Patterns of Selection of Human Movements III: Energy Efficiency,   Mechanical Advantage, and Walking Gait
  Human movements are physical processes combining the classical mechanics of the human body moving in space and the biomechanics of the muscles generating the forces acting on the body under sophisticated sensory-motor control. One way to characterize movement performance is through measures of energy efficiency that relate the mechanical energy of the body and metabolic energy expended by the muscles. We expect the practical utility of such measures to be greater when human subjects execute movements that maximize energy efficiency. We therefore seek to understand if and when subjects select movements with that maximizing energy efficiency. We proceed using a model-based approach to describe movements which perform a task requiring the body to add or remove external mechanical work to or from an object. We use the specific example of walking gaits doing external mechanical work by pulling a cart, and estimate the relationship between the avg. walking speed and avg. step length. In the limit where no external work is done, we find that the estimated maximum energy efficiency walking gait is much slower than the walking gaits healthy adults typically select. We then modify the situation of the walking gait by introducing an idealized mechanical device that creates an adjustable mechanical advantage. The walking gaits that maximize the energy efficiency using the optimal mechanical advantage are again much slower than the walking gaits healthy adults typically select. We finally modify the situation so that the avg. walking speed is fixed and derive the pattern of the avg. step length and mechanical advantage that maximize energy efficiency. 
Stuart Hagler
q-bio.QM