Patterns of Selection of Human Movements IV: Energy Efficiency, Mechanical Advantage, and Asynchronous Arm-Cranking

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. The characterization of the performance of human movements is a problem with important applications in clinical and sports research. 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. Such a characterization provides information about the performance of a movement insofar as subjects select movements with the aim of maximizing the energy efficiency. We examine the case of the energy efficiency of asynchronous arm-cranking doing external mechanical work, that is, using the arms to turn an asynchronous arm-crank that performs external mechanical work. We construct a metabolic energy model and use it estimate how cranking may be performed with maximum energy efficiency, and recover the intuitive result that for larger external forces the crank-handles should be placed as far from the center of the crank as is comfortable for the subject to turn. We further examine mechanical advantage in asynchronous arm-cranking by constructing an idealized system that is driven by a crank and which involves an adjustable mechanical advantage, and analyze the case in which the avg. frequency is fixed and derive the mechanical advantages that maximize energy efficiency.