Worm-like motion enabled by changing the position of mass center in the anisotropic environment

Abstract

The directional motion of a continuous worm induced by travelling the mass center of its body is studied in this paper. To this end, a new locomotion gait is constructed to derive the condition that the worm can move forward in one period. The interaction force between the worm body and environment is an anisotropic dry friction. The governing equation describing worm-like motion is firstly considered as a quasi-static case for a slow actuation history or for a larger friction. Then the solution of this equation is derived based on the specific form of the tension and its continuous distribution along the worm body. Furthermore, through the method of piecewise analysis of the motion, the expressions of the tension and the displacement along its body in each stage are specifically calculated. The net displacement over one period is further obtained. As a result, the condition that the directed motion of the worm can be effectively achieved. The results show that the worm can keep the body length unchanged by means of the given locomotion gait during the motion process.