Abstract

A 1-cm coin vibrational motor fixed to the center of a 4-cm square foam platform moves rapidly across granular media at a speed of up to 30 cm/s or about 5 body lengths/s. Fast speeds are achieved with dimensionless acceleration number, similar to a Froude number, up to 50, allowing the light-weight 1.4 g mechanism to remain above the substrate, levitated and propelled by its kicks off the surface. The mechanism is low cost and moves across granular media without any external moving parts. With 2-s exposure, we photograph the trajectory of the mechanism with an LED fixed to the mechanism. Trajectories can exhibit period doubling phenomena similar to a ball bouncing on a vibrating table top. A two-dimensional robophysics model is developed to predict mechanism trajectories. We find that a vertical drag force is required in the model to match the height above the surface reached by the mechanism. We attribute the vertical drag force to suction from air flow below the mechanism base and through the granular substrate. Our numerical model suggests that horizontal speed is maximized when the mechanism is prevented from jumping high off the surface. In this way, the mechanism resembles a galloping or jumping animal whose body remains nearly at the same height above the ground during its gait. Our mechanism and model illustrate that speed and efficiency of light-weight hoppers on granular media can be affected by aerodynamics and substrate permeability.

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