| The current state-of-the-art simulation motion platforms are based on parallel manipulators known as Gough-Stewart platforms or hexapods. These have limited motion range in both translational and angular senses, and are subject to singularities. An alternative novel kinematic architecture, the Atlas platform, has been developed at Carleton University. The Atlas platform achieves six degree of freedom motion by mounting the Atlas spherical platform on top of an XYZ translation platform. The Atlas rotational stage comprises a sphere manipulated by three omnidirectional wheels. Each wheel imparts a prescribed velocity to the sphere through friction enabling it to rotate about any desired axis with unlimited angular displacement. This thesis investigates four main issues including: unified and generalized kinematics of a sphere actuated by n omnidirectional wheels; the dynamics of a sphere actuated by omnidirectional wheels; vibration induced by omnidirectional wheels on an actuated sphere; and a comparison between classes of omnidirectional wheels in the context of the Atlas platform.;The kinematic model for the system was derived using a zero-slip approach yielding a basic Jacobian. The model was then generalized to include any number and type of omnidirectional wheels treating the various wheel designs as geometric classes. Results show non-negligible corrections in both magnitude and direction of the resulting angular motion of the sphere. The equations of motion for the system were obtained taking into account several non-rigid effects. The non-smooth shape of the wheels was taken as a positional input for vibration analysis. Comparison between omnidirectional wheel types was made from the standpoint of vibration and transmission efficiency, with mixed results, using a numerical integration program developed in Matlab. The program, developed with numerical simulation in mind, was then used to investigate the effects of various parameters on the behaviour of the platform. Thus, it is parameterized to enable further research on various design parameters. |
