Minimal step length necessary for recovery of forward balance loss with a single step

Although the boundary conditions necessary to trigger a step in reaction to a forward balance loss have been predicted in previous research, the relationship between minimal step length needed for balance recovery with this single step and the center of mass (COM) motion state (i.e., its position and velocity) remains unknown. The purpose of this paper was to present a theoretical framework within which the minimal step length needed for balance recovery can be estimated. We therefore developed a simplified four-segment sagittal model of human body stepping for balance recovery. The work-energy principle of the Newtonian mechanics was employed in the simulation to determine the amount of excess mechanical energy that can be absorbed as a function of step length and the corresponding eccentric joint work that can be generated in a single step. We found that an increase in initial forward velocity and a greater forward shift of the COM require a corresponding increase in the minimal step length needed for balance recovery. Furthermore, the minimal step length is also a function of the muscle strength at the ankle: the lower the muscle strength, the greater the minimal step length required. Our theoretical framework reduces the complexity associated with previous studies relying on forward dynamics and iterative optimization processes. This method may also be applied to study aspects of balance control such as the prevention of balance loss in the posterior or mediolateral direction.