Manuscript : Stable Running with Segmented Legs ∗ †

In human and animal running spring-like leg behavior is found. In a spring-mass model, running proves to be self-stable in terms of external perturbations or variations in leg properties (e.g. landing angle). However, biological limbs are not made of springs but, rather, consist of segments where springlike behavior can be localized at joint level. Here, we use a two-segment leg model to investigate the effects of leg compliance originating from joint level on running stability. Due to leg geometry a nonlinear relationship between leg force and leg compression is found. In contrast to the linear leg spring, the segmented leg is capable of reducing the minimum speed for self-stable running from 3.5 m/s in the spring-mass model to 1.5 m/s for almost straight joint configurations which is below the preferred transition speed from human walking to running (≈ 2 m/s). At moderate speeds the tolerated range of landing angle is largely increased (17 degrees at 5 m/s) compared to the linear leg spring model (2 degrees). However, for fast running an increase of joint stiffness is required to compensate the mechanical disadvantage of larger leg compression. This could be achieved by nonlinear springs enhancing joint stiffness in fast running.