Influence of biological joint stiffness on running stability

It is well-known that SLIP model is one of the best and simplest abstractions describing the dynamics of hopping and running in animal and human locomotion. Nevertheless, spring-like leg behavior depends on the compliance of limb multiple joints in animal and human locomotion. Therefore, we investigate the influence of biological joint stiffness on running stability based on two-segment leg model. A nonlinear relationship between the virtual leg spring force and the virtual leg spring compression is found because of a nonlinear biological joint torque-angular displacement relationship of elastic two-segment leg. The functional relationship between the virtual leg spring force and the virtual leg spring compression is established, and then based on biological limbs maximum compression in fast running, we establish the equation for solving the radius of cable pulley. At high speed the tolerated minimum dimensionless reference stiffness in two-segment leg model is largely decreased (17 at 29 m s^-1, β₀=110°) compared with linear leg spring model (45). In fast locomotion, the two-segment leg model with biological joint stiffness can demonstrate outstanding performance for stable running.