Workspace boundaries of in-parallel manipulator systems

An important design consideration in an in-parallel system is the reachable workspace of a reference point chosen on the end-effector. When a point is at its workspace boundary, it does not have a velocity component along the outward normal to the boundary. Starting from this simple intuition, the author determines the configurations of an in-parallel system in which the velocity of a reference point satisfies this property. Among these configurations are also the ones in which the reference point is at the boundary of the workspace. In this paper, the in-parallel systems are analyzed based on instantaneous properties of series chains as derived from the theory of screw systems. The conditions of existence of the boundary configurations are given in terms of conditions on a special screw system associated with the end-effector.<>