Motivated by experimental studies of insects, we develop a three-degree-of-freedom, energetically conservative, rigid body model with a pair of elastic legs in intermittent contact with the ground. The resulting piecewise-holonomic mechanical system exhibits periodic gaits whose neutral and asymptotic stability characteristics are due to intermittent foot contact, and are largely determined by geometrical criteria. We study how dynamics depend on physical parameters such as mass, moment of inertia, leg length, leg stiffness, and leg touchdown angle. We develop exact and approximate scaling relations that predict gait scaling in response to individual parameter changes, and suggest that the model is relevant to the understanding of locomotion dynamics across species.

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