Transcript A Dynamical Systems Approach to Lower Extremity Running

Kinetics of Hula Hooping:
An Exploratory Analysis
Tyler Cluff
D. Gordon E. Robertson
Ramesh Balasubramaniam
School of Human Kinetics
Faculty of Health Sciences
University of Ottawa, Ottawa, Canada
Physics of Hula Hooping
Conservation of angular momentum
 Small, carefully initiated impulses exerted
on the interior periphery of hoop
 Vertical component to oppose gravity
 Dynamic equilibrium achieved by coupled,
sustained oscillations about joints of lower
extremity

Hula Hoop (front view)
Bob McDonald (Quirks & Quarks)
Previous Research

Balasubramaniam and Turvey (2004):
– Ig Nobel award winning project in physics (2004)
– 95% of variance accommodated by just two modes
 the first mode was a hip dynamical system; foreaft motion of the hips maintained rotational motion
 the second mode (eigenvalue) was a knee
dynamical system for vertical stability
– larger hoop sizes required more emphasis on the role
of the knees to maintain motion of the vertical
regulatory component
Hula Hoop (side view)
Purpose

The purpose of this research was to
compare the conclusions reached using
dynamical systems theory with those of
inverse dynamics/moment power analyses.

Are the two theories in agreement with
regards to the involvement of the hips and
knees in maintaining oscillatory motion of
the hoop?
Methods Flow Chart
Three experienced female participants
5 x 30 s trials at resonant frequency with
small hoop (70 cm)
Vicon Workstation:
5 MX13 cameras (200 Hz)
2 Kistler force platforms
22 marker trajectories
Visual3D v3.79:
7-segment lower body model
Inverse dynamics and moment powers
Sample Data
Inverse Dynamics
method for determining the minimal forces
and moments at each joint
 based on the kinematics of the motion,
body segment parameters and measured
external forces (via force platforms)

First divide limb into segments
Make free body
diagrams
(FBD) of each
segment
Add all known forces to FBD
Weight
Ground
reaction force
Apply Newton/Euler Laws of
Motion to Terminal Segment
Start analysis
with foot to
compute ankle
forces and
moments
Apply reactions to next segment
in kinematic chain
Apply reactions of
foot to distal end
of leg segment to
compute knee
forces and
moments
Repeat with next segment in
chain or begin up another limb
Repeat for thigh
segment to
obtain hip
forces and
moments
Moment Power

product of joint angular velocity (w) and
net moment of force (M) at same joint
PM = M w

usually caused by muscle contractions
especially when motion does not reach
ends of range of motion
Results
• each figure shows three repetitions averaged across
five trials (error bars are ± 1 SD)
• frequencies were from to 1.6 to 1.7 Hz
• vertical axes are normalized to body mass
• top curves are hip, middle are knee, bottom are ankle
• left side data are from the left limb and vice versa
Results – hip ab/adductor moments
• hip abductors dominated throughout
• left and right sides were 180 degrees out-of-phase
• adductors performed minor role and little work
Figure 1. Ab/adductor moments of the ankle, knee and hip joints (Subject 1).
Results – ab/adductor powers
• all subjects had similar patterns of the hip
abductors and adductors
• work done at knee was likely not muscular but was
likely done by joint structures
• little or no work done at ankles
Figure 2. Abductor/adductor powers of the ankle, knee and hip joints (Subject 1).
Results – ab/adductor powers
• hip abductors produced negative work
• immediately afterwards positive work (prestretching?)
• followed by a brief pause or adductor work while
contralateral abductors performed positive work
Figure 2. Abductor/adductor powers of the ankle, knee and hip joints (Subject 1).
S1 Results – knee extensor strategy
• knee extensors dominated throughout
• left and right sides out-of-phase
• ankle plantiflexors also contributed
Figure 3. Flexor/extensor moments of the ankle, hip and knee (Subject 1).
S1 Results – knee extensor strategy
• knee extensors produced positive then negative work
• while left side did positive work, right did negative work
• little work by plantiflexors or hip moments
Figure 4. Flexor/extensor powers of the ankle, hip and knee (Subject 1).
S2 Moments – hip-ankle strategy
• hip and knee flexors and extensors are involved
• ankle plantiflexors dominated throughout
Figure 5. Flexor/extensor moments of the ankle, knee and hip joints (Subject 2).
S2 Powers – hip-ankle strategy
• hip flexors and plantiflexors of left side produced the
majority of the positive work; right hip extensors assisted
• little work by knee moments
Figure 6. Flexor/extensor powers of the ankle, knee and hip joints (Subject 2).
S3 Moments – whole leg strategy
• similar to subject 2 but both sides produced equal magnitudes
• both sides were only slightly out of phase
Figure 7. Flexor/extensor moments of the ankle, knee and hip joints (Subject 3).
S3 Powers – whole leg strategy
• left knee flexors & extensors and plantiflexors provided most
work with assistance from both hip flexors
• right knee extensors and plantiflexors provided negative work
Figure 8. Flexor/extensor powers of the ankle, knee and hip joints (Subject 3).
Summary
All subjects used the hip abductors to maintain
hoop horizontal rotational equilibrium
 With same experimental conditions each subject
adopted a different strategy to maintain hoop’s
vertical equilibrium
 Subject 1 relied on the knee extensors
 Subject 2 relied on the hip moments and
ankle plantiflexors
 Subject 3 incorporating the flexors/extensors
of the knee and hip and ankle plantiflexors

Summary
Agreement between dynamical systems
theory and inverse dynamics/moment
power analyses but in unpredictable ways
 Care must be taken when averaging
subjects together (can hide individual
strategies)
 Kinematics alone cannot define causes of
motion

Questions?