Investigation of the relationship between steps required to stop and propulsive force using simple walking models

To prevent falls in the elderly, it is essential to evaluate their gait stability and identify factors that negatively affect it. Although one of the probable factors is a decrease in propulsive force of walking, the relationship between the force and the gait stability has not been fully clarified. To this end, two simple walking models were used to investigate the relationship between the propulsive force and the number of steps required to stop, denoted N. N was calculated as the number of steps required for the rimless wheel to stop and was treated as a variable which is an indirect indicator of stability. A lower N corresponds to the gait being closer to a stopped state. The propulsive force was calculated using the push-off impulse applied to the simplest walking model during the step-to-step transition. To account for the effects of the double support phase in human walking, the gravitational impulse, which is the integral of the body weight (gravitational force) over the double support time, was applied to the step-to-step transition equation of the models. The models revealed that the propulsive force is reduced by two factors: the reduction in step length and the reduction in walking speed. In the former, N increases; in the latter, N decreases. The former is consistent with previous experimental results on human gait, whereas the latter has not been experimentally investigated. These results may provide important insights in clarifying the relationship between the stability and the propulsive force in human gait.