃗
= 𝑟 𝑐𝑚
⃗⃗⃗⃗⃗⃗ × 𝑅𝐹
ℎ
⃗⃗⃗⃗⃗⃗⃗
= |𝑟 𝑐𝑚
⃗⃗⃗⃗⃗⃗ |sin𝜃 |𝑅𝐹
ℎ
⃗⃗⃗⃗⃗⃗⃗
|) was used to determine which factors the individual
used to increase/ decrease angular impulse: RFh magnitude, position vector magnitude, angle between
RFh and position vectors, or duration of moment applied. As opposed to representing moment as
perpendicular distance multiplied by force magnitude, direction and position vector magnitude were
decoupled. This was useful to distinguish between a difference in stance width, CM trajectory-velocity
control, or force orientation associated with changes in the direction of the reaction force.
Joint Kinetics
Joint kinetics during turn initiation were determined for both the turn and push leg using measured
ground reaction forces, 3D segment kinematics, and body segment parameters [5]. Resultant net joint
moments calculated for the ankle, knee, and hip were then represented about different axes
(perpendicular to leg plane, functional joint axes, segment reference systems axes) to characterize the
mechanical demand imposed on muscles involved in control of the lower extremities.
25

Kinematics and kinetics were synchronized by interpolating kinematic data (100Hz) to match the kinetic
data frequency (1200Hz) using the cubic spline function. As a spline function, this also automatically
differentiated marker and segment center of mass position data to estimate velocities and accelerations.
Net joint forces were calculated using ground reaction forces, segment masses, segment endpoints, and
segment center of mass acceleration[4].
For each segment, the interpolated endpoint positions were used to calculate segment orientations.
Quaternion parameterization was used to calculate angular velocity of a segment between time samples
(𝜔⃗ ⃗
𝑠𝑒𝑔𝑚𝑒𝑛𝑡 ). This angular velocity was smoothed and interpolated using the cubic spline function for the
purposes of calculating angular acceleration (𝑎 ). Net joint moments were calculated using these angular
velocities and accelerations (expressed in local/segment anatomic reference systems).
Quaternion parameterization was used to calculate the functional joint axis between two segments,
equivalent to the angular velocity between segments (𝜔⃗ ⃗
𝑗𝑜𝑖𝑛𝑡 ). This calculation is outlined below:
Step 1: Segment Quaternions
Using tracking markers, each segment’s direction cosine matrix (DCM) relative to inertial coordinate
system was calculated and converted to quaternion representation.

Step 2: Joint Angle
The relationship between q1 and q2 at an instant in time was calculated. This relationship (q12) is in the
form of a quaternion transformation from q1 to q2 using quaternion multiplication.

𝑞 2 = 𝑞 1⊗ 𝑞 12
pre-multiply both sides by inverse of q1
𝑞 1
−1
⊗ 𝑞 2
= 𝑞 1
−1
⊗ 𝑞 1⊗ 𝑞 12
Cancel via quaternion multiplication properties
𝑞 1
−1
⊗ 𝑞 2
= 𝑞 12
Now you have the quaternion rotation transformation from segment 1 to segment 2

Inertial
Coordinate
System
Segment 1
DCM1
Segment 2
DCM2
Segment 2
q 2
Segment 1
q 1
q 2
q 1
DCM1
DCM2
26

This q12 provided the 𝑛̂ vector about which to rotate segment 1 and the 𝜑 scalar amount of rotation
about 𝑛̂. In other words, q1 is rotated about 𝑛̂ by 2𝜑 to be aligned with q2 at an instant of time.

Step 3: Angular velocity between segments
Time derivative of the joint angle was used to calculate the angular velocity between segments through
time.
𝜔̅
2
1
= 2
𝑑𝑞 12
𝑑𝑡
⊗ 𝑞 12
−1

Step 4: Functional Joint Axes
Angular velocity 𝜔̅
2,𝑖 1
was expressed at each time in the local anatomic reference systems (𝜔̅
𝑎𝑛𝑎 ,𝑖 ) for each
segment so that it represents an anatomically-relevant articulation between segments. The functional
joint axes (FJA) was chosen as the 𝜔̅
𝑎𝑛𝑎 ,𝑖 closest to the mean 𝜔̅
𝑎 𝑛𝑎 ,𝑖 during the functional movement. The
origin of the angular velocity expressed in each segments was equivalent to the shared segment endpoint
(functional joint center).

Muscle Recruitment
The electromyography (EMG) data were filtered using a 4th order zero-phase butterworth band-pass filter
(10-400Hz) and quantified using root mean squared values in 20ms average bins. EMG data were
normalized to the maximum binned values during isometric manual muscle tests [3][7], [13], [14].
Statistics
Robust statistical methods that perform well under non-normality and small sample sizes were carefully
selected for use in this study (personal correspondence with Rand Wilcox). Through this process
a probability-based measurement was identified to determine how likely the value of interest is to belong
in one experimental condition vs. different condition within-subject [15]. This statistical method is a
conservative way to handle statistics in a small sample size without assuming normality.
The probability for each variable of any turn condition trial being less than any other turn condition trial
was calculated such that each dancer served as his/her control (R, open-source). Assuming local
independence (i.e. no order effect for trials within a condition), and that turn type trials were independent
(i.e. pirouette trials were not directly tied to piqué trials) for each subject, p-values were calculated for
each dancer using Cliff’s analog of the Wilcoxon-Mann-Whitney test.[16], [17] This method was chosen
because it deals well with small numbers of trials per condition[17]. A step-down Fisher-type method was
then applied to control the familywise error rate (α = 0.05) over multiple comparisons, modified so that
the level of significance becomes α/k at each k
th
iteration[18]–[20]. The statistical method chosen provides
more flexibility by allowing heteroscedasticity across dancers[21]. This statistical method is highly
q 1
q 2
q 12 q 1
1
1
2 4 2
3
3
sin ˆ
2
ˆ sin sin cos ˆ
2 2 2
sin ˆ
2
n
q
qq
n
q
n

  








 




    





qn
q 12=
q 2
27

dependent upon the distribution of p-values for each variable measured because the level for significance
becomes α/k at each k
th
iteration[20]. Therefore, the presentation of within-subject results provides a
relatively conservative estimate of significant differences between turn conditions. As the number of trials
increase per condition, Cliff’s method can achieve lower p-values. Despite typical performance of at least
seven successful turns, in some cases, only five trials were available for analysis as a result a data collection
error, which may limit the ability to reach statistically significant results.

References
[1] S. J. Piazza, A. Erdemir, N. Okita, and P. R. Cavanagh, “Assessment of the functional method of hip
joint center location subject to reduced range of hip motion,” J. Biomech., vol. 37, no. 3, pp. 349–
356, Mar. 2004.
[2] A. Leardini, A. Cappozzo, F. Catani, S. Toksvig-Larsen, A. Petitto, V. Sforza, G. Cassanelli, and S.
Giannini, “Validation of a functional method for the estimation of hip joint centre location,” J.
Biomech., vol. 32, no. 1, pp. 99–103, Jan. 1999.
[3] F. Kendall, E. McCreary, P. Provance, M. Rodgers, and W. Romani, Muscles, testing and function:
with posture and pain, 5th ed. Baltimore, MD: Williams and Wilkens, 2005.
[4] P. De Leva, “Adjustments to Zatsiorsky-Seluyanov’s segment inertia parameters,” J. Biomech., vol.
29, no. 9, pp. 1223–1230, 1996.
[5] P. De Leva, “Joint center longitudinal positions computed from a selected subset of Chandler’s
data,” J. Biomech., vol. 29, no. 9, pp. 1231–1233, 1996.
[6] A. Cappello and A. Cappozzo, “Multiple anatomical landmark calibration for optimal bone pose
estimation,” Hum. Mov. Sci., vol. 16, pp. 259–274, 1997.
[7] C. J. De Luca, M. Kuznetsov, L. D. Gilmore, and S. H. Roy, “Inter-electrode spacing of surface EMG
sensors: reduction of crosstalk contamination during voluntary contractions.,” J. Biomech., vol.
45, no. 3, pp. 555–61, Feb. 2012.
[8] K. M. Jackson, “Fitting of mathematical functions to biomechanical data,” Biomed. Eng. IEEE
Trans., vol. BME-26, no. 2, pp. 1978–1980, 1979.
[9] M. H. Schwartz and A. Rozumalski, “A new method for estimating joint parameters from motion
data.,” J. Biomech., vol. 38, no. 1, pp. 107–16, Jan. 2005.
[10] L. Held, “Lower extremity control and dynamics of landings with horizontal momentum
redirection,” 2011.
[11] International Society of Biomechanics, “Kistler Force Plate Formulae,” 2015. [Online]. Available:
http://isbweb.org/software/movanal/vaughan/kistler.pdf.
[12] L. A. Held, “LOWER EXTREMITY CONTROL AND DYNAMICS OF LANDINGS,” 2011.
28

[13] H. Taylor and C. De Luca, “Development of new protocols and analysis procedures for the
assessment of LBP by surface EMG techniques,” J. Rehabil. Res. Dev., vol. 34, no. 12, pp. 415–427,
1997.
[14] C. J. De Luca, L. D. Gilmore, M. Kuznetsov, and S. H. Roy, “Filtering the surface EMG signal:
Movement artifact and baseline noise contamination.,” J. Biomech., vol. 43, no. 8, pp. 1573–9,
May 2010.
[15] R. Wilcox, Modern Statistics fo the Social and Behavioral Sciences. Boca Raton, FL: Taylor &
Francis Group, 2012.
[16] N. Cliff, Ordinal Methods for Behavioral Data Analysis. Mahwah, NJ: Lawrence Erlbaum
Associates, Inc., Publishers, 1996.
[17] M. Neuhäuser, C. Lösch, and K.-H. Jöckel, “The Chen–Luo test in case of heteroscedasticity,”
Comput. Stat. Data Anal., vol. 51, no. 10, pp. 5055–5060, Jun. 2007.
[18] Y. Hochberg, “A sharper Bonferroni test for multiple tests of significance,” Biometrika, vol. 75, pp.
800–802, 1988.
[19] Y. Hochberg and A. C. Tamhane, Multiple Comparison Procedures. Hoboken, NJ, USA: John Wiley
& Sons, Inc., 1987.
[20] R. Wilcox and F. Clark, “Robust Multiple Comparisons Based on Combined Probabilities From
Independent Tests,” J. Data Sci., vol. 13, no. 1, pp. 1–11, 2015.
[21] M. J. Crowder and D. J. Hand, Analysis of Repeated Measures, 1st ed. New York: Chapman &
Hall/CRC, 1990.

29

Chapter 4. Modification of Impulse Generation during Piqué Turns with
Increased Rotational Demands
Introduction
Negotiating challenges during the performance of functional weight-bearing activities involves effective
interaction between the neuromuscular system, musculoskeletal system, and the environment. In
locomotor tasks such as turning-while-walking, the trajectory of the center of mass (CM) is controlled
relative to the base of support via reaction forces (RF) generated during foot contact. The reaction force
regulation must be coordinated such that the linear and angular impulse requirements of the task are
satisfied while maintaining balance. These task requirements create potential conflicts in control priorities
in that generation of angular impulse about the CM involves RF components that are not aligned with the
desired CM trajectory. For example, achieving the mechanical objectives during turning-while-walking can
be particularly challenging for individuals with musculoskeletal and/or neural impairments (e.g., older
adults at risk of falling, individuals with Parkinson’s disease, Stroke survivors, individuals with hip joint
dysfunction, people using lower limb prostheses, etc.) [1]–[6]. By advancing our understanding of how
individuals with a range of physical capabilities successfully satisfy competing mechanical objectives under
progressively more challenging turning conditions, we can personalize intervention strategies to improve
performance of gait-related tasks [7]–[10].
Examination of an individual’s control priorities during well-practiced and goal-directed tasks provides
insight into subsystem coordination used to satisfy mechanical objectives at the whole-body level. For
example, during the take-off phase of the back and reverse somersaults, the trunk and leg systems were
coordinated to facilitate control of the RF relative to the CM to generate required linear and angular
impulse [7-9]. By using a within-subject experimental design, it was determined that more than one
multijoint control strategy effectively satisfied the mechanical objectives of the take-off phase [7-9]. While
muscle activation patterns were unique to an individual, they were consistent with the mechanical
demand imposed on the ankle, knee, and hip during impulse generation [7-9]. In the case of locomotor
tasks such as turning or cutting maneuvers, each leg plays a distinct role in generating the RF required to
control both linear and angular momentum of the body [11-13,17].
Turns performed by dancers provide a unique opportunity to understand how skilled individuals
successfully satisfy competing mechanical objectives prior to and during the turn. The piqué turn is a well-
practiced and goal-directed task that imposes conflicting mechanical objectives. The performance
specifications for a piqué require that the CM translate only in the lateral direction while the body rotates
about the CM while supported by a single leg [Figure 4-1]. Piqué turns are often initiated from a static
position while the body mass is supported by the “push leg”. During the “turn initiation phase”, linear and
angular impulse is generated, leading to the desired initial conditions of the “turn phase” that follows.
During the turn phase, the CM continues to travel in the lateral direction and the body rotates while
supported only by the “turn leg” (Figure 4-1,Figure 4-2).
In other tasks involving whole body rotation, increases in rotation requirements were satisfied by
increasing the magnitude of the resultant horizontal RF (RFh) at one or both legs [17]. To satisfy the linear
momentum requirements of these tasks, individuals coordinated the regulation of the RFh between legs
using subject-specific strategies [9-19] In the case of the piqué turn, we expected that the RFh of each leg
would contribute to the angular impulse generated to meet the rotational demands of the task, yet be
30

coordinated so that the net linear impulse is aligned with the desired lateral trajectory of the CM.
Additionally, because the push leg is in contact with the ground for the whole turn initiation phase, we
expected that it would contribute more angular impulse generation than would the turn leg. Examination
of linear and angular impulse regulatory mechanisms used by elite performers to accommodate
competing mechanical objectives during turning tasks likely to assist in designing systems to improve
performance and reduce the risk of injury in turning tasks.

