| This thesis investigates the dynamics of self-propelling mechanisms with rolling constraints. We first consider the dynamics of a vertically upright disk, rolling rectilinearly with three eccentric masses. We design trajectories of the masses for constant acceleration, first using a static model, and then using a dynamic model. The dynamic model considers constant and varying potential energy cases separately. Trajectories conserving potential energy are quite similar to those obtained from the static model. We present optimal approaches to tracking an acceleration profile and provide simulation results. We generalize the problem by considering self-propelling mechanisms for a rolling sphere. We study a four mass extension of the disk, with tetrahedral arrangement of spokes, followed by a three mass mechanism with skewed spokes, perpendicular to each other. For both mechanisms, we conclude from simulations and observations that numerical solution of the dynamic equations cannot give bounded trajectories. A static model however gives bounded trajectories for reasonable magnitudes of accelerations. A geometric criterion is developed for both mechanisms to check feasibility of an acceleration profile. Finally, we present a self-propelling mechanism that uses momentum wheels for propulsion. Although this mechanism is simple, the model is valid in the absence of external torque. Hence practical implementation may not be feasible. |
