Back-bending in the sagittal plane is common in many animals during legged locomotion and could be useful for robots. However, to our knowledge, there exists no analytical mechanistic model of sagittal-plane back bending legged locomotion of quadrupeds. Such a mechanistic model and knowledge derived from it is expected to enable direct analysis and insight into back bending locomotion and can be applied to the study of biomechanics or the design of robots. Here a whole-body mechanistic model is developed and governing equations of motion are derived to provide insight into the mathematical structure of the system dynamics. The model is energy conserving, consisting of massless elastic legs pinned to two body segments. The two body segments are pin-joined together with a rotational spring. The massless legs are returned to a resting angle relative to the body during swing phase. We discover: 1) Whole-body configuration variables simplify the resulting equations of motion. 2) The sagittal-plane back-bending two-segment model of legged locomotion yields stable periodic gaits.

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