Figure 4-1: Exemplary kinematics of a piqué turn. The mechanical objective of the piqué turn is to translate laterally
and complete rotations about a vertical axis through the center of mass. The turn initiation phase is initiated from a
static position and then ends at last contact with the push leg.
By identifying effective solutions used by skilled performers under progressively more challenging turning
conditions, we can evaluate potential trade-offs between these subject-specific control strategies [7,20-
21]. The goal of this study was to determine how individuals use the push and turn leg to regulate angular
and linear impulse generated during initiation of laterally translating turning tasks with increased
rotational demands. We hypothesized that during the turn initiation phase, (1) as rotation demands of
the turn increase, individuals will increase net angular impulse and maintain net lateral impulse
generated, (2) the push leg will generate more angular and linear impulse than will the turn leg for both
single and double turns, (3) as rotation demands of the turn increase, individuals will increase the net
angular impulse generated by increasing the moment applied by the push leg more than by increasing
that applied by the turn leg, (4) as rotation demands of the turn increase, individuals will increase net
angular impulse by increasing resultant horizontal reaction force (RFh) magnitude at each leg, and (5)
individuals will coordinate the generation of anterior/ posterior impulse generated by each leg during the
turn initiation phase to satisfy the CM trajectory requirements. These hypotheses were tested by
comparing how dancers generate linear and angular impulse while performing single and double piqué
turns.
31

Methods
Professional ballet and contemporary dancers with similar levels of experience and training (n=10, female,
age: 16-38, >9 years of dance experience) volunteered to participate and provided informed consent in
accordance with the institutional review board for human subjects. All subjects were free of lower
extremity injury at the time of data collection. Prior to data collection, participants warmed up and
practiced the experimental tasks until they felt well-practiced and familiar with the experimental setup.
Dancers were asked to perform standard piqué turns that required rotation of the whole body while
supported by one leg while travelling laterally in a straight line. Rotational demands were systematically
increased by requiring varying degrees of whole-body rotation (single (pk1) ~360° rotation, double (pk2
~720° rotation)). Task trajectory was identified using a target pole to remind the dancer of the desired
direction of translation. The speed of the turn’s initiation phase was controlled using 80-82 bpm music,
similar to timing restrictions in choreography dictated by tempo. Participants wore self-selected footwear
and arranged for preferred frictional characteristics for turning (i.e., ballet slippers, rosin, etc.). Turns were
performed until at least five successful turns were achieved under each condition. Five successful turns
were typically achieved in less than seven attempts.
Reaction forces generated during foot contact were measured using force plates (1200 Hz, Kistler,
Amherst, NY). Segment kinematics were captured using a retro reflective 16-camera motion capture
system (100 Hz, Natural Point, Optitrak, Corvallis, OR). Three-dimensional kinematics were recorded at
100 Hz using Natural Point cameras (n=16) and Acquire3D software (C-Motion, Germantown, MD). These
data were used to determine the initial CM position and to verify successful completion of tasks.
Horizontal CM trajectory was determined using the initial horizontal position of the CM at the task
initiation and the resultant horizontal RF generated by each leg [20]. RF was normalized by body weight
and impulse was normalize by body mass.
The piqué turns performed in study were initiated from a static position with the body weight supported
by the push leg. During the turn initiation phase, the linear and angular impulse needed to perform the
piqué turn is generated. The turn initiation phase was determined from the time when the lateral
component of the horizontal RF (RFh) of the push leg exceeded 10N until termination of push leg ground
contact (Figure 4-2). Late in the turn initiation phase, there was a period of double-limb support after the
initial contact of the Turn Leg with the ground (Figure 4-2, double support phase). Differences in impulse
generation between legs and turn conditions were determined by comparing the magnitude and
orientation of the RFh during the turn initiation phase. Angular impulse about a vertical axis passing
through the CM during the turn initiation phase was determined using the cross product of the position
vectors from the CM to each point of RF application (center of pressures for the Turn and Push legs) and
the RFhs. The free moment applied by each leg was also determined [13], [21].
To study the mechanisms used to increase the moment applied at each leg about the CM, the variables
contributing to the moment applied by each leg from the RFh were quantified during a subphase of each
leg’s ground contact time prior to peak moment applied by each leg. This subphase was defined as the
25% turn initiation phase duration prior to peak moment (“peak moment subphase”) applied by each leg
in each turn condition (boxed areas in Figure 5-6 show this subphase). This phase was selected to best
represent what was modulated during the rise to peak moment applied by each leg for most dancers
(Figure 4-6, boxed areas). Mean (SD) moment, RFh magnitude, position vector magnitude, and sinθ
(where θ is the angle between the RFh and position vectors) were calculated during this subphase.
32

Figure 4-2: Phases of the piqué turn with exemplary kinematics. During the turn initiation phase, the linear and
angular impulse needed to perform the piqué turn is generated. The turn initiation phase was determined from the
time when the lateral component of the horizontal RF (RFh) of the push leg exceeded 10N until termination of push
leg ground contact. Late in the turn initiation phase, there was a short period of double-limb support after the
initial contact of the turn leg with the ground.
Between task differences in mean angular impulse, lateral impulse, moment, and variables contributing
to the moment applied about the CM under each turn condition were compared using statistical analysis
software R (open-source). Group differences of these values between turn conditions were assessed using
paired t-test comparisons. Within-subject comparisons of the probability for each variable of any single
piqué trial being less than any double piqué trial was calculated (R, open-source). P-values were calculated
for each dancer using Cliff’s analog of the Wilcoxon-Mann-Whitney test [22], [23]. This method was
chosen because it deals well with small numbers of trials per condition [23]. A step-down Fisher-type
method was then applied to control the familywise error rate (α = 0.05) over multiple comparisons,
modified so that the level of significance becomes α/k at each k
th
iteration [24]–[26]. The statistical
method chosen provides more flexibility by allowing heteroscedasticity across dancers [27]. This statistical
method is highly dependent upon the distribution of p-values for each variable measured because the
level for significance becomes α/k at each k
th
iteration [26]. Therefore, the presentation of within-subject
results provides a relatively conservative estimate of significant differences between turn conditions.
Results
Dancers generated greater mean net angular impulse during the initiation of double piqué turns
compared to during single piqué turns. The difference in net angular impulse generated was significant as
a group (p = .0005) and individually for four of ten dancers (brackets, Figure 4-3). The increase in mean net
angular impulse from single to double piqué turns ranged from 7.6 % to 118.6 % within dancer (eight of
ten dancers increased mean net angular impulse by more than 14.8 %). In general, angular impulse
generation was attributed to free moment contributions early in the turn initiation phase and control of
the RFh relative to the CM later in the turn initiation phase (exemplary subject 3, Figure 4-5).
33

Figure 4-3: Mean (SD) normalized angular impulse generated about the center of mass by the push leg (orange) and
turn leg (purple) of each dancer during the turn initiation phase of single (pk1) and double (pk2) piqué turns. The
mean net angular impulse (gray) tended to increase as the rotation requirements increased. The push leg dominated
the angular impulse generation during the turn initiation phase of both the single and double turns. Brackets indicate
within-subject significant differences between turn conditions when tested at α = .05 level and adjusted for multiple
comparisons.
As rotation demands of the turning task increased, the net lateral impulse generated during the initiation
of piqué turns tended to decrease. The difference in net lateral impulse generated was significant as a
group (p = .001, Figure 4-4) and individually for two of ten dancers (brackets, Figure 4-4). The mean change
in lateral CM velocity during the turn initiation phase decreased by more than 0.05 m/s when performing
a double turn as compared to a single turn in eight of the ten dancers (the piqué was initiated from a static
position) (Figure 4-4). The majority of net lateral impulse generated during turn initiation for both single
and double turns was generated by the push leg (Figure 4-4, push vs. turn leg).
34

Figure 4-4: Mean (SD) normalized linear impulse generated in the lateral direction by the push and turn legs of each
dancer (Sub 1-10) during the turn initiation phase of single (pk1) and double (pk2) piqué turns. Net lateral linear
impulse generated (gray) tended to decrease with increased rotational demand. The push leg (orange) dominated
the lateral impulse generation of both single and double turns. Brackets indicate within-subject significant differences
between turn conditions when tested at α = .05 level and adjusted for multiple comparisons.
As expected, the majority of angular impulse was generated by the push leg for both turn conditions and
all subjects (Figure 4-3, push leg vs. turn leg). As rotational demand increased, the increase in angular
impulse generated by the turn leg exceeded the increase in that generated by the push leg. Seven of ten
dancers increased the mean angular impulse generated by the push leg by more than 0.01 Nms/kg,
whereas, ten of ten dancers increased the mean angular impulse generated by the turn leg by more than
0.01 Nms/kg (push leg pk1 vs. pk2 and turn leg pk1 vs. pk2, Figure 4-3). Within-subject analysis indicated
that eight of ten dancers significantly increased mean angular impulse generated by the turn leg, and one
dancer significantly increased mean angular impulse generated by the push leg (brackets, Figure 4-3).
As rotational demands increased, dancers increased the mean moment applied by one or both legs using
subject-specific combinations of reaction force and moment arm regulation during each leg’s peak-
moment subphase. Differences in mean moment for each leg were significant as a group (p = .0008 push
leg, p = .00002 turn leg) and individually for two dancers at the push leg and nine dancers at the turn leg
(asterisks, Figure 4-6 B&D). Dancers used subject-specific combinations of RFh regulation and position
vector magnitude increases (Figure 4-6 A&C, exemplar Figure 4-5). Within-subject analyses indicated that
the moment applied by the push leg increased primarily from reaction force redirection (two dancers,
significantly so), without changes in the push leg’s position vector length from the CM or increases in
reaction force magnitude (with the exception of subject 9) (asterisks, Figure 4-6A). In contrast, the moment
applied by the turn leg increased via a combination of reaction force redirection (five dancers), increased
reaction force magnitude (five dancers), and increased position vector magnitude (three dancers)
identified using within-subject analyses (asterisks, Figure 4-6C).
35

Figure 4-5: Control strategy used by an individual dancer (Subject 3) to increase net angular impulse generated during
the initiations of single (pk1, green) to double (pk2, blue) piqué turns. (A) Push and Turn Leg mean (SD) moment vs.
time curves showing an increase in moment applied by each leg about a vertical line through the center of mass.
Mean (SD) free moment superimposed in gray on the push leg’s moment-time curve to show its large contribution to
the total moment-time curve of the push leg. Light gray shows single piqué free moment, while darker gray shows
larger free moment application during double piqués. (B) Increased mean (SD) |RFh| applied to the turn leg during
rise to peak moment applied as rotational demand increased (C) |RFh| redirection was used by both legs to increase
mean (SD) sinθ in doubles vs. singles. Boxed area displays 25% turn initiation phase duration prior to peak moment
applied by each leg in each turn condition (“peak moment subphase”).
36

Figure 4-6: Subject-specific mechanisms (A,C) used to increase moment applied by the RFh at (A) push leg and (C)
turn leg (B, D) indicate the mean (SD) average moment applied by the (B) push leg and (D) turn leg during the peak
moment subphase at each leg. Checkmarks indicate a sustained increased in the variable’s mean value that
exceeded its standard deviation, asterisks indicate within-subject significant differences between turn conditions
when tested at α = .05 level and adjusted for multiple comparisons. Group mean comparison indicated increases in
push leg sinθ (p = .001), turn leg |RFh| (p = .0002), turn leg sinθ (p = .00002), and turn leg |rcm| (p = .005).
37

The net moment was generated by different mechanisms early compared to late during the turn initiation
phase for both single and double piqué turns. Early in the turn initiation phase, before the turn leg made
initial contact with ground, the free moment contributed positively to the push leg’s angular impulse
generation for all subjects and both turn conditions (free moment of Figure 4-5A). The free moment
application was generally sustained for longer than half of the turn initiation phase, as in the exemplar
data displayed (free moment of Figure 4-5A). Within-subject analyses indicated that two of ten dancers
increased the free moment with increased rotation, which contributed to the observed increase in angular
impulse generated by the push leg. Later in the turn initiation phase, typically after the turn leg made
initial contact with the ground, the net moment applied increased to its peak magnitude during a relatively
short period of time. Within-subject analyses indicated that six of ten dancers increased the window of
opportunity to generate angular impulse with the turn leg by initiating turn leg contact earlier within the
turn initiation phase as rotation demand increased.
By coordinating the reaction force generation between legs, the net horizontal impulse in the
anterior/posterior direction remained minimal with increases in rotational demands. As a result, the
magnitude of changes in CM velocity in the anterior/posterior direction tended to be less than 0.15 m/s,
which is consistent with the mechanical objectives of the piqué turn at the whole-body level. Within-
subject analyses indicated that as rotational demand increased, seven of ten dancers increased the
anterior impulse generated by the push leg and nine of ten dancers increased the posterior impulse
generated by the turn leg. However net impulse in the anterior posterior direction remained minimal,
contributing to a change in anteroposterior velocity less than 0.2m/s (Figure 4-7).

Figure 4-7: Mean (SD) normalized linear impulse generated in the anterior and posterior direction by the push leg
(orange) and turn legs (purple) of each dancer (Sub 1-7) during the turn initiation phase of single (pk1) and double
(pk2) piqué turns. By coordinating reaction force generation between legs, the net horizontal impulse (gray) in the
anterior/posterior direction remained minimal with increases in rotational demands.
38

Discussion
In this study, the control strategies used by skilled dancers to regulate linear and angular impulse
generation during well-practiced and goal-directed turns were investigated. Comparisons of reaction
forces generated by each leg during the performance of single and double piqué turns performed by
dancers provided an opportunity to determine how skilled individuals successfully satisfy competing
mechanical objectives during turns. The skilled dancers in this study controlled angular impulse generation
during the piqué turn using both legs. Mechanisms used to increase net angular impulse generation
between single and double piqué turns varied across dancers and between push and turn legs. Different
mechanisms for regulating angular impulse generated by each leg (e.g. modify RFh direction and/or
magnitude) are important to consider when designing interventions that aim to improve dancer
technique. Understanding how skilled dancers coordinate the linear and angular impulse generated by
each leg during piqué turns may also assist in the identification of effective strategies individuals can use
to regulate RF in relation to their CM trajectory while maintaining balance in other activities of daily life.
To mitigate the effect of experimental conditions on the results, efforts were made to mimic the typical
dance performance environment and a within-subject design was used. By covering each forceplate and
surrounding area with dance flooring surface and by encouraging dancers to use their own footwear,
dancers were able to establish their preferred foot-surface frictional characteristics. The dance flooring
selected provided typical frictional characteristics found on stages and in studios, but was rigid such that
it did not interfere with force transmittance. Additionally, music with a controlled tempo was used to
standardize the speed of the turn initiation phase across participants, consistent with what a dancer is
likely to encounter when satisfying constraints imposed by choreography. The within-dancer design
provided an opportunity to determine how an individual dancer modified her own control strategies when
performing turns with increased rotational demands (each individual serves as her own control). Even
with the small sample size used, differences in the control mechanisms used by each dancer to regulate
impulse during turning tasks were identified.
Early in the turn phase, the free moment contributed to the majority of moment applied by the push leg
and was sustained over half the duration of the turn initiation phase. The free moment was applied while
the turn leg and pelvis rotated laterally about the push leg’s support. It provided a means for the body
above the push leg to rotate in the positive direction while the reaction force at the push leg generated
lateral impulse to translate the CM. The free moment magnitudes measured in this study are within the
order of magnitude of those previously reported for turning while walking [13].
Increases in angular impulse later in the turn initiation phase as rotational demand increased were
attributed primarily to the redirection of the RFh generated by the push leg and combinations of RFh
magnitude and moment arm regulation at the turn leg. Most dancers maintained or decreased the RFh
magnitude at the turn leg. These results are contrary to the RFh regulation strategy used during the golf
swing, during which, increased rotation demands were satisfied by increasing the magnitude of the RFh
of one or both legs [17]. Similar to the golf study, the coordination of reaction force generation between
legs served as an effective means to satisfy the net linear impulse requirements of the task.
The extent to which net angular impulse increased from angular impulse generated by the turn leg was
surprising, considering the timing and kinematic context of the turn leg’s ground contact during the turn
initiation phase. Specifically, the turn leg made contact with the ground using only the forefoot as a
support surface and was in contact with the ground for approximately 0.2 s. Despite the turn leg’s initial
39

