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 through detailed analysis using a dynamic model. The analysis 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 limacons, the variable potential energy trajectories are the most general and allow greater acceleration. Following the strategy for constant acceleration maneuvers, we give a simple approach to tracking an acceleration profile and provide simulation results.
