A general modification to the kinematics model of the Atlas spherical orientation platform is presented. The Jacobian is augmented to include the effects of dual row omnidirectional wheels (i.e., two offset races of free spinning rollers). The results indicate that ignoring the offset between races can result in a significant error in the evaluation of the sphere angular velocity vector in response to a prescribed set of omnidirectional wheel velocities. The methodology presented in this paper is general and can be applied to the analysis of other mechanical systems employing dual row omnidirectional wheels.

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Mechanism and Machine Theory
Department of Mechanical and Aerospace Engineering

Weiss, A. (A.), Langlois, R.G, & Hayes, M.J.D. (2009). The effects of dual row omnidirectional wheels on the kinematics of the Atlas spherical motion platform. Mechanism and Machine Theory, 44(2), 349–358. doi:10.1016/j.mechmachtheory.2008.03.013