velocity prior to ground contact in the lateral and posterior direction, its initial interaction with the ground
was typically marked with the RFh sweeping from an alignment that generated positive lateral impulse,
to posterior impulse (more aligned with sinθ=1°), and finally, braking impulse. The portion of this phase
with posteriorly-directed reaction force tended to increase the moment applied by the turn leg and
combat the anterior impulse generated by the push leg that would otherwise translate the dancer
anteriorly. The RFh magnitude was small (ranging from 0-30% BW) due to the need for the turn leg’s RFh
to attenuate to facilitate balance maintenance during the turn phase following, but the mean moment
applied by the turn leg during its rise to peak moment was similar to that applied by the turn leg (Figure
4-6 B&C). This provides context for the observation that many dancers used an increase in turn leg ground
contact time and/or an increase of magnitude of the position vector between the turn leg’s point of force
application and the body’s CM. The increase of position vector magnitude tended to result from a
decrease in lateral CM velocity rather than an increased step width (only observed in one dancer). This is
similar to the control strategy observed to facilitate balance in challenging tasks by keeping base of
supports closer to the slowly translating CM while maintaining small-magnitude horizontal reaction forces
during gait [1][28].
Turning is an important part of daily activity with multiple, and often, competing mechanical objectives.
Comparisons of reaction forces generated by each leg during the performance of single and double piqué
turns performed by dancers provided an opportunity to determine how skilled individuals successfully
satisfy competing mechanical objectives during initiation of turns. Advancing our understanding of the
mechanical strategies used by individuals to regulate impulse generated during turns provides the
framework to identify and evaluate feasible control strategies. The results indicate that as the rotation
demands of the piqué turn increased, the net angular impulse generated increased whereas net horizontal
impulses did not increase. The decrease in lateral impulse was associated with a larger position vector
between the turn leg and CM, which assisted in increasing the moment applied by the turn leg. The push
leg generated more angular impulse than did the turn leg for both single and double turns. In general, the
angular impulse generated was attributed to free moment contribution early and redirection of the RFh
relative to the CM later in the turn initiation phase. As rotational demands increased, increased angular
impulse generation was achieved primarily by redirection of the RFh at both legs. By coordinating the
generation of reaction forces between legs, the net horizontal impulse in the anterior/posterior direction
remained minimal. These technique-related findings can assist in the design of customized feedback
technologies that aim to facilitate skill acquisition and improve dance performance [7].
References
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[12] M. E. Cinelli, A. E. Patla, and F. Allard, “Strategies used to walk through a moving aperture.,” Gait
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[13] P. C. Dixon, J. Stebbins, T. Theologis, and A. B. Zavatsky, “Ground reaction forces and lower-limb
joint kinetics of turning gait in typically developing children.,” J. Biomech., pp. 1–8, Oct. 2014.
[14] D. L. Jindrich and R. J. Full, “Many-Legged Maneuverability: Dynamics of Turning in Hexapods,” J.
Exp. Biol., vol. 202, pp. 1603–1623, 1999.
[15] K. Hase, R. B. Stein, I. Chen, Y. Yang, R. Chan, and R. Wang, “Turning Strategies During Human
Walking,” J. Neurophysiol., vol. 81, pp. 2914–2922, 1999.
[16] B. C. Glaister, M. S. Orendurff, J. a Schoen, and G. K. Klute, “Rotating horizontal ground reaction
forces to the body path of progression.,” J. Biomech., vol. 40, no. 15, pp. 3527–32, Jan. 2007.
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[18] J. . Mcnitt-Gray, T. Yokoi, and C. Millward, “Landing Strategy Adjustments Made by Female
Gymnasts in Response to Drop Height and Mat Composition,” J. Appl. Biomech., vol. 9, pp. 173–
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[20] P. De Leva, “Adjustments to Zatsiorsky-Seluyanov’s segment inertia parameters,” J. Biomech., vol.
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Associates, Inc., Publishers, 1996.
[23] M. Neuhäuser, C. Lösch, and K.-H. Jöckel, “The Chen–Luo test in case of heteroscedasticity,”
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Independent Tests,” J. Data Sci., vol. 13, no. 1, pp. 1–11, 2015.
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Hall/CRC, 1990.
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42

Chapter 5. Modification of Impulse Generation during Pirouette Turns
with Increased Rotational Demands
Introduction
Turns performed by dancers provide a unique opportunity to understand how skilled individuals
successfully satisfy competing mechanical objectives prior to and during the turn. The pirouette turn is a
well-practiced and goal-directed task that imposes conflicting mechanical objectives. The performance
specifications for a pirouette require that the center of mass (CM) translates from the initial starting
position (within the base of support during double-limb stance) towards the anterior turn stance leg (“turn
leg”) while the body rotates about the CM (Figure 5-1,Figure 5-2). Pirouette turns are often initiated from
a static position while the body mass is supported by both legs. During the “turn initiation phase”, linear
and angular impulse are generated, leading to the desired initial conditions of the “turn phase” that
follows. During the turn phase, the CM terminates its travel in the direction towards the turn leg and the
body rotates while supported only by the turn leg (Figure 5-1).
Previous studies of the pirouette have been focused on balance and momentum during the turn phase,
with limited experimental measurements of the ground reaction forces (RF) through the duration of the
initiation of a pirouette [1]–[8]. However, theoretical explanations of potential torque generation used
during the pirouette by Laws provide preliminary groundwork for experimental work to elucidate
mechanical strategies for angular impulse generation [1], [2], [4]. Sugando and Laws found that optimal
pirouette performance resulted from torque generated during turn initiation with most of a dancer’s
weight supported by the turn leg (at an instant at beginning of turn initiation) and with a widened stance
[3]. Additionally, they found that advanced dancers were more capable of using a widened stance as
compared to learning dancers [3].
In other tasks involving whole body rotation that were initiated with double limb support, increases in
rotation requirements were satisfied by increasing the magnitude of the resultant horizontal reaction
force (RFh) at one or both legs [9]. To satisfy the linear momentum requirements of these tasks,
individuals coordinated the regulation of the RFh between legs using subject-specific strategies [9-19] In
the case of the pirouette turn, we expect RFh of each leg will contribute to the angular impulse generated
to meet the rotational demands of the task, yet be coordinated so that the net linear impulse is aligned
with the desired lateral trajectory of the CM.

Figure 5-1: Exemplary kinematics of a pirouette turn through turn phases.
43

Figure 5-2: During the turn initiation phase, the linear and angular impulse needed to perform the pirouette turn is generated.
The turn initiation phase was determined from the time when the X component of the horizontal RF (RFh) of the push/ turn leg
exceeded 10N until termination of push leg ground contact.
The purpose of this study was to determine how individuals use the push and turn leg to regulate angular
and linear impulse generated during initiation of turning tasks with increased rotational demands. By
identifying effective solutions used by skilled performers under progressively more challenging turning
conditions, we can evaluate potential trade-offs between these subject-specific control strategies [7,20-
21]. We hypothesized that during the turn initiation phase, (1) as rotation demands of the turn increase,
individuals will increase net angular impulse and maintain net linear impulse generated, (2) the push leg
will generate more angular and linear impulse than will the turn leg for both single and double turns, (3)
as rotation demands of the turn increase, individuals will increase net angular impulse by increasing
resultant horizontal reaction force (RFh) magnitude at each leg. These hypotheses were tested by
comparing how dancers generate linear and angular impulse while performing single and double pirouette
turns.
Methods
Professional ballet and contemporary dancers with similar levels of experience and training (n=10, female,
age: 16-36, >9 years of dance experience) volunteered to participate and provided informed consent in
accordance with the institutional review board for human subjects. All subjects were free of lower
extremity injury at the time of data collection. Prior to data collection, participants warmed up and
practiced the experimental tasks until they felt well-practiced and familiar with the experimental setup.
Dancers were asked to perform standard pirouette turns that required rotation of the whole body while
supported by one leg with minimal CM translation towards the turn phase stance leg. Rotational demands
were systematically increased by requiring varying degrees of whole-body rotation (single (pir1) ~360°
rotation and double (pir2) ~720° rotation). The speed of the turns’ initiation phase was controlled using
80-82 bpm music, similar to timing restrictions in choreography dictated by tempo. Participants wore self-
selected footwear and arranged for preferred frictional characteristics for turning (i.e., ballet slippers,
rosin, etc.). Turns of increased rotation requirements were performed until at least five successful turns
were achieved under each condition. Five successful turns were typically achieved in less than seven
attempts.
44

Reaction forces generated during foot contact were measured using force plates (1200 Hz, Kistler,
Amherst, NY). Segment kinematics were captured using a retro reflective 16-camera motion capture
system (100 Hz, Natural Point, Optitrak, Corvallis, OR). Three-dimensional kinematics were recorded at
100 Hz using Natural Point cameras (n=16) and Acquire3D software (C-Motion, Germantown, MD). These
data were used to determine the initial CM position and to verify successful completion of tasks.
Horizontal CM trajectory was determined using the initial horizontal position of the CM at the task
initiation and the resultant horizontal RF generated by each leg [14]. RF was normalized by body weight
and impulse was normalized by body mass.
The pirouette turns performed in study were initiated from a static position with the body weight
supported by both push and turn leg (in “fourth position”). During the turn initiation phase, the linear and
angular impulse needed to perform the pirouette turn are generated. The turn initiation phase is
determined from the time when the medial components of the horizontal reaction forces (RFh) of the
turn or push leg exceeded 10N until termination of push leg ground contact. Differences in impulse
generation between legs and turn conditions were determined by comparing the magnitude and
orientation of the RFh during the turn initiation phase. Angular impulse about a vertical axis passing
through the CM during the turn initiation phase will be determined using the cross product of the position
vectors from the CM to each point of reaction force application (center of pressures for the Turn and Push
legs) and the RFhs. The free moment applied by each leg was also determined [15], [16].
To study the mechanisms used to increase the moment applied at each leg about the CM, the variables
contributing to the moment applied by each leg from the RFh were quantified during a subphase of each
leg’s ground contact time prior to peak moment applied by each leg. This subphase was defined as the
25% turn initiation phase duration prior to peak moment (“peak moment subphase”) applied by each leg
in each turn condition (boxed areas in Figure 5-6 show this subphase). This phase was selected to best
represent what was modulated during the rise to peak moment applied by each leg for most dancers
(boxed areas, Figure 5-6). Mean (SD) moment, RFh magnitude, and position vector magnitude were
calculated during this phase.
Between task differences in mean angular impulse, lateral impulse, moment, and variables contributing
to the moment applied about the CM under each turn condition were compared using statistical analysis
software R (open-source). Group differences of these values between turn conditions were assessed using
paired t-test comparisons. Within-subject comparisons of the probability for each variable of any single
piqué trial being less than any double piqué trial was calculated (R, open-source). P-values were calculated
for each dancer using Cliff’s analog of the Wilcoxon-Mann-Whitney test [22], [23]. This method was
chosen because it deals well with small numbers of trials per condition [23]. A step-down Fisher-type
method was then applied to control the familywise error rate (α = 0.05) over multiple comparisons,
modified so that the level of significance becomes α/k at each k
th
iteration [24]–[26]. The statistical
method chosen provides more flexibility by allowing heteroscedasticity across dancers [27]. This statistical
method is highly dependent upon the distribution of p-values for each variable measured because the
level for significance becomes α/k at each k
th
iteration [26]. Therefore, the presentation of within-subject
results provides a relatively conservative estimate of significant differences between turn conditions.

45

Results
Dancers generated greater mean net angular impulse during the initiation of double pirouettes compared
to during single pirouettes. The difference in net angular impulse generated was significant as a group (p
= .00001) and individually for ten of eleven dancers (brackets, Figure 5-3). The increase in mean net
angular impulse from single to double piqué turns ranged from 12.9% to 81.8% within-subject (Figure 5-3,
net pir1 vs. pir2). Generally, the increase in net angular impulse with increased rotation was attributed to
reaction force regulation at both legs, with minimal changes in position vector length.

Figure 5-3: Mean (SD) normalized angular impulse generated by the push and turn legs of each dancer (Sub1-11) during the turn
initiation phase of single (pir1) and double (pir2) pirouette turns. Net angular impulse (gray) increased from single to double
pirouettes (in ten dancers, significantly so). Eight of eleven dancers generated more angular impulse with the turn leg vs. the push
leg for both single and double pirouettes. Brackets indicate within-subject significant differences between turn conditions when
tested at α = .05 level and adjusted for multiple comparisons.
As rotation demands of the turning task increased, net linear impulse remained aligned with the desired
direction of CM displacement (Figure 5-4,Figure 5-5, net impulse pir1 vs. pir2). All dancers generated a
net change in mediolateral velocity less than 0.25 m/s and anterior velocity less than 0.5 m/s. The majority
of the linear impulse towards the turn leg’s base of support was generated by the push leg. Across dancers,
each leg increased the mean medial impulse generated, without large changes in the net impulse towards
the turn leg. The net impulse in the anterior direction was generated mainly by the push leg, but the role
of the turn leg towards anterior impulse generation was not consistent across subjects (Figure 5-5).
46

Figure 5-4: Mean (SD) normalized linear impulse generated in the lateral direction by the push and turn legs of each dancer (Sub
1-11) during the turn initiation phase of single (pir1) and double (pir2) pirouette turns. Net mediolateral impulse remained aligned
with the desired direction of travel. The push leg (orange) dominated the mediolateral impulse generation in the desired direction
of travel during both single and double turns. Brackets indicate within-subject significant differences between turn conditions
when tested at α = .05 level and adjusted for multiple comparisons.

