Locomotion analysis of a vibration-driven system with three acceleration-controlled internal masses

The controlled motion of a rigid body in the horizontal plane is investigated in this article. Three internal and acceleration-controlled masses are used to actuate the system. Dry friction acting between the system and the plane is isotropic. The dynamics of two basic motions of the system, that is, rectilinear and rotary motions, are first studied. Then by combining these two basic types of motions, planar locomotion of the system is constructed. Two typical planar trajectories of the system, that is, oblique lines and curve lines, are proposed and both approached with folding lines. The slope of the oblique lines and the curvature of the curves can be adjusted by varying the drive parameters, and the planar locomotion is thus controlled. To achieve a maximum average velocity, the drive parameters are optimized.