Mechanical Work Performance Constraints and Timing Govern Human Walking: A Modified Inverted Pendulum Model for Single Support

Human walking is often considered an inverted pendulum during single support, suggesting conservative dynamics. Gait consists of discrete steps connected by mechanically costly transitions. We examine how step length, walking speed, and work capacity jointly constrain walking mechanics. Using a powered simple walking model, minimum speed required to complete a step of given length is derived based on gravitational work; below this threshold, forward progression becomes mechanically infeasible, and the next heel-strike occurs early, producing shorter steps. Comparisons with empirical step length-speed relationships show that humans walk at higher speeds and require greater push-off work, indicating energy dissipation. We extend pendular dynamics by incorporating hip torque, a linearized axial force model, and muscle intervention. This framework reproduces key GRF features, including the M-shaped profile, without prescribing force trajectories a priori. Fitted parameters suggest reduced average loading (CBaseline < 1), active mid-stance unloading (Am < 0), and narrowly timed muscle action (small{sigma} m). Parameter studies show that increasing step length or speed increases transition work and peak forces, while hip torque timing indicates mechanical cost is minimized when energy modulation occurs after mid-stance. These findings indicate that preferred walking speed emerges from feasibility and work-capacity constraints, not energetic optimality alone.