Figure 5-5: Mean (SD) normalized linear impulse generated in the anterior direction by the push and turn legs of each dancer (Sub
1-11) during the turn initiation phase of single (pir1) and double (pir2) pirouette turns. Net anterior linear impulse remained
aligned with the desired direction of travel. Brackets indicate within-subject significant differences between turn conditions when
tested at α = .05 level and adjusted for multiple comparisons.
The contribution of each leg to net angular impulse in both single and double pirouettes was linked with
stance configuration strategies. The turn leg generated a majority of the angular impulse for eight of
eleven dancers for both single and double turns (Figure 5-3, push vs. turn legs). Three dancers who
generated more angular impulse with the push leg (Subjects 4, 7 and 10) initiated the turn with the CM
closer to the turn leg’s base of support than did the other eight dancers. This resulted in a larger position
vector from the CM to the push leg throughout the phase. Dancers applied larger moments about the CM
47

with the leg that had the larger positon vector at that time. The turn leg’s moment-time curve tended to
be maintained at a peak value whereas the push leg’s moment-time curve was marked by a quick rise to
peak and drop-off as the leg departed the ground (as in the case of exemplar case of Subject 2, Figure
5-6A). This was consistent with reaching a peak moment application of the turn leg while its position
vector magnitude was larger, as the CM approached support by the turn leg so that the body was
supported by the turn leg during the turn phase following (Figure 5-6D). Eight of eleven dancers applied
the peak moment of the turn leg prior to applying the peak moment of the push leg (as in the exemplar
case of Subject 2, Figure 5-6).
As rotational demands increased, dancers increased the mean moment applied by one or both legs using
subject-specific mechanisms during each leg’s peak-moment subphase. Differences in mean moment for
each leg were significant as a group (p = .0004 push leg, p = .00002 turn leg, Figure 5-7 B&D) and
individually for ten dancers at the push leg and eight dancers at the turn leg. Dancers used subject-specific
combinations of RFh regulation and position vector magnitude increases (Figure 5-7 A&C, exemplar Figure
5-6). Within-subject analyses indicated that the moment applied by the push leg increased primarily from
RFh magnitude increase (nine of eleven dancers) and redirection (eight of eleven dancers), without
changes in the push leg’s position vector (with the exception of subject 9) (asterisks, Figure 5-7A). In
contrast, the moment applied by the turn leg increased primarily from RFh magnitude increase (nine of
eleven dancers), rather than RFh redirection (two of eleven dancers) or increases in the turn leg’s position
vector length from the CM (one dancer) identified using within-subject analyses (asterisks, Figure 5-7C).
48

Figure 5-6: Exemplar mechanical strategy used by an individual dancer (Subject 2) to increase net angular impulse from single
pirouettes (pir1, green) to double pirouettes (pir2, blue) using the push leg (left) and turn leg (right) (A) Mean moment (SD) vs.
time curves shows an increase in moment applied about the CM by each leg. The turn leg’s peak moment occurred prior to the
push leg’s, which is consistent with reaching a peak moment application prior to the turn leg’s position vector magnitude decrease
as the center of mass displaces towards the turn leg. (B) Mean RFh magnitude (SD) does not show an increase as rotational
demand increased (C) Mean theta (SD) shows redirection in both legs tend to redirect RFh to bring sinθ closer to 1 during doubles
vs. singles. Boxed areas display 25% turn initiation phase duration prior to peak moment applied by each leg in each turn condition
(“peak moment subphase”).
49

Figure 5-7: Subject-specific mechanisms (A,C) used by dancers to increase moment applied by the RFh at (A) push leg and (C) turn
leg (B, D) indicate the mean (SD) average moment applied by the (B) push leg and (D) turn leg during the peak moment subphase
at each leg. Checkmarks indicate a sustained increased in the variable’s mean value that exceeded its standard deviation, asterisks
indicate within-subject significant differences between turn conditions when tested at α = .05 level and adjusted for multiple
comparisons. Group mean comparison indicated increases in push leg |RFh| (p = .0000007.), push leg sinθ (p = .001), turn leg
|RFh| (p = .000004), and turn leg sinθ (p = .007).
50

Discussion
In this study, the control strategies used by skilled dancers to regulate linear and angular impulse
generation during well-practiced and goal-directed turns were investigated. Comparisons of reaction
forces generated by each leg during the performance of single and double pirouette turns performed by
dancers provided an opportunity to determine how skilled individuals successfully satisfy competing
mechanical objectives during turns. The skilled dancers in this study controlled angular impulse generation
during the pirouette turn using both legs. Mechanisms used to increase net angular impulse generation
between single and double pirouette turns varied across dancers and between push and turn legs.
Different mechanisms for regulating angular impulse generated by each leg (e.g. modify RFh direction
and/or magnitude) are important to consider when designing interventions that aim to improve dancer
technique. Advancing our knowledge of mechanisms used to regulate linear and angular impulse during
turning is expected to facilitate the design of personalized interventions to improve balance regulation
and turning performance [23].
To mitigate the effect of experimental conditions on the results, efforts were made to mimic the typical
dance performance environment and a within-subject design was used. By covering each forceplate and
surrounding area with dance flooring surface and by encouraging dancers to use their own footwear,
dancers were able to establish their preferred foot-surface frictional characteristics. The dance flooring
selected provided typical frictional characteristics found on stages and in studios, but was rigid such that
it did not interfere with force transmittance. Additionally, music with a controlled tempo was used to
standardize the speed of the turn initiation phase, consistent with what a dancer is likely to encounter
when satisfying constraints imposed by choreography. The within-dancer design provided an opportunity
to determine how an individual dancer modified her own control strategies when performing turns with
increased rotational demands (each individual serves as her own control). Even with the small sample size
used, differences in the control mechanisms used by each dancer to regulate impulse during turning tasks
were identified.
Increases in angular impulse were attributed primarily to increases in RFh magnitude generated by one
or both legs as number of turns increased. Increases in RFh magnitude to facilitate increased rotational
demand was similar to the strategy used during the golf swing, during which, increased rotation demands
were satisfied mainly by increasing the magnitude of the RFh of one or both legs [19]. In both studies, the
coordination of reaction force generation between legs served as an effective means to satisfy the net
linear impulse requirements of the task. In this study, the primary means of increasing moment applied
by both legs was to increase the RFh magnitudes, however, in the push leg, there were more instances of
redirecting the RFh to increase the moment applied about the CM (Figure 5-7). Additionally, the turn leg’s
contribution to the desired net anterior impulse tended to increase with increased rotation. This suggests
that as the push leg’s RFh was redirected to satisfy increases in angular impulse using components
perpendicular to the desired anterior translation of the CM, the turn leg was coordinated to help generate
anterior impulse more in double turns as compared to single turns.
How angular impulse was generated during the initiation of a pirouette provide contrast to findings of the
strategies used by the same individuals during the initiation of piqué turns of increased rotations (subjects
1-10). Despite the large contribution of the free moment to the generation of anterior impulse during
initiation of piqué turns when performed by the same individuals, the free moments at each leg remained
minimal during pirouette initiation (Specific Aim I Results). This may be due to the advantage of double
51

limb support during the pirouette’s initiation. Early in the piqué turn’s initiation, the net moment was
comprised mostly of the free moment while the body segments rotated in the turn direction and the CM
displaced away from the single-leg base of support (due to a RF acting laterally and through the CM to
satisfy the task’s linear requirements). During double limb stance (as in the golf swing and pirouette) the
body can tolerate larger RFh generated by each leg that are not aligned with the desired net linear impulse
from each leg because the legs have the opportunity to simultaneously oppose each other to minimize
extraneous net linear impulse. Therefore, control of the magnitude of the RFh can be used as the primary
means to initiate the rotation of the body above the ground contacts.
The contribution of each leg to net angular impulse in both single and double pirouettes was linked with
stance configuration strategies. While the CM horizontal position resides somewhere within the base of
support initially, stylistic differences between schools of ballet provided context for some range across
subjects regarding the initial CM positioning closer to the turn leg or to the push leg. Dancers who initiated
the turn with a larger position vector between the CM and the turn leg’s base of support generated more
mean angular impulse with the turn leg during both single and double pirouettes. Conversely, dancers
who initiated the turn with the CM closer to the turn leg, generated more angular impulse with the push
leg in both single and double turns. There may be advantages and disadvantages to each strategy for each
individual. For example, if the CM is closer to the turn leg, the CM displacement requirement is minimized,
and the push leg is free to generate the majority of the angular impulse, using the benefit of a larger
position vector. Conversely, if the push leg’s ground contact does not have enough friction (due to the
size of the vertical component of the reaction force) to facilitate a large medial horizontal component
while the turn leg supports most of the body weight, the strategy of the CM closer to the turn leg is not
advantageous.
Turning is an important part of daily activity with multiple, and often, competing mechanical objectives.
Comparisons of reaction forces generated by each leg during the performance of single and double
pirouette turns performed by dancers provided an opportunity to determine how skilled individuals
successfully satisfy competing mechanical objectives during initiation of turns. These technique-related
findings can assist in the design of customized feedback technologies that aim to facilitate skill acquisition
and improve dance performance [23].

References
[1] K. Laws and L. Fulkerson, “The slowing of pirouettes,” Kinesiol Med Danc., no. Idd, 1992.
[2] K. L. Laws, “The Analysis of Turns in Dance,” Danc. Res. J., vol. 11, no. 1, pp. 12–19, 1978.
[3] A. Sugano and K. Laws, “Physical analysis as a foundation for pirouette training,” Med. Probl.
Perform. Art., vol. 18, no. March, pp. 29–32, 2002.
[4] K. Laws, “Momentum transfer in dance movement,” Med. Probl. Perform. Art., vol. 13, pp. 136–
145, 1998.
[5] M. Lott and K. Laws, “The Physics of Toppling and Regaining Balance during a Pirouette.,” J. Danc.
Med. Sci., vol. 16, no. 4, pp. 167–174, 2012.
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[6] C.-W. Lin, S.-J. Chen, F.-C. Su, H.-W. Wu, and C.-F. Lin, “Differences of ballet turns (pirouette)
performance between experienced and novice ballet dancers.,” Res. Q. Exerc. Sport, vol. 85, no.
3, pp. 330–40, Sep. 2014.
[7] J. Kim, M. Wilson, and K. Singhal, “Generation of vertical angular momentum in single, double,
and triple-turn pirouette en dehors in ballet,” Sport. Biomech., vol. 13, no. 3, pp. 215–229, 2014.
[8] E. Biringen, “Analysis of Pirouette Execution for Improved Performance,” Med. Probl. Perform.
Art., vol. 25, pp. 1–3, 2010.
[9] J. L. McNitt-Gray, J. Munaretto, A. Zaferiou, P. S. Requejo, and H. Flashner, “Regulation of
reaction forces during the golf swing.,” Sports Biomech., vol. 12, no. 2, pp. 121–31, Jun. 2013.
[10] W. Mathiyakom, J. L. McNitt-Gray, and R. Wilcox, “Lower extremity control and dynamics during
backward angular impulse generation in backward translating tasks.,” Exp. brain Res., vol. 169,
no. 3, pp. 377–88, Mar. 2006.
[11] J. . Mcnitt-Gray, T. Yokoi, and C. Millward, “Landing Strategy Adjustments Made by Female
Gymnasts in Response to Drop Height and Mat Composition,” J. Appl. Biomech., vol. 9, pp. 173–
190, 1993.
[12] W. Mathiyakom, J. L. McNitt-Gray, and R. Wilcox, “Lower extremity control and dynamics during
backward angular impulse generation in forward translating tasks.,” J. Biomech., vol. 39, no. 6,
pp. 990–1000, Jan. 2006.
[13] P. S. Requejo, J. L. McNitt-Gray, and H. Flashner, “An approach for developing an experimentally
based model for simulating flight-phase dynamics.,” Biol. Cybern., vol. 87, no. 4, pp. 289–300,
Oct. 2002.
[14] P. De Leva, “Adjustments to Zatsiorsky-Seluyanov’s segment inertia parameters,” J. Biomech., vol.
29, no. 9, pp. 1223–1230, 1996.
[15] P. C. Dixon, J. Stebbins, T. Theologis, and A. B. Zavatsky, “Ground reaction forces and lower-limb
joint kinetics of turning gait in typically developing children.,” J. Biomech., pp. 1–8, Oct. 2014.
[16] J. P. Holden and P. R. Cavanagh, “The free moment of ground reaction in distance running and its
changes with pronation.,” J. Biomech., vol. 24, no. 10, pp. 887–97, Jan. 1991.
[17] N. Cliff, Ordinal Methods for Behavioral Data Analysis. Mahwah, NJ: Lawrence Erlbaum
Associates, Inc., Publishers, 1996.
[18] M. Neuhäuser, C. Lösch, and K.-H. Jöckel, “The Chen–Luo test in case of heteroscedasticity,”
Comput. Stat. Data Anal., vol. 51, no. 10, pp. 5055–5060, Jun. 2007.
[19] Y. Hochberg, “A sharper Bonferroni test for multiple tests of significance,” Biometrika, vol. 75, pp.
800–802, 1988.
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[20] Y. Hochberg and A. C. Tamhane, Multiple Comparison Procedures. Hoboken, NJ, USA: John Wiley
& Sons, Inc., 1987.
[21] R. Wilcox and F. Clark, “Robust Multiple Comparisons Based on Combined Probabilities From
Independent Tests,” J. Data Sci., vol. 13, no. 1, pp. 1–11, 2015.
[22] M. J. Crowder and D. J. Hand, Analysis of Repeated Measures, 1st ed. New York: Chapman &
Hall/CRC, 1990.
[23] J. L. McNitt-Gray, K. Sand, C. Ramos, T. Peterson, L. Held, and K. Brown, “Using technology and
engineering to facilitate skill acquisition and improvements in performance,” Proc. Inst. Mech.
Eng. Part P J. Sport. Eng. Technol., vol. 229, no. 2, pp. 103–115, Jun. 2015.

54

Chapter 6. Whole-Body Balance Regulation during the Turn Phase of
Piqué and Pirouette Turns
Introduction
Piqué and pirouette turns are fundamental to dance and serve as well-practiced tasks that can be
performed with increased rotational requirements (e.g. single, double, etc.) [1]. The piqué turn is
performed in a series while translating, whereas the pirouette involves minimal displacement of the
center of mass (CM) and termination typically in a stationary position (e.g. “fifth position”) (Figure 6-1).
These differences in termination phase objectives are likely to affect maintenance of balance during the
turn phase. Additionally, both turns impose a challenging constraint during the turn phase: the dancer
must spin with single-limb stance supported by an extended leg (extended knee and plantarflexed ankle)
with a very small base of support (the forefoot) [2], [3]. Identifying control strategies used by elite dancers
to maintain stability during whole-body rotation tasks of increased rotational demand can inform
coaching cueing or design of training tools for novice dancers.

