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Wheel Walking™


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Head Carrying

Head carrying has been a common practice for a long time in human history throughout the world. Some women in Africa are able to carry produce baskets weighing as much as 70 percent of their body weight. The women can carry as much as 20 percent of their weight with no extra effort. Researchers were not able to explain the underlying mechanism.

Nepalese Porters

Porters are able to carry, on the average, loads almost equal to their body weight using an oversized basket (doko) and a strap on their head (naamlo). The strap runs underneath the doko and over the crown of the head. The study done by the team of Dr. Heglund showed the amazing energy efficiency of the Nepalese porters, but they were unable to show underlying mechanism of how to conserve energy while walking.

Wheel Definition and History

A wheel is a circular component rotating on an axial bearing. Wheels, in conjunction with axles, allow heavy objects to be moved easily. When it is used for transport application, a wheel reduces friction greatly by rolling. In order for wheels to rotate, an external force (torque) has to be applied about its axis. The external force (pushing or pulling) applied to wheels allows wheels to rotate. The invention of the spoke wheel allowed the construction of a swifter and lighter wheel.

Spoke Wheels

Only a small segment of wheel can touch the ground at a time. Humans and other animals including insects may be using this principle for efficient locomotion. If a human is using wheel-like locomotion while walking with bipedal gait, the human may be using each leg as a spoke of each wheel rotating about the hip joint and each foot as a segment of the wheel contacting with the ground. The rigidity of the legs can function like wheel-spokes, and the feet can provide traction on the ground while supporting and distributing the weight of the body.

The center of mass located just above and front of the hip joint will provide the rotational torque by force of gravity. Keeping the COM (center of mass) in position to provide torque energy over the hip joint will be important for movement of wheel-like locomotion. Swing movement of the legs with lifting of leg mass will provide the necessary momentum for COM creating wheel-like locomotion of the body.

Ideally, wheel-like locomotion will require minimal collision of swing leg upon landing. And wheel-like locomotion will require proper friction on the foot of stance leg for traction while torque energy is applied with movement of swing leg and its effect on COM trajectory. Needed energy for walking and running can be reduced to the energy for lifting and forward-moving of the swing-leg while maintaining rigidity of the stance-leg with traction on the ground. The lifting and forward-swing of the leg will provide maintenance of torque necessary for locomotion. Also, mechanisms of energy-efficient leg extension during stance phase need to be explored.

On different terrains on Earth, bipedal gait with wheel-like locomotion will be a very efficient way of overcoming obstacles (eg, stairs)-unlike the regular wheel.

Six Determinants of Gait Model

In an article published in 1953, Saunders et al presented an analytical paper on human locomotion (THE MAJOR DETERMINANTS IN NORMAL AND PATHOLOGICAL GAIT, J. B. dec. M. Saunders ; Verne T. Inman ; Howard D. Eberhart, J Bone Joint Surg Am, 1953 Jul;35(3):543-558). In the theory, they described that the economical way of movement of the body is through achievement of the sinusoidal pathway of low amplitude. They used a compass model and explained the major determinants of gait to minimize vertical displacement of COM and gradual deflection through multiple mechanism. They posited that the inability to maintain one or more of the major determinant mechanisms will an cause increase of energetic cost. They also used some of pathological gait patterns to explain the theory.

Some scholars (Dynamic Principles of Gait and Their Clinical Implications Arthur D. Kuo and J. Maxwell Donelan Physical Therapy February 2010 vol. 90 no. 2 157-174) interpreted that the theory was applying strict level trajectory of COM during locomotion. Certainly, human body structure is not compatible for strict level trajectory of COM during walking. Also, artificial application of the strict level trajectory of COM during walking will be costly from being off the preferred (normal) gait (Arch Phys Med Rehabil. 2009 Jan;90(1):136-44 Metabolic and mechanical energy costs of reducing vertical center of mass movement during gait. Gordon KE, Ferris DP, Kuo AD)

It appears that the theory was a good descriptive study based on excellent observation but was not able to provide the importance of swing leg action on change of COM trajectory. Also, they were not able to provide any insight into the mechanism for running.

