Leg stiffness increases with gait speed to maximize propulsion energy during push - off

Compliant walking models have been used to account for the gait dynamics associated with compliant lower limbs [1, 2], and leg compliance has been quantified as a form of vertical lower limb stiffness [3]. However, the vertical stiffness of the lower limb has been defined by the ratio of the force change to the displacement change based on a formulation of Kvert ≈ ΔF/Δx without considering a full dynamic equation, , thus has a limited ability to represent gait dynamics. As a system parameter, the stiffness of a compliant walking model determines the system characteristics, such as the gait cycle period and the amplitude ratio of center of mass (CoM) oscillations to an external force. Therefore, quantification of the leg stiffness of a compliant walking model and the change in stiffness at different gait speeds would allow a better understanding of the contributions of spring-like leg behavior to gait dynamics. In this study, we calculated the effective leg stiffness of human subjects walking at four different speeds by simulating a damped compliant walking model that was slightly modified from existing compliant walking models [1, 2]. To examine correlations between leg stiffness and the oscillatory behavior of the CoM during the single support phase, the damped natural frequency of the single compliant leg was compared with the duration of the single support phase. To interpret the change in leg stiffness with gait speed from an energetic perspective, the theoretical leg stiffness that maximized the elastic energy stored in the compliant leg at the end of the single support phase was calculated as a function of leg stiffness and gait speed and was then compared with human leg stiffness data.