Semi-analytical approach for analyzing walking load

In this paper, a bi-parametric perturbation method is proposed to solve the kinematic motions of the human walking load simulated by an inverted-pendulum model consisting of a mass point, spring limbs, and roller feet. In order to establish the kinematic motions of the first and second single- and double-support phases, the Lagrangian variation method is used. Given a set of model parameters, desired walking speed, and initial states, the perturbation solution is used to study the influences of roller radius, stiffness, impact angle, walking speed, and mass on the ground reaction forces (Fz and Fxy), step length, cadence, and duration time. The analytical results show that the peak values of Fz and Fxy are proportional to stiffness, impact angle, and walking speed, but inversely proportional to the roller radius.