Body flexibility effects on foot loading in quadruped bounding based on a simple analytical model

Abstract

Body flexibility plays an important role in the bounding gait of quadruped animals. In a previous study, we investigated the effects of body flexibility on foot loading by comparing two different physical models, with and without a flexible body-joint. Testing both models with equal mechanical energy revealed two conflicting results: Body flexibility reduced the maximum ground reaction force, but a stiffer body exhibited a smaller maximum ground reaction force than a highly flexible body. Because of the complex nature of the model dynamics, the mechanisms underlying these results are unclear. In the current study, we used a simplified analytical model by assuming physical constraints on our previous model to clarify the dynamic roles of body flexibility, particularly regarding foot loading. Approximate periodic solutions were derived by linearization of the governing equations and provide an explanation for our conflicting results. Furthermore, we discussed the biological relevance of our findings using a comparison of our analytical results with observations of movement in cheetahs. Our findings will not only improve the understanding of motor control mechanisms for fast locomotion in quadruped animals, but also provide a guiding principle for the mechanical and control design of legged robots capable of fast locomotion.