Dynamic Analysis of Rectilinear Motion of a Self-Propelling Disk With Unbalance Masses

Abstract

This paper investigates the dynamics of a rolling disk with three unbalance masses that can slide along radial spokes equispaced in angular orientation. The objective is to design trajectories for the masses that satisfy physical constraints and enable the disk to accelerate or move with constant velocity. The disk is designed to remain vertically upright and is constrained to move along a straight line. We design trajectories for constant acceleration, first using a static model, and then through detailed analysis using a dynamic model. The analysis based on the dynamic model considers two separate cases; one where the potential energy of the system is conserved, and the other where it continually varies. Whereas trajectories conserving potential energy are quite similar to those obtained from the static model, the variable potential energy trajectories are the most general. A number of observations related to the system center-of-mass are made with respect to both trajectories. Following the strategy for constant acceleration maneuvers, we give a simple approach to tracking an acceleration profile and provide some simulation results.