Mechanical Work Rate Minimization and Freely Chosen Stride Frequency of Human Walking: A Mathematical Model

The interplay between the work done to move the body centre of mass with respect to the environment (external work) and the work done to move the limbs with respect to the body (internal work) has been shown experimentally partially to determine the freely chosen stride frequency during walking. A mathematical model that estimates the two components of the mechanical work is proposed. The model, according to the criterion of work rate minimization (both positive and positive plus negative), is able to predict the natural stride frequency as a function of the average progression speed. The adequacy of the model and the validity of the assumptions have been checked against measurements of natural stride frequency in 11 subjects walking on a treadmill at several speeds (range 1–3 m s-1). Comparison with theoretical predictions shows good agreement with the minimization of positive work rate at low speeds, while at high speeds the stride frequency is better explained by the model for minimum positive plus negative work rate.