Figure 6-1: Mechanical goals of Piqué and Pirouette turns by phase. The phases of interest to study balance
maintenance differences between piqué and pirouettes are their turn phases. White dashed line is representative of
the CM trajectory.
The primary goal of the turn phase is to rotate the body while maintaining balance. Under static
conditions, balance is achieved by maintaining the CM positioned above the base of support. During this
time, the net vertical and horizontal forces acting on the body are minimal, consistent with minimal linear
acceleration of the CM. Vertical alignment of the CM relative to the base of support can be achieved by
redirecting the reaction force (RF), and/or by reconfiguring segments. Maintenance of balance in other
locomotor activities also involves control of the RF relative to the CM trajectory during task performance
[5]–[8]. For instance, in straight line gait, the moments applied by the RFs about the CM assists in
55

maintaining the CM trajectory within the base of support. Should the CM trajectory overshoot the
boundaries of the base of support, the risk of a fall increases [6]. Maintenance of balance during a turn
may be challenged or facilitated through constraints imposed by dance choreography. Previous
experimentally-validated modelling simulation studies have shown that ability to redirect RF relative to
the CM increases when the joints of the lower extremity are flexed [4]. Turns in dance are often performed
with a straight support leg (e.g, piqué and pirouette turns) and as a result, redirection of RF as a means to
regulate balance is not facilitated.
How a turn is initiated is expected to affect how balance is achieved and maintained during the turn. For
example, during the turn initiation phase of piqué and pirouette turns, the net angular impulse generated
by experienced dancers tended to increase with increases in rotational demands ( single vs double turn)
whereas the linear impulse generated perpendicular to the desired CM trajectory by one or both legs
changed between rotation conditions (Specific Aim I Results & Specific Aim II Results). Despite these
changes in linear impulse generation between single and double turns, the net linear impulse remained
aligned with the desired CM trajectory. To achieve these mechanical objectives of each turn at the whole
body level, the differences in CM trajectory requirements imposed by the piqué and pirouette turns is
expected to affect the initial CM velocity and CM displacement during the turn phase.
Balance maintenance during the turn is also likely to be associated with the performance-related goals
and tolerances afforded by the termination phase. In the termination phase, the rotation of the whole
body is reduced whereas the CM trajectory will be consistent with the mechanical objectives of the
subsequent phase of the task. For instance, when CM translation is to be maintained (e.g. turning while
walking and piqué turns), the step taken during termination is consistent with the desired CM trajectory
(non-zero CM velocity) [9]. In a turn-and-stop task (e.g. pirouette turn), the CM velocity needs to be
attenuated at a time when the CM is over the base of support [10]. For both turns, the termination phase
is often defined by the time when the non-support leg, or “gesture leg” (previously referred to as the
“push leg” during the turn initiation phase) begins its descent towards the ground.
As rotational demands increase, balance maintenance control strategies are expected to be modified in
accordance with the performance specifications of the task. Typically, in choreography, if more turns are
required more time is permitted during the turn phase. As a result, it is expected that turns with multiple
rotations impose a need to position the CM over the base of support for longer periods of time.
Maintaining the CM position over the base of support for a longer period of time may require more
corrective actions that involve regulation of the RFs relative to the CM. Previous research has found that
dancers performing pirouettes do not behave as if they are rigid bodies (e.g. a top). Lott and Laws found
that gyro-dynamic effects such as precession did not apply to pirouettes performed by dancers [11]. Their
kinematic-based results indicate that a dancer would topple out of a multiple-revolution turn based on
initial COM-base of support alignment at the beginning of the turn phase unless corrective actions were
initiated during the turn [11].
The purpose of this study was to compare balance regulation during the turn phase between piqué and
pirouette turns and between single and double rotations. We hypothesized that during the turn phase:
(1) the initial CM velocity during the piqué turn would be greater than that during the pirouette in the
direction of the turn leg’s base of support, (2) the average angle between the base of support – CM and
vertical during a pirouette would be smaller than the average angle during a piqué turn, and (3) as the
rotational demands increase, the RF will be regulated relative to the CM to maintain base of support and
56

CM vertical alignment. These hypotheses were tested by using a within-subject comparison of how
balance is regulated at the whole-body level (CM vs. base of support vs. RF) during the turn phase of
successfully-performed single and double pirouette and piqué turns.
Methods
Professional ballet and contemporary dancers with similar levels of experience and training (n=10, female,
age: 16-36, >9 years of dance experience) volunteered to participate and provided informed consent in
accordance with the institutional review board for human subjects. All subjects were free of lower
extremity injury at the time of data collection. Prior to data collection, participants warmed up and
practiced the experimental tasks until they felt well-practiced and familiar with the experimental setup.
Dancers were asked to perform standard piqué (pk) and pirouette (pir) turns that required rotation of the
whole body while supported by one leg. Rotational demands were increased by requiring varying degrees
of whole-body rotation (single (pk1, pir1) ~360° rotation and double (pk2, pir2) ~720° rotation. The speed
of the turns’ initiation phase was controlled using 80-82 bpm music, similar to timing restrictions in
choreography dictated by tempo. Participants wore self-selected footwear and arranged for preferred
frictional characteristics for turning (i.e., ballet slippers, rosin, etc.). Turns of increased rotation
requirements were performed until at least five successful turns were achieved under each condition. Five
successful turns were typically achieved in less than seven attempts.
Reaction forces generated during foot contact were measured using force plates (1200 Hz, Kistler,
Amherst, NY). Body segment kinematics were captured simultaneously in the frontal, sagittal, and
transverse planes (60 Hz Panasonic, Secaucus, NY & 300 Hz Casio, Dover, NJ) and were used to verify
successful completion of tasks. Segment kinematics were captured using a retro reflective 16-camera
motion capture system (100 Hz, Natural Point Optitrak, Corvallis, OR). Three-dimensional kinematics were
recorded at 100 Hz using Natural Point cameras (n=16) and Acquire3D software (C-Motion, Germantown,
USA). Segment kinematics were used to determine CM position and velocity [12].
The piqué and pirouette turns performed in study were initiated from a static position with the body
weight supported by either the push leg (piqués) or both legs (pirouettes). During the turn initiation phase
prior to the phase of interest, the linear and angular impulse needed to perform the piqué and pirouette
turn were generated. During the turn phase immediately following, both turns impose a challenging
constraint: the dancer must spin with single-limb support on an extended leg (extended knee and
plantarflexed ankle) and contact the ground with a very small base of support (the forefoot). The push leg
during the initiation of the turn is known as the “gesture leg” during the turn phase [2], [3], [11], [13].
During this phase, the vertical alignment of the CM relative to the base of support (using the angle
between a vertical vector and a vector from the center of pressure to CM “base of support-CM”) was
calculated as measures of balance maintenance. Reaction forces in each direction were analyzed and the
control of the RF was assessed via calculations of the moment applied about the CM. The turn phase
ended when the termination phase began. The beginning of the turn termination was determined as the
time that the “gesture leg” began its path back to the ground (determined by the vertical height of the
gesture foot’s CM).
Between task differences in mean CM vertical alignment, ground reaction forces in each direction, and
moment about each plane under each turn condition were compared using statistical analysis software R
(open-source). Comparisons across dancers were analyzed using a paired t-test. Within-subject, the
probability for each variable of any single piqué trial being less than any double piqué trial was calculated
57

within each dancer (R, open-source). P-values were calculated for each dancer using Cliff’s analog of the
Wilcoxon-Mann-Whitney test[14], [15]. This method was chosen because it deals well with small numbers
of trials per condition[15]. A step-down Fisher-type method was then applied to control the familywise
error rate (α = 0.05) over multiple comparisons, modified so that the level of significance becomes α/k at
each k
th
iteration[16]–[18]. The statistical method chosen provides more flexibility by allowing
heteroscedasticity across dancers[19]. This statistical method is highly dependent upon the distribution
of p-values for each variable measured because the level for significance becomes α/k at each k
th

iteration[18]. Therefore, the presentation of within-subject results provides a relatively conservative
estimate of significant differences between turn conditions.
Results
Initial CM velocity in the direction of the base of support was greater during the piqué turn phase than
during the pirouette turn phase for all dancers. The CM velocity during the piqué and pirouette turn
phases was significantly different as a group (single piqué vs. pirouette p =.00000004, double piqué vs.
pirouette p = .00000004) and individually for eight of ten dancers (brackets, Figure 6-3, exemplar Figure
6-2). Additionally, the initial horizontal distance between the CM and the turn phase’s base of support
tended to be greater during piqué than during pirouette turns. The CM distance to the turn leg’s base of
support was significantly different as a group during double turns (p = .000007 double piqué vs. pirouettes,
Figure 6-4, exemplar Figure 6-2) and individually for six dancers during single turns and seven dancers
during double turns (brackets, Figure 6-4).

Figure 6-2: Comparison of initial center of mass velocity towards and distance to the turn phase’s base of support (BoS) during
the turn phase of single (green) and double (blue) piqué turns (asterisk) and pirouette (circles) turns for an exemplar subject (3).
This dancer’s initial center of mass velocity towards the turn phase’s base of support was greater in piqué turns than in
pirouettes. Additionally, the initial distance between the center of mass and the base of support was greater in the piqué than in
the pirouette.
58

Figure 6-3: Mean (SD) initial horizontal center of mass velocity towards the turn leg’s base of support (BoS) at the beginning of
the turn phase of single (green) and double (blue) piqué (pk) and pirouette (pir) turns. Piqué turn phases were initiated with larger
center of mass velocity in the direction of desired center of mass displacement. Brackets indicate within-subject significant
differences between turn conditions when tested at α = .05 level and adjusted for multiple comparisons.

Figure 6-4: Mean (SD) initial center of mass horizontal distance to the turn leg’s base of support (BoS) at the beginning of the turn
phase of single (green) and double (blue) piqué (pk) and pirouette (pir) turns. Piqué turn phases were initiated with larger center
of mass velocity in the direction of desired center of mass displacement, but a larger initial distance between the center of mass
and turn phase base of support horizontal position (with the exception of subject 4 and 10). Brackets indicate within-subject
significant differences between turn conditions when tested at α = .05 level and adjusted for multiple comparisons.
As expected, the average angle between the base of support - CM and a vertical vector (CM vertical
alignment) during a pirouette turn phase was smaller than during a piqué turn phase. This vertical
alignment angle was significantly different as a group for both single and double turns (single piqués vs.
pirouettes p = .0000003 and double piqués vs. pirouettes p = .000003) and individually for eight of ten
dancers (brackets, Figure 6-6, exemplar Figure 6-5). On average across dancers, the CM was aligned within
5° from vertical throughout the turn phase and for both single and double pirouette turns compared to a
larger mean vertical alignment angle during piqué turns (in general, between 10° and 15° for single and
between 5° and 10° for doubles) (Figure 6-6). Additionally, the base of support and CM were vertically
59

aligned (<15°) for a longer time during pirouettes than during piqué turn phases (p = .00006 single piqué
vs. pirouettes, p = .00000002 double piqué vs. pirouettes, Figure 6-7). On average across dancers, the CM
was within 15° vertical alignment for 100% of turn phase duration of pirouettes compared to a range of
approximately 45%-80% of turn phase duration of a piqué turns (Figure 6-7).

Figure 6-5: Vertical alignment of center of mass-base of support during single (green) and double (blue) pirouette (left) and
piqué (right) turns for an exemplar subject (3). Zero degrees corresponds to center of mass (solid circle) being positioned directly
over base of support. These graphs show that the center of mass during the pirouette was more vertically aligned (mean <5°)
than it was during the performance of a single piqué (mean ~15°). Additionally, the turn phase of the single piqué was short
(<0.5 sec), such that the turn phase ended soon after the center of mass-base of support reached a 5° vertical alignment. The
increase in turn phase duration between singles and doubles displayed in these graphs is also representative of all dancers who
participated.

Figure 6-6: Mean (SD) vertical alignment of center of mass (CM)-base of support (BoS) throughout the turn phase of single (green)
and double (blue) piqué (pk) and pirouette (pir) turns. Single and double pirouette turns maintained average alignment within 5°
from vertical, whereas, piqué turns’ mean vertical alignment angle was greater. There were significant increases in alignment
from single to double piqué turn (n=9), primarily because the single piqué turn phases ended as the center of mass reached within
5° vertical alignment with the base of support and the double turns were sustained for longer when the center of mass was
positioned within 5° of vertical alignment with the base of support. Brackets indicate within-subject significant differences
between turn conditions when tested at α = .05 level and adjusted for multiple comparisons.
60

Figure 6-7: Mean (SD) duration that the center of mass was over the base of support (within 15° vertical alignment (darker bars)
and within 5° vertical alignment (lighter bars)) during both single (green) and double (blue) piqué (pk) and pirouette (pir) turn
phases. For both turn types, the mean percent duration within 15° and 5° increased or was maintained with increased rotational
demands (n=10).
In double pirouette and piqué turns, more RF regulation was used in order to maintain CM vertical
alignment for a longer period of time (Figure 6-8, exemplar Figure 6-9). One measure of RF regulation was
to increase braking force to slow the CM’s approach to the base of support (braking force, Figure 6-8). The
mean braking force early in the turn phase (during 0.2 s- 0.4 s) increased significantly with increased
rotation for both turn conditions (p = .0000003 piqués, p = .0009 pirouettes) and individually for seven of
ten dancers (brackets, Figure 6-10, exemplar Figure 6-9). Another RF regulation strategy included
increasing the RF’s action to reduce the rotation of the CM about the base of support in the primary
direction of travel (sagittal plane moment, Figure 6-8). The mean sagittal plane moment early in the turn
phase (during 0.2 s – 0.4 s) increased significantly in both turn conditions with increased rotation (p =
.0000004 piqués, p = .001 pirouettes) and individually for six of ten dancers (brackets, Figure 6-11).
Additionally, within-subject analyses indicated that nine of ten dancers significantly increased the mean
vertical alignment of the CM during double piqué turns compared to single piqué turns (gray brackets,
Figure 6-6). This was primarily due to the finding that single piqué turn phases ended as the CM reached
the horizontal position of the base of support and the double turns were sustained after the CM was
positioned above the base of support.
61

Figure 6-8: Desired balance alignment between center of mass (CM) and base of support (BoS) and reaction force regulation (RFy,
RFz) strategies that can be used to accomplish the desired balance alignment during the turn. Increased braking force would slow
the center of mass’s approach velocity towards the base of support, while the resultant reaction force may slow the center of
mass’s rotation about the base of support if it is oriented anterior to the center of mass [6], [20].

Figure 6-9: Exemplar (subject 3) increased braking force from single (green) to double (blue) pirouette and its associated
increased moment (tending to slow rotation of the center of mass (CM) about the base of support (BoS)) early in the turn phase.
62

Figure 6-10: Mean (SD) braking force (y-direction) during the beginning of the turn phase (0.2-0.4s) of single (green) and double
(blue) piqué (pk) and pirouette (pir) turns. For both turn types and all dancers, the mean braking force increased with rotational
demand. Brackets indicate statistically significant differences between single and double rotations. Brackets indicate within-
subject significant differences between turn conditions when tested at α = .05 level and adjusted for multiple comparisons.

