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Fig. 1. A simple model demonstrates how a rolling foot can affect walking energetics. (A) Modeling the legs as pendulums supporting the body center of mass (COM), a step can be produced by passive limb dynamics with no energy input (McGeer, 1990a). Work is required, however, in the step-to-step transition to redirect the COM velocity. This can be accomplished with positive push-off work performed by the trailing leg, and negative collision work by the leading leg (Kuo, 2002). These leg actions redirect the pre-transition COM velocity v_pre to a post-transition velocity v_post. For point feet, the net directional change in velocity is equal to the angle between the legs, 2. (B) A model with arc feet applies collision at the heel of the leading leg, and push-off at the toe of the trailing leg. This reduces the directional change in COM velocity and therefore the step-to-step transition work. (C) COM velocity change may be understood geometrically. The pre-transition velocity v_pre is directed perpendicular to the line from the trailing leg's rolling point of ground contact to the COM. Push-off, directed along this line (angle /2 from vertical), causes a change in velocity (v_mid=v_pre+v_push-off). A periodic gait is achieved if push-off and collision velocity changes (v_push-off and v_collision, respectively) are of the same magnitude, so that v_post is equal in magnitude to v_pre but directed according to rolling of the leading leg. Work is proportional to the square of each velocity change. As the arc foot radius (, defined as a fraction of leg length L) increases, less step-to-step transition work is needed. There is no redirection of COM velocity for a radius equal to leg length, =1.

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