A rolling contact joint is formed when two adjacent links roll without slipover each other. When the rolling profiles are circular, the joint can be physically realized by a pair of revolute joints coupled by gears or cables. In this paper, we investigate the forward, inverse, and rate kinematics of a spatial three degree-of-freedom serial chain with rolling contact joints that have equal circular profiles. We show analytically and geometrically that there are 32 inverse kinematic solutions. Singularities occur whenever the point of interest on the end effector lies on either of two planes defined by the lines of contact between the joints.

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