Figure 6-11: Mean (SD) moment tending to slow the center of mass’s rotation about the base of support as it translates towards
the base of support during the beginning of the turn phase (0.2-0.4s) of single (green) and double (blue) piqué (pk) and pirouette
(pir) turns. For both turn types and all dancers, sagittal moment tending to slow the center of mass’s rotation about the base of
support increased with rotational demand. Brackets indicate statistically significant differences between single and double
rotations. Brackets indicate within-subject significant differences between turn conditions when tested at α = .05 level and
adjusted for multiple comparisons.

63

Discussion
The purpose of this study was to compare balance regulation at the whole-body level during the turn
phase of piqué and pirouette turns with increases in rotational demands. After the initiation of both piqué
and pirouette turns, the turn phase required whole body rotation while maintaining balance in a
challenging kinematic context. The differences in how the pirouette and piqué turn is initiated and
terminated provided a systematic comparison between balance maintenance during turns with (piqué)
and without CM translation (pirouette). Comparisons between the piqué and pirouette, for both single
and double turns, revealed that the CM during the pirouette was more vertically aligned than was the CM
during the piqué turn. Throughout the turn phase of a pirouette, the dancers’ CM was aligned within 15°
from vertical (the mean alignment for both single and double pirouettes was less than 5° for all subjects).
Additionally, because double turn phases had a longer duration for both piqué and pirouette turns, the
RFs were regulated early relative to the CM to provide near zero CM velocity when the CM approached
the horizontal position of the base of support during doubles as compared to singles. This regulation
included increased braking force and an increased moment that acted to slow the CM’s rotation about
the base of support in the primary direction of travel for each turn type.
To mitigate the effect of experimental conditions on the results, efforts were made to mimic the typical
dance performance environment and a within-subject design was used. By covering each forceplate and
surrounding area with dance flooring surface and by encouraging dancers to use their own footwear,
dancers were able to establish their preferred foot-surface frictional characteristics. The dance flooring
selected provided typical frictional characteristics found on stages and in studios, but was rigid such that
it did not interfere with force transmittance. Additionally, tracking markers were specifically arranged for
each dancer to prevent interference with normal kinematics during these turns (i.e., shank tracking cuff
location on the turn leg relative to the gesture leg’s foot path along the shank). The within-dancer design
provided an opportunity to determine how an individual dancer modified her own control strategies when
performing each turn condition (each individual serves as her own control). Even with the small sample
size used, differences in the control mechanisms used by each dancer to regulate impulse during turning
tasks were identified.
Initial CM velocity during the turn phase of pirouette and piqué turns were consistent with previous
research regarding linear impulse generated during the turn initiation phase (Specific Aim I Results &
Specific Aim II Results). Linear impulse generated during piqué turn initiation and the piqué turn phase’s
initial CM velocity were greater than that during the pirouette initiation and turn phases (Specific Aim I
Results & Specific Aim II Results). Additionally, the initial distance to the CM during the turn phase of a
piqué was larger than during the turn phase of a pirouette. This larger initial horizontal distance during
the piqué was associated with a delay in vertical alignment of the CM and base of support, despite the
larger initial CM velocity towards the turn base of support compared to that during the pirouette. On
average, the turn phase duration of single piqué turns was 0.5 sec, and ended when the CM reached an
average of 5° vertical alignment. In contrast, the single pirouette’s turn phase reached an average 5°
vertical alignment within an average 0.03 s of the turn phase, with a turn phase duration of 1 second
(Figure 6-5,Figure 6-12). This difference in phase duration was also associated with the kinematic finding
that single piqué turns typically reached an average body rotation ranging from 200°-250°, compared to
the average body rotation ranging from 300°-350° during a single pirouette across subjects (Figure 6-13).
Less rotation completed during a piqué turn phase and its shorter turn phase duration were acceptable
for successful turn performance because of the linear and angular tolerances built into the piqué turn’s
64

termination phase. The piqué termination phase affords additional body rotation and translation during
the transition to the sequential piqué turn, whereas, the pirouette’s termination phase brings angular and
linear momentum to zero.

Figure 6-12: Mean (SD) turn phase duration and time until the center of mass was vertically aligned at least 10 ° from vertical for
single (green) and double (blue) piqué (pk) and pirouette (pir) turns. Phase duration increased as rotational demand increased for
both turn types. Additionally, mean time until the center of mass was aligned within 10 ° of vertical was smaller in pirouette turns
compared to piqué turns.

Figure 6-13: Mean (SD) estimates of body rotation completed during single (green) and double (blue) pirouette (pir) and piqué
(pk) turns. This was estimated by tracking the angular orientation of the horizontal-plane projected pelvis R-L axis. More mean
body rotation was completed during the turn phase of pirouettes as compared to piqué turns (for both single and double
rotations). The difference in amount of body rotation provides kinematic context for differences between center of mass vertical
alignments across turn types.
As rotational demands of both turns increased, the turn phase duration increased (Figure 6-12), and so
too did the need to maintain balance by regulating the RFs relative to the CM. Overall, the mean of the
CM vertical alignment was smaller during double turns than it was during single turns. This was associated
with larger braking (-y) forces and a larger applied moment to prevent overshooting the base of support
as the CM rotates about the base of support in the primary direction of travel (anterior for pirouettes,
lateral for piqués). In some cases (n=7), the vertical RF was also modulated during this time, which may
afford the ability to either move the center of pressure relative to the CM (when the vertical RF is less
than body weight’s magnitude), or to use increased vertical RF (greater than body weight’s magnitude) to
facilitate RF redirection. Both of these strategies were identified in a subset of dancers who participated
in this study.
65

The experimentally-measured translating, sliding, and spinning (small) base of support, an extended
stance knee, and counter-balance gesture leg provide certain limitations and opportunities for postural
and RF control. Investigating if postural adjustments at the trunk, stance, and gesture legs during the turn
phase contribute to successful turn performance is a reasonable line of inquiry following this investigation
of whole-body balance measures during the turn. Further, modelling the dance turn phase balance from
a multi-link controls-perspective using experimentally-obtained kinematics and kinetics would be a
unique challenge in order to elucidate how dancers were able to regulate the RFs [21].
This study identified whole-body measures of balance during the turn phase of single and double
pirouette and piqué turns. For the skilled dancers in this study, their initial CM velocity during the piqué
turn was greater than that during the pirouette in the direction of the turn leg’s base of support, but the
horizontal distance from the initial CM position to the turn leg’s base of support was greater in piqué turns
than in pirouettes. The average vertical alignment of the CM during a pirouette was smaller than the
average angle during a piqué turn. These findings are consistent with the larger CM’s initial distance to
the base of support during a piqué turn phase and the overall turn phase objectives of a piqué to translate
vs. to “turn and stop”, as in a pirouette. Finally, as the rotational demands increased, the ground reaction
forces were regulated relative to the CM. By controlling the braking force and moment applied about the
CM the potential for the CM to overshoot the horizontal positon of the base of support in the primary
direction of travel was limited.

66

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readiness.,” J. Dance Med. Sci., vol. 14, no. 3, pp. 82–8, Jan. 2010.
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[4] J. Munaretto, “Modeling human regulation of momentum while interacting with the
environment,” University of Southern California, 2011.
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pp. 1–8, Oct. 2014.
[6] W. Mathiyakom and J. L. McNitt-Gray, “Regulation of angular impulse during fall
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[8] D. L. Jindrich, T. F. Besier, and D. G. Lloyd, “A hypothesis for the function of braking
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[11] M. Lott and K. Laws, “The Physics of Toppling and Regaining Balance during a
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[12] P. De Leva, “Adjustments to Zatsiorsky-Seluyanov’s segment inertia parameters,” J.
Biomech., vol. 29, no. 9, pp. 1223–1230, 1996.
[13] A. Imura and M. R. Yeadon, “Human Movement Science Mechanics of the Fouetté turn,”
vol. 29, pp. 947–955, 2010.
[14] N. Cliff, Ordinal Methods for Behavioral Data Analysis. Mahwah, NJ: Lawrence Erlbaum
Associates, Inc., Publishers, 1996.
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heteroscedasticity,” Comput. Stat. Data Anal., vol. 51, no. 10, pp. 5055–5060, Jun. 2007.
[16] Y. Hochberg, “A sharper Bonferroni test for multiple tests of significance,” Biometrika,
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[21] M. Tanabe, Hiroko, Fujii, Keisuke, Suzuki, Yasuyuki, Kouzaki, “A Model for Robustness
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Biomechanics, 2015, pp. 916–917.

68

Chapter 7. Lower Extremity Control during Turns Initiated with and
without Hip External Rotation
Introduction
The performance of turning tasks reflects the ongoing interaction between the nervous system,
musculoskeletal system, and reaction forces generated at the foot-surface interface during foot contact.
Turns requiring varied rotation and translation demands often involve satisfying multiple, and often,
competing mechanical objectives at the whole body and segment levels. At the whole body level, the
ground reaction forces (GRF) generated by each leg must be regulated in relation to the center of mass
(CM) trajectory during foot contact so that the net linear and angular impulse requirements, specific to
the turning task, are satisfied. At the segment level, the GRF generated must be coordinated in relation
to segment motion to facilitate multi-joint control without increasing risk of injury. Failure to
simultaneously satisfy these mechanical objectives at the whole-body and segment levels can result in
poor outcomes. Studying how an individual satisfies the mechanical objectives of comparable tasks with
varied kinematic contexts has been effective in elucidating subject-specific control preferences in goal-
directed movements [1], [2], [2]–[4]. Knowledge of the control and dynamics used by an individual to
initiate and perform turns under a variety of conditions can inform development of intervention tools to
facilitate skill acquisition for individuals with varied physical capacities.
Turns in dance are well practiced-goal directed tasks that can be performed using different initial
kinematic contexts (Specific Aim I Results & Specific Aim II Results). Classical ballet turns are typically
initiated and performed with the hips externally rotated, whereas, more modern choreography requires
dancers to also be proficient in performing tasks with neutral hip alignment. The pirouette is a well-
practiced turn often initiated in neutral and externally rotated hip positions by contemporary, modern,
and contemporary-ballet dancers. This provides an opportunity to investigate how dancers satisfy the
same mechanical objectives at the total body level when generating GRFs using different leg kinematics.
Previous research has shown that skilled dancers coordinate forces generated during turn initiation to
achieve the linear and angular impulse needed to complete the required number of rotations (Specific
Aim I Results & Specific Aim II Results). Mechanisms used to increase net angular impulse generation
between single and double piqué and pirouette turns tended to be subject-specific and involved
modification of the horizontal component of the reaction force (RFh, magnitude and/or direction) and the
position vector from the CM to the point of force application. The orientation of the leg relative to the
corresponding resultant GRF is expected to influence the mechanical demand imposed on the lower
extremity [2]. By determining the multijoint control strategies used by skilled dancers when generating
comparable horizontal GRFs from parallel or externally rotated leg positions, we can advance our
understanding of the mechanical demands imposed in classical and contemporary dance.
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Figure 7-1: Phases and exemplar kinetics and kinematics during a single classical pirouettes (pir, left) and parallel pirouettes
(ppir, right).
The purpose of this study was to compare impulse generation strategies of each leg and associated muscle
recruitment strategies during the turn initiation phase of pirouettes performed with and without hip
external rotation. We hypothesized that at the whole-body level, the net linear and net angular impulse
generated during the turn initiation phase will remain the same for pirouette turns initiated with and
without external hip rotation. At the leg subsystem level, we hypothesized that turns initiated with and
without external hip rotation will involve different joint kinetics and muscle recruitment patterns. These
hypotheses were tested by comparing how the turn and push legs of individual dancers generated impulse
during the turn initiation phase of single pirouettes initiated with and without hip external rotation.
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Methods
Professional ballet and contemporary dancers with similar levels of experience and training (n=5, >9 years
dancing) volunteered to participate and provided informed consent in accordance with the institutional
review board for human subjects. All subjects were free of lower extremity injury at the time of data
collection and were able to perform triple pirouettes in both conditions consistently. Prior to data
collection, participants warmed up and practiced the experimental tasks until they felt well-practiced and
familiar with the experimental setup.
Dancers were asked to perform standard single pirouette turns initiated with hip external rotation, also
referred to as “classical” pirouettes (pir) and pirouette turns initiated with neutral hip alignment, also
referred to as “parallel” pirouettes (ppir). Pirouettes require rotation of the whole body on one leg with
minimal CM translation towards the turn phase stance leg. The speed of the turn initiation phase was
controlled using 80-82 bpm music, consistent with timing restrictions imposed by choreography dictated
by tempo. Participants wore self-selected footwear and arranged for preferred frictional characteristics
for turning (i.e., ballet slippers, rosin, etc.). Turns were performed until at least five successful turns were
achieved under each condition. Five successful turns were typically achieved in less than seven attempts.
Reaction forces generated during foot contact were measured using force plates (1200 Hz, Kistler,
Amherst, NY). Segment kinematics were captured using a retro reflective 16-camera motion capture
system (100 Hz, Natural Point Optitrak, Covallis, OR). Three-dimensional kinematics were recorded at 100
Hz using Natural Point cameras (n=16) and Acquire3D software (C-Motion, Germantown, USA). These data
were used to determine the initial CM position and to verify successful completion of tasks. Horizontal
CM trajectory was determined using the initial horizontal position of the CM at the task initiation and the
resultant horizontal GRF generated by each leg [5]. Impulse was normalized by body mass.
Segment kinematics of markers worn during task performance were used to determine total body CM,
the orientation of each leg subsystem as well as linear and angular kinematics of the lower extremity
segments [5]. Body segment parameters and segment reference systems consistent with inertial tensors
were defined in accordance with DeLeva, 1996 [5]. Functional joint centers of the ankle, knee, and hip
were estimated according to Schwartz et al using custom Matlab code [6]. These functional joint centers
served as segment endpoints and were used to estimate the CM of each segment from body segment
parameters [5]. The ankle, knee, and hip joint positions were used to define a “leg plane” and a vector
perpendicular to the leg plane. The degree of alignment of the resultant GRF relative to the leg plane was
used to determine to what degree out of plane moments (e.g. abductor/adductor) were imposed by the
resultant net joint forces at the ankle, knee and hip. Segment angular velocities and were estimated by
using quaternion parameterization and angular and linear accelerations were obtained through
differentiation of the built-in cubic spline function of Matlab (CSAPS). The orientation of the functional
knee joint axes was determined from the knee joint angular velocity calculated using quaternion
parameterization. The orientation of this functional knee joint axes was used to present the component
of the knee net joint moment (NJM) acting about the functional knee joint axes representing the
articulation of the individual’s knee during unloaded swings [7].
The pirouette turns performed in study were initiated from a static position with the body weight
supported by both push and turn leg (in “fourth position”). During the turn initiation phase, the linear and
angular impulse needed to perform the pirouette turn are generated. The turn initiation phase is
determined from the time when the lateral component of the horizontal GRF of the turn or push leg
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exceeded 10N until termination of push leg ground contact (Figure 7-1). Angular impulse about a vertical
axis passing through the CM during the turn initiation phase was determined using the cross product of
the position vector from the CM to the point of GRF application (center of pressures for the Turn and Push
legs). The free moment applied by each leg was also determined as a contributor to total moment [8], [9].
Activation of superficial hip muscles were monitored using surface electromyography (EMG) (Konigsberg),
amplified, and digitized (1200 Hz, National Instruments A/D board) along with the ground reaction force
data using custom software. Dual electrodes with an inter-electrode distance of 1 cm were placed over
the muscle belly, parallel to the muscle fibers (Noraxon, Scottsdale, AZ). The EMG data were filtered using
a 4th order zero-phase butterworth band-pass filter (10 Hz -400 Hz) and quantified using root mean
squared values in 20ms average bins. EMG data were normalized to the maximum binned values during
isometric manual muscle tests [10].
Between-task differences in linear and angular impulse were compared using statistical analysis software
R (open-source). Across dancers, a paired t-test was used to test the null hypothesis that mean angular
and linear impulse was the same between turn conditions. Within-subject comparisons of the probability
for angular or linear impulse to be different between turn conditions was calculated (R, open-source). P-
values were calculated for each dancer using Cliff’s analog of the Wilcoxon-Mann-Whitney test [11], [12].
This method was chosen because it deals well with small numbers of trials per condition [12]. A step-down
Fisher-type method was then applied to control the familywise error rate (α = 0.05) over multiple
comparisons, modified so that the level of significance becomes α/k at each k
th
iteration [13]–[15]. The
statistical method chosen provides more flexibility by allowing heteroscedasticity across dancers [16]. This
statistical method is highly dependent upon the distribution of p-values for each variable measured
because the level for significance becomes α/k at each k
th
iteration [15]. Therefore, the presentation of
within-subject results provides a relatively conservative estimate of significant differences between turn
conditions.
Results
Angular and linear impulse generated in both turn conditions was sufficient to successfully complete
similar desired mechanical objectives at the whole-body level. Net angular and linear impulse generation
during the turn initiation phase tended to be greater during pirouettes initiated with hip external rotation
than during pirouettes initiated without hip external rotation. Differences in impulse generation between
turn conditions were consistent with the changes dancers made to their initial stance configuration. All
dancers initiated the turn with the CM closer to the turn legs’ base of support. As a group, the net angular
impulse was significantly different between turn conditions (p = .005) and individually for three of five
dancers (brackets, Figure 7-2). Additionally, the angular impulse generated by the turn leg was
significantly different across turn conditions as a group (p = .004) and individually for three of five dancers
(brackets, Figure 7-2). As a group, the net linear impulse in each direction was significantly different
between turn conditions (anterior impulse (+y, p = .003), lateral impulse (+x, p = .04)) and individually for
two of five dancers in each linear impulse direction (brackets, Figure 7-3).
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Figure 7-2: Mean (SD) mass-normalized net (gray), turn leg (purple), and push leg (orange) angular impulse for pirouettes with
hip external rotation (pir, solid bars) and parallel pirouettes (ppir, hashed bars). Consistent with dancers initiating the parallel
pirouette turn with the center of mass closer to the turn leg, the turn leg’s angular impulse generated was less than that generated
during pirouettes with hip external rotation (except subject 1). Brackets indicate within-subject significant differences between
turn conditions when tested at α = .05 level and adjusted for multiple comparisons.

