Wheel design optimization for locomotion in granular beds using resistive force theory

Abstract

Inspired by hypotheses of Resistive Force Theory, a general dimensionless form for granular locomotion has been discovered, which instructs how to scale size, mass, and driving parameters to relate dynamic behaviors of different locomotors in the same granular media. These scalings are experimentally confirmed with wheel pairs of various shapes and sizes under many driving conditions in a common sand bed. How the relations may be derived alternatively by assuming Coulombic yielding and how the relations can be augmented to predict wheel performance in different ambient gravities is also explained. Next, a rotating-flap wheel that consists of a central hub connected to five flaps that can actuate to a certain angle open was designed, built, and tested. Experiments were completed on the wheel by performing a series of tests varying the angle of the flaps and the drawbar force the wheel tows. The results indicate a trend toward higher velocities and powers at larger flap angles. Conversely, with larger drawbar forces the trend indicates lower velocities and higher powers. A MATLAB simulation was also created to model granular locomotion with different wheel shapes, including the rotating-flap wheel. Finally, future work extending the analysis of the rotating-flap wheel to encompass a "smart" wheel that is able to actuate given certain external conditions is discussed.