1. 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

2. Physics of Hula Hooping Conservation of angular momentum Conservation of angular momentum Small, carefully initiated impulses exerted on the interior periphery of hoop Small, carefully initiated impulses exerted on the interior periphery of hoop Vertical component to oppose gravity Vertical component to oppose gravity Dynamic equilibrium achieved by coupled, sustained oscillations about joints of lower extremity Dynamic equilibrium achieved by coupled, sustained oscillations about joints of lower extremity

3. Hula Hoop (front view) Bob McDonald (Quirks & Quarks)

4. Previous Research Balasubramaniam and Turvey (2004): 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; fore- aft 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

5. Hula Hoop (side view)

6. Purpose The purpose of this research was to compare the conclusions reached using dynamical systems theory with those of inverse dynamics/moment power analyses. 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? Are the two theories in agreement with regards to the involvement of the hips and knees in maintaining oscillatory motion of the hoop?

7. 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

8. Sample Data

9. Inverse Dynamics method for determining the minimal forces and moments at each joint 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) based on the kinematics of the motion, body segment parameters and measured external forces (via force platforms)

10. First divide limb into segments Make free body diagrams (FBD) of each segment

11. Add all known forces to FBD Weight Weight Ground reaction force Ground reaction force

12. Apply Newton/Euler Laws of Motion to Terminal Segment Start analysis with foot to compute ankle forces and moments

13. Apply reactions to next segment in kinematic chain Apply reactions of foot to distal end of leg segment to compute knee forces and moments

14. Repeat with next segment in chain or begin up another limb Repeat for thigh segment to obtain hip forces and moments

15. Moment Power product of joint angular velocity (  ) and net moment of force (M) at same joint product of joint angular velocity (  ) and net moment of force (M) at same joint P M = M  usually caused by muscle contractions especially when motion does not reach ends of range of motion usually caused by muscle contractions especially when motion does not reach ends of range of motion

16. 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 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

17. Results – hip ab/adductor moments Figure 1. Ab/adductor moments of the ankle, knee and hip joints (Subject 1). hip abductors dominated throughout left and right sides were 180 degrees out-of-phase adductors performed minor role and little work hip abductors dominated throughout left and right sides were 180 degrees out-of-phase adductors performed minor role and little work

18. Results – ab/adductor powers Figure 2. Abductor/adductor powers of the ankle, knee and hip joints (Subject 1). 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 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

19. Results – ab/adductor powers Figure 2. Abductor/adductor powers of the ankle, knee and hip joints (Subject 1). hip abductors produced negative work immediately afterwards positive work (prestretching?) followed by a brief pause or adductor work while contralateral abductors performed positive work hip abductors produced negative work immediately afterwards positive work (prestretching?) followed by a brief pause or adductor work while contralateral abductors performed positive work

20. S1 Results – knee extensor strategy Figure 3. Flexor/extensor m oments of the ankle, hip and knee (Subject 1). knee extensors dominated throughout left and right sides out-of-phase ankle plantiflexors also contributed knee extensors dominated throughout left and right sides out-of-phase ankle plantiflexors also contributed

21. S1 Results – knee extensor strategy Figure 4. Flexor/extensor powers of the ankle, hip and knee (Subject 1). knee extensors produced positive then negative work while left side did positive work, right did negative work little work by plantiflexors or hip moments knee extensors produced positive then negative work while left side did positive work, right did negative work little work by plantiflexors or hip moments

22. S2 Moments – hip-ankle strategy Figure 5. Flexor/extensor m oments of the ankle, knee and hip joints (Subject 2). hip and knee flexors and extensors are involved ankle plantiflexors dominated throughout hip and knee flexors and extensors are involved ankle plantiflexors dominated throughout

23. S2 Powers – hip-ankle strategy Figure 6. Flexor/extensor powers of the ankle, knee and hip joints (Subject 2). hip flexors and plantiflexors of left side produced the majority of the positive work; right hip extensors assisted little work by knee moments hip flexors and plantiflexors of left side produced the majority of the positive work; right hip extensors assisted little work by knee moments

24. S3 Moments – whole leg strategy Figure 7. Flexor/extensor m oments of the ankle, knee and hip joints (Subject 3). similar to subject 2 but both sides produced equal magnitudes both sides were only slightly out of phase similar to subject 2 but both sides produced equal magnitudes both sides were only slightly out of phase

25. S3 Powers – whole leg strategy Figure 8. Flexor/extensor powers of the ankle, knee and hip joints (Subject 3). left knee flexors & extensors and plantiflexors provided most work with assistance from both hip flexors right knee extensors and plantiflexors provided negative work left knee flexors & extensors and plantiflexors provided most work with assistance from both hip flexors right knee extensors and plantiflexors provided negative work

26. Summary All subjects used the hip abductors to maintain hoop horizontal rotational equilibrium 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 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

27. Summary Agreement between dynamical systems theory and inverse dynamics/moment power analyses but in unpredictable ways 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) Care must be taken when averaging subjects together (can hide individual strategies) Kinematics alone cannot define causes of motion Kinematics alone cannot define causes of motion

28. Questions?