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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

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kinetics of hula hooping an exploratory analysis

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
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
previous research
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; 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
purpose
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
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

inverse dynamics
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
First divide limb into segments

Make free body diagrams (FBD) of each segment

add all known forces to fbd
Add all known forces to FBD
  • Weight
  • Ground reaction force
apply newton euler laws of motion to terminal segment
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 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 with next segment in chain or begin up another limb

Repeat for thigh segment to obtain hip forces and moments

moment power
Moment Power
  • product of joint angular velocity (w) and net moment of force (M) at same joint

PM= Mw

  • usually caused by muscle contractions especially when motion does not reach ends of range of motion
results
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
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
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 powers1
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
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 strategy1
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
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
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
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
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
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
summary1
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