Inverted Pendulum Model

In this theory, walking has been modeled as an inverted pendulum system. The stance leg acts as an inverted pendulum. The stance leg is considered as a weightless leg. The COM vaults over the weight-less rigid stance limb. Potential energy is exchanged into kinetic energy. In this model, the collision force upon heel-strike helps redirect the path of COM. The straight and rigid leg during stance phase helps humans save energy by using skeletal systems and saving muscle force to support body weight.

This model still does not take into account the practical weight of legs during locomotion. Also, the reverse pendulum analogy does not apply for double-support phase when the pendulum cannot swing (Dynamic Principles of Gait and Their Clinical Implications Arthur D. Kuo and J. Maxwell Donelan Physical Therapy February 2010 vol. 90 no. 2 157-174). And energy for pendulum movement of the swing leg is not considered in the model. Just simple passive motion with little energy cost has been viewed for leg swing. But in some studies, researchers found that the energy cost of swing leg seems to be important (the energetic costs of trunk and distal-limb loading during walking and running in guinea fowl Numida meleagris/ DJ Ellerby, et al: the Journal of Experimental Biology 209, 2064-2075, 2006). BR Umberger found that, at a typical walking speed, 29% of total muscular cost was used for leg swing (Umberger B. R. (2010). Stance and swing phase costs in human walking. J. R. Soc. Interface 7, 1329–1340 10.1098). These findings of high energy cost for leg swing is not explained in inverted pendulum model. Inverted pendulum model is also not well fitted to explain the running mechanism.

In a study by RR Neptune et al (Neptune RR, Zajac FE, Kautz SA. Muscle mechanical work requirements during normal walking: the energetic cost of raising the body’s center-of-mass is significant. J Biomech. 2004;37:817–25), the researchers found that the muscle energetic cost to raise the COM was significant. The significant muscle work to lift COM by extending knee and hip was not well explained by inverted pendulum model which implies straight leg in stance phase.

Dynamic Walking Model

Simple inverted pendulum model shows an economical way of walking but is not able to explain the cost of energy of walking. In the dynamic walking model, stance phase is based on the inverted pendulum model but collision energy loss of the leading leg works as negative energy for the COM pathway. This energy loss has to be compensated for by positive work which is done by the push-off of trailing leg. Push-off starting before collision was thought to help lower the cost of energy loss upon collision. Also, other positive muscle works and mechanisms have to be performed through the step-to-step transition.

In this model, cost of the active leg swing is considered to be roughly one third of the metabolic cost of walking. The rest is attributable to the cost of step-to-step transition. Various concepts including rigid feet with an arc functioning like a portion of a wheel are used in the model (Dynamic Principles of Gait and Their Clinical Implications Arthur D. Kuo and J. Maxwell Donelan Physical Therapy February 2010 vol. 90 no. 2 157-174) are used to show how humans are able to decrease the cost of step-to-step transition.

In this model, the negative work of the knee by flexion from collision and the positive work of the knee during extension to make a rigid structure during stance phase are not well explained.

Human legs functioning as Spoke Wheels

As discussed earlier, only a small segment of a wheel can touch the ground at a time. Humans and other animals including insects seem to be using this principle for efficient locomotion.

If a human is using wheel-like locomotion while walking on bipedal gait, the human may be using each leg as a spoke of a wheel rotating about the hip joint and each foot as a segment of the wheel contacting with the ground.

Rigidity of legs can function like wheel-spokes, and feet can provide traction on the ground while supporting and distributing the weight of body. The center of mass located just above and front of the hip joint will provide the rotational torque by force of gravity. Keeping the COM in position to provide torque energy over the hip joint will be important for movement of wheel-like locomotion. Swing movement of the legs with lifting of leg mass will provide the necessary momentum for COM, creating wheel-like locomotion of the body.

Ideally, wheel-like locomotion will require minimal collision of the swing leg upon landing. And wheel-like locomotion will require proper friction on the foot of stance leg for traction while torque energy is applied with movement of the swing leg and its effect on the COM trajectory.

Needed energy for walking and running can be simplified to the energy needed for lifting and forward movement of the swing-leg while maintaining rigidity of the stance-leg with traction on the ground. The lifting and forward-swing of the leg will provide maintenance of torque necessary for locomotion. Also, mechanisms of energy-efficient leg extension during stance phase need to be explored.

On different terrains on Earth, bipedal gait with wheel-like locomotion will be a very efficient way of overcoming obstacles (eg, stairs)-unlike the regular wheel.