This paper presents a general approach to the kinematics of an orientation motion platform utilizing a sphere actuated by omnidirectional wheels. The number and type of the omnidirectional wheels, as well as their position and orientation relative to the sphere are arbitrary, provided they are distinct. In this paper, the general kinematics are presented and illustrated by sample configurations with a range of omnidirectional wheel types and quantities. Moreover, no-slip conditions are identified, and the resulting expressions and their implications on the design of such a mechanical system are demonstrated by means of several benchmark examples.

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Keywords Kinematics, Omnidirectional wheels, Parallel manipulator
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Journal Journal of Mechanisms and Robotics
Weiss, A. (A.), Langlois, R.G, & Hayes, M.J.D. (2011). Unified treatment of the kinematic interface between a sphere and omnidirectional wheel actuators. Journal of Mechanisms and Robotics, 3(4). doi:10.1115/1.4004888