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.

Excessive hip flexion torque to prioritize leg swings in the elderly is likely to be a factor that reduces their propulsive force and gait stability, but the mechanism is not clear. To understand the mechanism, we investigated how propulsive force, hip flexion torque, and margin of stability (MoS) change when only the hip spring stiffness is increased without changing the walking speed in the simple walking model, and verified whether the relationship holds in human walking. The results showed that at walking speeds between 0.50 and 1.75 m/s, increasing hip spring stiffness increased hip flexion torque and decreased the propulsive force and MoS in both the model and human walking. Furthermore, it was found that the increase in hip flexion torque was explained by the increase in spring stiffness, and the decreases in the propulsive force and MoS were explained by the increase in step frequency associated with the increase in spring stiffness. Therefore, the increase in hip flexion torque likely decreased the propulsive force and MoS, and this mechanism was explained by the intervening hip spring stiffness. Our findings may help in the control design of walking assistance devices, and in improving our understanding of elderly walking strategies.