The singularity conditions of three-revolute-joint serial chain manipulators are investigated by considering the motion of an arbitrary point on a terminal link. A distinction is made between singular configurations (every point on the terminal link is singular) and singular surfaces (a chosen point on the terminal link lies on a singular surface). Of particular interest is a class of 3R manipulators—each manipulator within this class forms a third-order screw system. We outline the structural requirements for this 3R class, and then determine the singularity conditions for several cases. For several manipulators within this 3R class, we describe a strategy to develop four-revolute-joint kinematic modules for singularity-free movement with three Cartesian freedoms. The algorithm to control the kinematic modules is simple and can be implemented in real-time.

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