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. Hula Hoop

3. 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
-The physical basis of hula hooping is the conservation of angular momentum.
-The performer must exert small, but carefully initiated impulses on the interior periphery of the hoop.
-In its most basic form, this is accomplished with the hips.
-Simultaneously, a small vertical component of the impulse must be directed vertically, to oppose the force of gravity.
-Assuming that these conditions have been met, the hoop maintains stable oscillations; a state of dynamic equilibrium.

4. Previous Research Balasubramaniam and Turvey (2004):
95% variance accommodated by just two modes
in the large hoop condition, the first mode was a hip dynamical system; fore-aft motion of the hips maintained rotational motion
the second eigenvalue was a knee dynamical system
larger hoop size required more emphasis on the role of the knees to maintain motion of the vertical regulatory component

5. 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?

6. Methods Flow Chart three 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
The hula hoops (Wham-O Corporation, Torrence, CA) used in the experimental protocol were 80.4 cm (large) and 70.4 cm (small) in diameter and weighed approximately 200 g and 184 g, respectively.
Movements were recorded using a five camera Vicon (Lake Forest, CA) MX13 three-dimensional motion analysis system.
Reflective markers were positioned bilaterally on the participants’ limbs at the hallux, 1st and 5th metatarsophalangeal joints, calcaneus, medial and lateral malleoli, shank, medial and lateral femoral condyles, thigh, greater trochanter, and the anterior and posterior superior iliac spines, according to the uOttawa marker set.
Resonance frequency was varied by
The digitized marker coordinates were filtered with a 4th order Butterworth low-pass digital filter with a 4 Hz cut-off, due to the low frequency content of the data.
Joint centre estimates were performed according to the joint coordinate system (JCS) outlined by Grood and Suntay (1983), which were subsequently used to derive segmental kinematics.
The analog force platform signals were also filtered with a fourth order Butterworth low-pass digital filter with a cut-off frequency of 10 Hz. The joint and segment kinematics and force platform signals were then integrated into a standard link-segment model (Bresler & Frankel, 1950) used to calculate the joint angular velocities (rad/s), joint moments (Nm/kg) and moment powers (W/kg) at the ankle, knee and hip of both the right and left sides of the body.
Separate moment and power analyses were carried out for flexion/extension, abduction/adduction and axial rotations moments and moment powers for each subject. The results were then plotted and compared amongst subjects, forming a three participant, single-subject experimental design.
Visual3D v3.79:
7 segment model
Inverse dynamics and moment powers

7. Results
each figure shows three repetitions averaged across five trials (error bars are ± 1 SD)
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
-There was substantial involvement of the hip abductors in the skill of hula hooping.
-Since this was the case for all subjects, under all experimental conditions (hoop sizes and speeds), an exemplar figure was chosen from Subject 1 to be representative of the pattern observed for all subjects.
-Figure 1 exhibited repetitive activation of the hip abductors followed by a brief adductor burst while the contralateral side responded with opposing moments. In other words, the pattern of activation of the left and right side moments had them recruited 180 degrees out-of-phase with each other. For the subject illustrated, the right abductors are shown doing positive work at the onset of the motion, thus, the hoop was spun in a clockwise direction (toward the left hip). These results agree with those previously reported by Balasubramaniam and Turvey (2004), where the side-to-side motion of the hip, which represented the first eigenvalue generated by the K-L transformation accounted for the most variance and thus, was concluded to be the most important motion in the skill of hula hooping.

8. 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
-There was substantial involvement of the hip abductors in the skill of hula hooping.
-Since this was the case for all subjects, under all experimental conditions (hoop sizes and speeds), an exemplar figure was chosen from Subject 1 to be representative of the pattern observed for all subjects.
-Figure 1 exhibited repetitive activation of the hip abductors followed by a brief adductor burst while the contralateral side responded with opposing moments. In other words, the pattern of activation of the left and right side moments had them recruited 180 degrees out-of-phase with each other. For the subject illustrated, the right abductors are shown doing positive work at the onset of the motion, thus, the hoop was spun in a clockwise direction (toward the left hip). These results agree with those previously reported by Balasubramaniam and Turvey (2004), where the side-to-side motion of the hip, which represented the first eigenvalue generated by the K-L transformation accounted for the most variance and thus, was concluded to be the most important motion in the skill of hula hooping.
Figure 1. Ab/adductor moments of the ankle, knee and hip joints (Subject 1).

9. 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).

10. 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).

11. 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).

12. 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 2 shows Subject 1’s angular velocities, moments and powers during the flexion/extension of the ankle, hip and knee during hula hooping. This subject performed little work at the ankle and hip to sustain the hoop oscillations; instead she relied almost exclusively on the extensors of the knee to provide the necessary vertical impulses to prevent the hoop from descending gradually to the ground. Figure 2 shows that this subject produced net positive work by the extensors of the left leg and negative work by the extensors of the right leg in an asymmetrical pattern. Thus, only a brief vertical impulse applied once per revolution was needed to maintain vertical equilibrium of the hoop whereas horizontal equilibrium required impulses twice per revolution—one from the left hip abductors and one from the right.
Figure 4. Flexor/extensor powers of the ankle, hip and knee (Subject 1).

13. 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).

