How toe spacing affects impact dynamics during passive "foot" intrusions into granular media

Although efficient locomotion on granular media is challenging for animals and robots, some "sand-specialist" lizards have evolved to run rapidly on sand. Preliminary results from a study of subsurface foot movement revealed that these species space their toes approximately 3-5 particle diameters (pd) apart during a step, whereas slower, non-sand-specialist lizards often use spacings outside of this range. This is especially interesting because simulations and experiments have found that two horizontal, parallel cylinders intruded into a granular medium experience maximum force when spaced approximately 3 pd apart. To understand how toe spacing influences the intrusion dynamics of lizard feet, we studied 3D printed models of a simplified 3-toed "foot" dropped vertically into poppy seeds. Models with toes spaced 1, 3, 5, and 7 pd apart were released so as to achieve 3 intrusion speeds in the range used by running lizards (n = 5 trials/condition). High speed (1069 fps) video and 2-axis impact force measurements allowed us to measure how the force, torque, and work exerted by the granular medium during intrusion depends on toe spacing and speed. We relate these findings to lessons for the design of both robotic and prosthetic feet intended to navigate complex terrain.