Figure 7-3: Mean (SD) mass-normalized net (gray), turn leg (purple), and push leg (orange) linear impulse in (A) mediolateral (+X)
direction and (B) anterior (+Y) direction for pirouettes initiated with hip external rotation (pir, solid bars) and parallel pirouettes
(ppir, hashed bars). For both turn types, linear impulse was aligned with the travel direction towards the turn leg’s base of support.
Mean net linear impulse generated during parallel pirouettes was less than that generated during pirouettes with hip external
rotation, consistent with stance configuration changes leading to a smaller distance between the center of mass and turn leg’s
base of support. In general, the push leg generated the most linear impulse in the desired direction of travel. Brackets indicate
within-subject significant differences between turn conditions when tested at α = .05 level and adjusted for multiple comparisons.

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Each dancer maintained alignment of the GRF relative to the respective leg, even with changes in
horizontal GRF and leg plane orientation relative to the global reference system across pirouette types (as
in the exemplar data in Figure 7-1). On average, at least 90% of the GRF was aligned with the respective
leg plane (n=5, Figure 7-4) and at least 70% of the GRF was aligned with the respective foot’s longitudinal
axis (n=5, Figure 7-5) during turn initiation. GRFs during parallel pirouettes were more aligned with the
legs’ planes than during classical pirouettes. The least alignment between GRF and leg planes occurred
relative to the turn leg during the initiation of classical pirouettes, when the turn leg’s horizontal reaction
force was applying its maximum moment about a vertical axis through the CM (n=5). Within dancer, GRFs
during parallel pirouettes were more aligned with the respective leg planes than during classical
pirouettes. The greatest deviation between the GRF and the respective leg plane was observed for the
turn leg during the initiation of classical pirouettes at a time when the GRF contributed to the turn leg’s
peak moment applied about the CM (n=5).

Figure 7-4: The mean (SD) average percentage of the ground reaction force (GRF) aligned with the turn (purple) and push (orange)
leg planes in pirouettes initiated with hip external rotation (pir, solid bars) vs. pirouettes initiated with neutral hip alignment (ppir,
hashed bars) for each subject. On average throughout both turn conditions’ initiation phases, at least 90% of the ground reaction
force at the turn leg was aligned with the turn leg’s plane and at least 95% of the ground reaction force at the push leg was aligned
with the push leg’s plane.

Figure 7-5: The mean (SD) average percentage of the ground reaction force (GRF) aligned with the turn (purple) and push (orange)
feet longitudinal axes in pirouettes initiated with hip external rotation (pir, solid bars) vs. pirouettes initiated with neutral hip
alignment (ppir, patterned bars) for each subject. On average throughout the turn initiation phase, at least 95% of the ground
reaction force was aligned with the turn leg’s foot longitudinal axis and at least 70% of the ground reaction force was aligned with
the push leg’s foot longitudinal axis.
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A majority of the net joint moment (NJM) at the ankle, knee, and hip acted about an axis perpendicular
to the leg plane. This was the case even at the time of peak moment generation by the horizontal
components of the GRF about the CM (Figure 7-7,Figure 7-8). On average, the hip NJMs tended to be
greatest for the turn leg across dancer and turn types (Figure 7-8). The majority of the support moments
were aligned with the leg planes even at the time of each leg’s peak moment application about a vertical
axis through the body’s CM (Figure 7-7; >50% in plane, except the turn leg of subject 5 during classical
pirouettes).

Figure 7-6: For exemplar subject 4, the majority of the net joint moment magnitude (black) at each ankle, knee, and hip for both
push and turn leg acted about an axis perpendicular to the leg plane (turquoise).

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Figure 7-7: Mean (SD) sum of the components of the net joint moment at the ankle, knee, and hip that acted about an axis
perpendicular to the leg (blue) and total support moment (blue+black) at each leg during the peak moment applied by each leg
about a vertical line through the body’s center of mass during initiation of the single classical pirouette (pir1) and parallel pirouette
(ppir1) turns. Overall, more support moment was in plane of the push leg than it was of the turn leg. More turn leg support
moment was acting about the axis perpendicular to the turn leg plane in parallel pirouettes vs. classical pirouettes, consistent
with a larger percentage ground reaction force aligned with the turn leg plane in parallel pirouettes.

Figure 7-8: Mean (SD) amount of the net joint moment at the ankle, knee, and hip acting about an axis perpendicular to the leg
plane (turquoise) and the net joint moment not acting about an axis perpendicular to the leg plane (black) for pirouettes initiated
with hip external rotation (pir, left) and parallel pirouettes (ppir, right) at the time that each leg applied its peak moment about a
vertical line through the body’s center of mass. Relative distribution of the support moment between the ankle, knee, and hip
tended to be subject-specific at the push leg, but at this time during the initiation phase of both turn conditions and all dancers,
the turn leg hip had the largest net joint moment.
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During the turn initiation, differences in orientation of the tibia relative to the leg plane were observed
(Figure 7-9, greater than 8° n=5). Differences in tibia segment alignment relative to the leg plane affected
the distribution of the knee NJM when represented with respect to the tibia versus thigh reference frames
(Figure 7-10).

Figure 7-9: Mean (SD) orientation difference between the leg plane and anteroposterior axis of the tibia during classical (pir) and
parallel (ppir) pirouettes. Exemplary sagittal-plane kinematics (Subject 3) early (left) and late (right) in the turn initiation phase of
a classical pirouette (pir) displays the difference in orientation between the tibia and thigh (picture at the right shows how the
foot longitudinal axis points lateral and backwards as the thigh anteroposterior axis points lateral and forward).

Figure 7-10: Exemplar push leg knee moment vs. time during multiple trials (subject 4) expressed about anatomical references
systems described by De Leva and corresponding segment sagittal and frontal view free body diagrams (FBD) at time of peak net
joint moment [5]. A difference in orientation between the tibia and femur caused a redistribution of the knee moment about the
thigh’s segment reference system: (A) When the knee net joint moment is expressed about the tibia’s segment reference system,
there is primarily extensor moment and smaller abductor moment acting on the tibia, however, (B) when this knee moment is
expressed about the thigh’s segment reference system, the difference in alignment between the tibia and femur changed the
distribution between extensor and abductor moments.
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Turns initiated without external hip rotation involved different joint kinetics and hip and knee muscle
recruitment patterns than those initiated with hip external rotation (Figure 7-11,Figure 7-12, Figure 7-13).
Lower extremity NJMs expressed about the lower extremity segment reference systems and associated
muscle recruitment patterns for each leg during the turn initiation phase were subject specific (Figure
7-12, Figure 7-13). However, all dancers used combinations of push leg hip flexor and abductor moments
when expressed about the push leg thigh segment reference system (Figure 7-12A, exemplar Figure 7-11)
(primarily due to the adjacent moment at the knee, rather than proximal and distal joint moments, as was
the case shown in the thigh’s free body diagrams of Figure 7-10). Most dancers (except subject 2) used
combinations of turn leg hip extensor and abductor moments when expressed about the turn leg’s thigh
segment reference system (in contrast to the push leg, this was primarily due to proximal and distal joint
moments) (Figure 7-12B, exemplar Figure 7-11). Additionally, all dancers used ankle plantarflexor and
knee extensor moments at both legs and during both turn conditions (Figure 7-12). While muscle
recruitment patterns were subject-specific, they were consistent with the knee and hip joint moments
across turn conditions (as was the case in exemplar data shown in Figure 7-13).

Figure 7-11: Exemplar (subject 4) push leg ankle, knee, and hip joint moments about each segment’s reference system during the
turn initiation phase of pirouettes initiated with external rotation (pir, left) and parallel pirouettes (ppir). This dancer maintained
similar knee and hip joint moments across turn conditions, but changed the orientation of her foot relative to the ground reaction
force, which reduced the plantarflexor moment during a parallel pirouettes compared to during a classical pirouette.
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Figure 7-12: (A) Push leg and (B) turn leg mean (SD) average extensor (ext.) and abductor (abd.) joint moments expressed about
each segment reference system during the turn initiation phase of pirouettes initiated with hip external rotation (pir) and parallel
pirouettes (ppir). Across dancers, joint kinetic patterns were different. However, all dancers used combinations of push leg hip
flexor and abductor moments when expressed about the thigh’s segment reference system (primarily due to the adjacent moment
at the knee, rather than proximal and distal joint moments, as was the case shown in the thigh’s free body diagrams of Figure
7-10B). At the turn leg, dancers (except subject 2) used combinations of turn leg hip extensor and abductor moments when
expressed about the thigh’s segment reference system. Additionally, all dancers used ankle plantarflexor and knee extensor
moments in both turn conditions and legs.
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Figure 7-13: Muscle recruitment was consistent with joint kinetics at the hip and knee. Exemplar (subject 2) push leg mean (SD)
root mean squared, binned, and normalized muscle recruitment patterns (% maximum binned value during a manual muscle test
(MMT)) and associated hip and knee joint kinetics during the initiation phase of pirouettes initiated with external rotation (pir)
and parallel pirouettes (ppir). For this dancer, during parallel pirouettes, there was less knee extensor and hip flexor moments,
which was consistent with less rectus femoris recruitment (and more biceps femoris activation).
Discussion
The purpose of this study was to compare impulse generation strategies of each leg and associated muscle
recruitment strategies during the turn initiation phase of pirouettes performed with and without hip
external rotation. Dancers in this study were asked to perform single pirouettes initiated from neutral and
external rotated hip positions. Examination of linear and angular impulse generated during turn initiation
revealed changes in impulse generation consistent with the discovery of changes in the initial stance
position between turn conditions. Pirouettes initiated from a neutral position tended to start with the CM
closer to the turn leg than the push leg. Consistent with this change in stance, less net linear impulse was
needed to initiate the pirouette with hips neutral as compared to initiation with hips externally rotated
Figure 7-3). Additionally, less angular impulse was generated by the turn leg during pirouettes initiated
without hip external rotation, which contributed to the smaller net angular impulse between turn types
(Figure 7-2). As a result, there were differences in horizontal GRF and leg plane orientation relative to the
global reference system across pirouette types. However, GRFs maintained alignment with each dancer’s
lower extremities. Consistent with this finding, a majority of the net joint moment (NJM) at the ankle,
knee, and hip acted about a vector perpendicular to the leg plane. When the NJM were distributed across
each lower extremity segment reference system, differences in tibia segment alignment relative to the
leg plane affected the distribution of the knee NJM when represented with respect to the tibia versus
thigh reference frames (Figure 7-10). Using segment reference system representation of the NJM, turns
initiated with and without external hip rotation involved different joint kinetics and hip and knee muscle
80