14. 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 3 shows the angular velocities, moments and powers about the joints of the lower extremities during flexion and extension for Subject 2.
-This subject used a different mechanism for providing vertical stability of the hula hoop.
-She applied a net plantiflexor moment at the left ankle that performed positive work, while there was a small burst of negative work performed by the plantiflexors of the right ankle. Thus, she regulated and sustained vertical displacement of the hoop using her left ankle plantiflexors while the right plantiflexors were essentially inactive.
In the case of subject 2 the involvement of the flexors and extensors of the hips was also important in sustaining oscillations of the hoop. The flexors and extensors alternated between concentric and eccentric work, performing net positive work by the right hip moment and both positive and negative work by the left hip moment. The hip moment performs its positive flexor work simultaneous with the left plantiflexor’s moment presumably to allow for the hip to move vertically but maintain the upper body’s vertical position. In other words, extension at the ankle can cause upward displacement of the entire body but by flexing at the hip the upper body remains stationary.
-Another finding that warrants mention is that the activations of both hip moments were concurrent, a strategy that was previously proposed by Balasubramaniam and Turvey (2004) as being paramount in successful hula hooping attempts. Presumably, simultaneously activating the hip flexors prevents side-to-side motion that could unnecessarily perturb the vestibular mechanism. In summary, Subject 2 utilized a strategy that incorporated the left ankle plantiflexors and both hip flexors in maintaining hoop oscillations, while there was little involvement from the knee moments of force.
Figure 6. Flexor/extensor powers of the ankle, knee and hip joints (Subject 2).

15. 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).

16. 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
Furthermore, moment power analysis revealed that the plantiflexors of the left ankle performed net positive work, whereas those of the right ankle performed net negative work.
-The extensors of the left knee performed positive work throughout the trials while those of the right knee performed predominantly negative work. On the other hand, both hip flexors and extensors contributed bursts of positive and negative work but in amounts intermediate as the compared to the other two subjects.
-Subject 3 adopted a more balanced strategy that incorporated the plantiflexors of the ankle, the extensors of the knee and the flexors and extensors of the hip.
Figure 8. Flexor/extensor powers of the ankle, knee and hip joints (Subject 3).

17. Summary
All subjects used the hip abductors to maintain hoop 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
Agreement between dynamical systems theory and inverse dynamics/moment power analyses but in unpredictable ways
Care must be taken when averaging subjects together
-As demonstrated in the figures that accompany this discussion the skill of hula hooping is an entirely complex and variable skill.
-For instance, although all subjects experienced the same experimental conditions they adopted three different strategies in maintaining oscillations of the hoop. For instance, subject 1 relied almost exclusively on the extensors of the knee, the strategy previously described by Balasubramaniam and Turvey (2004), who found by means of the dynamical systems theory that a smaller hoop led to increased involvement of the knee to adjust the vertical displacement of the hoop. However, the balanced strategy adopted by subject 3 and the ankle-hip strategy adopted by subject 2 fail to agree with the results previously reported in the literature. In fact, rather than demonstrating increased involvement of the moments of the knee, subject 2 adopted a strategy that required little work from the knee extensors. However, due to the linked nature of the lower extremity the plantiflexors of the ankle permitted the necessary extension of the lower extremity.
-Conclusions:
Despite the different conclusions drawn by the dynamical systems theory and an inverse dynamics analysis regarding the involvement of the flexors and extensors in hula hooping, the two theories are in agreement with respect to the involvement of the abductors of the hip. For instance, this paper demonstrated that all subjects consistently relied on the abductors of both hips to sustain hoop oscillations. Similarly, Balasubramaniam and Turvey (2004) demonstrated that the side-to-side motion of the hip was the primary eigenvalue that consistently accounted for the greatest proportion of the variance of the K-L transformation. As a result, more research is needed to investigate the involvement of potential mediating variables such as segment proportions, for example, before further developing our understanding of this complex skill.

18. Questions?
-As demonstrated in the figures that accompany this discussion the skill of hula hooping is an entirely complex and variable skill.
-For instance, although all subjects experienced the same experimental conditions they adopted three different strategies in maintaining oscillations of the hoop. For instance, subject 1 relied almost exclusively on the extensors of the knee, the strategy previously described by Balasubramaniam and Turvey (2004), who found by means of the dynamical systems theory that a smaller hoop led to increased involvement of the knee to adjust the vertical displacement of the hoop. However, the balanced strategy adopted by subject 3 and the ankle-hip strategy adopted by subject 2 fail to agree with the results previously reported in the literature. In fact, rather than demonstrating increased involvement of the moments of the knee, subject 2 adopted a strategy that required little work from the knee extensors. However, due to the linked nature of the lower extremity the plantiflexors of the ankle permitted the necessary extension of the lower extremity.
-Conclusions:
Despite the different conclusions drawn by the dynamical systems theory and an inverse dynamics analysis regarding the involvement of the flexors and extensors in hula hooping, the two theories are in agreement with respect to the involvement of the abductors of the hip. For instance, this paper demonstrated that all subjects consistently relied on the abductors of both hips to sustain hoop oscillations. Similarly, Balasubramaniam and Turvey (2004) demonstrated that the side-to-side motion of the hip was the primary eigenvalue that consistently accounted for the greatest proportion of the variance of the K-L transformation. As a result, more research is needed to investigate the involvement of potential mediating variables such as segment proportions, for example, before further developing our understanding of this complex skill.