Supporting the design process for running biped robots, analytical models are presented for two aspects of running: the duty factor (DF) of the gait, and the stiffness value of the leg. For a given running speed, an optimal DF exists that minimizes the energy expenditure. We present a formula for the optimal DF based on a model of the energetics, and the results are compared to both human data and simulation results. In addition, a model is presented for the stiffness value of the leg as a function of the physical properties, speed, and DF. The
Gait Resonance Point
is proposed as a design target for compliant running. At this point, the gait matches the spring resonance and the stiffness value becomes independent of the DF.