recruitment patterns than those initiated with hip external rotation. However, for both turn types, most
participants used primarily extensor moments at the ankle and knee, flexor and abductor moment at the
push leg’s hip, and extensor and abductor moments at the turn leg’s hip (Figure 7-12). While muscle
recruitment patterns were subject-specific, they were consistent with the knee and hip joint moments
across turn conditions.
To mitigate the effect of experimental conditions on the results, efforts were made to mimic the typical
dance performance environment and a within-subject design was used. By covering each forceplate and
surrounding area with dance flooring surface and by encouraging dancers to use their own footwear,
dancers were able to establish their preferred foot-surface frictional characteristics. The dance flooring
selected provided typical frictional characteristics found on stages and in studios, but was rigid such that
it did not interfere with force transmittance. Music with a controlled tempo was used to standardize the
speed of the turn initiation phase, consistent with what a dancer is likely to encounter when satisfying
constraints imposed by choreography. Additionally, tracking markers were specifically arranged for each
dancer to limit interference with normal kinematics during these turns (i.e., shank tracking cuff location
on the turn leg relative to the gesture leg’s foot path along the shank). The within-dancer design provided
an opportunity to determine how an individual dancer modified her own control strategies when
performing each turn condition (each individual serves as her own control). Even with the small sample
size used, differences in the control mechanisms used by each dancer to regulate impulse during turning
tasks were identified. Ranges of linear and angular impulse generated by these individuals were similar to
those reported in previous studies of impulse generation during the initiation of pirouettes (Specific Aim
II Results).
Dancers seemed to simplify control and avoid the need for out of plane net joint moments by aligning the
GRF with the leg plane under both turn conditions. By maintaining relatively tight control of the GRF
relative to the leg plane ( >90%), the majority of the net joint moments at the ankle, knee, and hip of each
leg tended to acted about the axes perpendicular to the leg plane. These findings and representation of
joint kinetics in relation to the leg plane provide kinematic context for comparing lower extremity joint
kinetics across turn conditions. Performance benefits of GRF alignment relative to the leg plane have not
been fully discerned. For example, dancers with relatively large hip net joint moment acting about an axis
perpendicular to the leg plane axis (subjects 2 & 5, Figure 7-8) also tended to complete the turn initiation
phase in less time than other dancers. There may be other potential benefits and drawbacks associated
with maintaining small out-of-plane loads or tolerating more out-of-plane loads in order to more quickly
generate angular impulse, simplify control during particular phases of the turn, or more effectively
distribute load within the lower extremity.
In the dancers studied, there were notable differences in the orientation of the tibia relative to the leg
plane during pirouette initiation. The relative angle between the tibia and leg plane orientation ranged
from 8°-60° on average throughout the turn initiation phase across subjects. In contrast, the functional
joint axes of the knees for these participants were well aligned with the femoral condyles. These results
indicate that there was more hinge-like behavior at the knee during unloaded knee flexion and extension,
whereas during force generation during turn initiation the tibia and leg plane were not aligned as they
were during the calibration movement. Representing joint kinetic results using two different reference
systems provides a means to discuss control during force generation from the perspective of control about
the functional joint axis in an unweighted condition and in relation to axes defined by the segment
reference systems and leg plane (Figure 7-14; exemplar subject 4 push leg knee). Previous work regarding
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the “turnout” used by classical ballet dancers suggests screening dancers in relatively static positions to
assess how much of the turnout is achieved using hip external rotation or below-the-thigh rotation [17]–
[22]. This study suggests that the use of contextually-relevant functional screening may be important
when assessing functional turnout in dancers. This difference in alignment between tibia and leg plane
also contributed to a redistribution of the knee moment about the thigh’s reference system (Figure 7-10).
The difference in orientation between the tibia and leg plane may have been used as a means of orienting
the point of force application a distance away from the CM during generation of angular impulse while
maintaining most of the GRF aligned with the leg planes and longitudinal axes of the feet.

Figure 7-14: Exemplar (subject 4) shows that despite the (A) net joint moment at the push leg’s knee primarily acting about a
vector perpendicular to the leg plane, (B) the net joint moment did not primarily act about the functional joint axes of the knee
calculated during a functional calibration movement relative to the shank segment reference system.
Interpretation of lower extremity control using different reference systems presents advantages. Analysis
of turns at the total body level showed that the GRF angle and magnitude was different between turn
conditions throughout the turn initiation phase. However, by investigating the relationship between the
GRF and the leg plane, it was determined that control of the GRFs in relation to the respective leg plane
resulted in comparable hip joint kinetic patterns in both turn conditions and across dancers. Differences
between dancers in control at the ankle and knee is in part attributed to differences in lower extremity
segment alignment during GRF generation. Tight control of the GRF relative to the leg plane appears to
be an effective means for simplifying control of the lower extremity and for taxing muscles of the lower
extremity with the greatest cross-sectional area (flexors and extensor) as compared to the smaller muscles
involved in the control of out of plane motion [23], [24]. More extensive monitoring of lower extremity
muscles involved in the control of abduction-adduction and internal and external rotation may provide
additional insight in future studies.
In summary, while the mechanical objectives of both pirouettes were comparable, the dancers studied
changed their initial stances. Dancers initiated the parallel turn with a smaller distance between the CM
and turn leg’s base of support than during classical pirouettes. This changed the required linear impulse
generation and impacted each leg’s context to generate angular impulse between turn types. Joint
kinetics were consistent with each leg’s kinematic context within each turn, but were subject-specific.
Dancers maintained similar hip joint moment patterns at each leg across turn types.
82

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Abstract (if available)

Abstract Turning is fundamental to locomotion, yet, not fully understood from a control and dynamics perspective. Without advances in our current understanding, clinical populations may continue to struggle to change direction while walking and bipedal robots will fail to execute turns as performed by humans. This work focused on identifying the mechanical strategies dancers used to satisfy multiple mechanical objectives during fundamental dance turns. The overarching goal of this research was to understand how dancers effectively control their bodies to interact with their environment during turns requiring varied amounts of rotation and translation. With this knowledge, training procedures for dancers can be improved through more specific cuing from dance teachers or through development of interactive technology to provide feedback. While there may be fundamental differences in the capabilities of clinical populations compared to skilled ballet and contemporary dancers, by studying solutions experts use under progressively more challenging conditions, insight is gained regarding control priorities that can be mapped to help other populations. ❧ During turns, each leg plays a distinct role in generating the reaction forces required to control both linear and angular momentum of the body. The reaction force regulation over time, generates linear and angular impulse needed for the desired movement. However, angular impulse about the body's center of mass involves reaction force components that are not aligned with the desired center of mass trajectory, which imposes conflicts in control priorities. Through coordination of each leg’s reaction force generation, the aforementioned conflicts can be appeased. ❧ Turns performed by dancers provided a unique opportunity to understand how skilled individuals successfully satisfy multiple mechanical objectives. Specifically, “piqué” and “pirouette” turns with inherent variations of rotation and translation were studied to determine how dancers satisfy linear and angular momentum requirements, while maintaining balance. Each turn serves as a well-practiced task that can be performed with increased rotational requirements (e.g. single, double). Additionally, both turns impose a specific postural challenge during the turn phase: the dancer must spin while supported by a single leg (extended knee and plantarflexed ankle) and a very small base (the forefoot). The differences in how pirouette and piqué turns are terminated also provided a systematic comparison between balance maintenance during a translating turn (piqué) and a “turn-and-stop” displacement turn (pirouette). By using a within-subject experimental design, control preferences of an individual across tasks were identified, which may be used in the design of personalized feedback to improve performance. ❧ In this series of studies, skilled dancers performed single and double piqué and pirouette turns while each leg was supported by a forceplate. During each turn, reaction forces were measured using dual forceplates (1200 Hz) while three dimensional kinematics were simultaneously captured (100 Hz). At the whole-body level, linear and angular impulse generated by the push and turn legs during turn initiation and contributing factors to impulse generation (resultant horizontal reaction force, sinθ, position vector magnitude) were quantified and compared across the group and within a dancer (α = .05). During the turn phase, balance regulation was compared between piqué and pirouette turns and between single and double turns across the group and within a dancer. At the segment-level, the contributions at the ankle, knee, and hip during impulse generation were compared between pirouette turns initiated with and without hip external rotation. ❧ Modification of Impulse Generation during Piqué Turns with Increased Rotational Demands: The purpose of this study was to determine how skilled dancers (n=10) used the push and turn leg to regulate angular and linear impulse generated during the initiation phase of piqué turns performed with increased rotational demands. During the initiation of a piqué turn, a dancer interacts with the environment to generate lateral and angular impulse in order to satisfy the lateral and rotational momentum requirements. The piqué turn is initiated with single leg support from the “push leg” and the turn phase occurs with single leg support from the “turn leg”. The turn initiation phase ends as the push leg departs the ground, shortly after the turn leg makes initial contact with the ground. ❧ Results indicate that in order to increase the amount of body rotation from the performance of a single piqué turn to a double piqué turn, dancers tended to increase the net angular impulse generated and decrease the mean lateral impulse generated. The push leg contributed more angular and lateral impulse compared to the turn leg in both single and double turns. However, all dancers studied increased angular impulse generated by the turn leg, despite its contact with an extended knee, plantarflexed ankle, and contact only with the forefoot during a short duration (~0.2 s). As number of turns performed increased, dancers increased the push leg’s mean anterior impulse generation and the turn leg’s mean posterior impulse generation, consistent with mechanisms to increase angular impulse. The push leg tended to increase the mean moment applied about the center of mass via redirecting the reaction force, whereas the turn leg used combinations of modulation of the reaction force (magnitude and direction) and increased position vector length (either via decreased center of mass velocity towards the turn leg, and/or by contacting the ground earlier with the turn leg as the center of mass was approaching the turn leg’s ground contact). Control strategies used by dancers during progressively more challenging turning tasks tended to be subject-specific. By coordinating the generation of reaction forces between legs, the net horizontal impulse in the anterior/posterior direction remained minimal, despite impulse regulation used to achieve increased rotational demands. ❧ Modification of Impulse Generation during Pirouette Turns with Increased Rotational Demands: The purpose of this study was to determine how skilled dancers (n=11) used the push and turn leg to regulate angular and linear impulse generated during the initiation phase of pirouette turns performed with increased rotational demands. During the initiation of a pirouette turn, a dancer generates linear and angular impulse in order to satisfy the linear center of mass displacement and angular momentum requirements. The pirouette turn is initiated with double leg support from both the push leg and turn leg. The turn initiation phase ended as the push leg departed from the ground. ❧ Results indicate that as rotational demands increased from performance of a single pirouette turn to a double pirouette turn, dancers increased the mean net angular impulse generated and maintained minimal linear impulse generated towards the turn leg’s base of support. The contribution of each leg to net angular impulse in both single and double pirouettes was linked with stance configuration strategies. While the center of mass horizontal position resides somewhere within the base of support initially, stylistic differences between schools of ballet provided context for some range across subjects regarding the initial center of mass positioning closer to the turn leg or to the push leg. Dancers who initiated the turn with a larger position vector between the center of mass and the turn leg’s base of support generated more mean angular impulse with the turn leg during both single and double pirouettes. Conversely, dancers who initiated the turn with the center of mass closer to the turn leg, generated more angular impulse with the push leg in both single and double turns. However, all dancers studied generated more linear impulse in the direction of the turn leg’s base of support with the push leg than they did with the turn leg. Overall, dancers increased the horizontal reaction force magnitude at one or both legs in order to increase the moment applied about the center of mass. The push leg also tended to increase the mean moment applied about the center of mass via redirecting the reaction force. As was the case during piqué turn initiation, by coordinating the generation of reaction forces between legs, changes in the mean net horizontal impulse perpendicular to the desired center of mass trajectory remained minimal, despite impulse regulation at each leg used to achieve increased rotational demands. ❧ Whole-Body Balance Regulation during the Turn Phase of Piqué and Pirouette Turns: The purpose of this study was to compare balance regulation strategies used by skilled dancers (n=10) during the turn phase between piqué and pirouette turns and between single and double turns. After the initiation of both piqué and pirouette turns, the turn phase required whole body rotation while maintaining balance in a challenging kinematic context. However, differences in how the pirouette and piqué turn is terminated provided a systematic comparison between balance maintenance during a translating turn (piqué) and a “turn-and-stop” or minimal displacement turn (pirouette). As rotational demands increase, it was expected that turns with multiple rotations impose a need to position the CM over the base of support for longer periods of time. Maintaining the CM position over the base of support for a longer period was expected to require more corrective actions that involve regulation of the reaction forces relative to the center of mass. ❧ Comparisons between the piqué and pirouette, for both single and double turns, revealed that the center of mass during the pirouette was more vertically aligned than was the center of mass during the piqué turn. Throughout the turn phase of a pirouette, the dancers’ center of mass was aligned within 15° from vertical (the mean alignment for both single and double pirouettes was less than 5° for all subjects, n=10). As rotational demand increased in both turns, the ground reaction forces were regulated relative to the CM. By controlling the braking force and moment applied about the CM the potential for the CM to overshoot the horizontal positon of the base of support in the primary direction of travel was limited. ❧ Lower Extremity Control during Turns Initiated with and without Hip External Rotation: The purpose of this study was to compare impulse generation strategies used by skilled dancers (n=5) at each leg and the associated muscle recruitment strategies during the turn initiation phase of pirouettes performed with and without hip external rotation. Classical ballet turns are typically initiated and performed with the hips externally rotated, whereas, more modern choreography requires dancers to also be proficient in performing tasks with neutral hip alignment. This provided an opportunity to investigate how dancers satisfy the same mechanical objectives at the total body level when generating ground reaction forces using different leg kinematics. In addition to comparing impulse generation strategies, activation of superficial hip muscles were monitored using surface electromyography (1200 Hz) and joint kinetics during turn initiation were determined for both legs using measured ground reaction forces, 3D segment kinematics, and body segment parameters. ❧ Results indicate that differences in impulse generation between turn conditions were consistent with initial stance configuration. Despite differences in ground reaction force orientations between turn conditions, on average, at least 90% of the ground reaction force was aligned with the respective leg plane for both turn conditions. In addition, a majority of the net joint moment at the ankle, knee, and hip acted about an axis perpendicular to the leg plane. However, differences in tibia segment alignment relative to the leg plane affected the distribution of the knee net joint moment when represented with respect to the tibia versus the thigh reference system. During both turn types, most participants used primarily extensor moments at the ankle and knee, flexor and abductor moment at the push leg’s hip, and extensor and abductor moments at the turn leg’s hip. While muscle recruitment patterns were subject-specific, they were consistent with the knee and hip joint moments across turn conditions. ❧ The technique-related findings of this series of studies indicated that dancers coordinated both legs to regulate the reaction forces during the initiation and turn phases of piqué and pirouette turns. Dancers used subject-specific mechanisms to increase angular impulse generated during turn initiation. However, at the segment-level, during the initiation of pirouettes with varied initial hip kinematics, dancers tended to align their lower extremities with each reaction force in a way that simplified control at the hip across tasks. These whole-body and segment-level results can be used to inform the design of customized feedback technologies that aim to facilitate skill acquisition and improve dance performance.

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Asset Metadata

Creator Zaferiou, Antonia (author)

Core Title Control and dynamics of turning tasks with different rotation and translation requirements

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Biomedical Engineering

Publication Date 09/24/2015

Defense Date 08/28/2015

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

Tag biomechanics,joint kinetics,kinematics,kinetics,lower extremity,momentum,OAI-PMH Harvest,redirection,turning

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor McNitt-Gray, Jill (committee chair), Flashner, Henryk (committee member), Kulig, Kornelia (committee member), Requejo, Philip (committee member)

Creator Email antoniazaferiou@gmail.com,zaferiou@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c40-187305

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Identifier etd-ZaferiouAn-3951.pdf (filename),usctheses-c40-187305 (legacy record id)

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Document Type Dissertation

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