A Simple Model of Bipedal Walking Predicts the Preferred Speed–Step Length Relationship

TLDR

The cost of force divided by time reflects the recruitment of fast muscle fibers for large forces over short durations. The study uses a simple passive dynamic walking model with active powering to investigate humans’ preferred speed–step length relationship. The model tests metabolic costs comprising stance‑leg toe‑off mechanical work and swing‑leg oscillation forces. The preferred speed–step length relationship is best explained by minimizing swing‑leg force divided by time, with toe‑off mechanical work also contributing, whereas swing‑leg mechanical work alone is less influential.

Abstract

We used a simple model of passive dynamic walking, with the addition of active powering on level ground, to study the preferred relationship between speed and step length in humans. We tested several hypothetical metabolic costs, with one component proportional to the mechanical work associated with pushing off with the stance leg at toe-off, and another component associated with several possible costs of forcing oscillations of the swing leg. For this second component, a cost based on the amount of force needed to oscillate the leg divided by the time duration of that force predicts the preferred speed–step length relationship much better than other costs, such as the amount of mechanical work done in swinging the leg. The cost of force/time models the need to recruit fast muscle fibers for large forces at short durations. The actual mechanical work performed by muscles on the swing leg appears to be of relatively less importance, although it appears to be minimized by the use of short bursts of muscle activity in near-isometric conditions. The combined minimization of toe-off mechanical work and force divided by time predicts the preferred speed–step length relationship.