Two viewpoints on the unconstrained motion of parallel manipulators at or near singular configurations

At a singular configuration the end-effector of a parallel manipulator may become underconstrained, i.e. instantaneous motion may become possible. The unconstrained motion may be only instantaneous, or it can result in finite motion, also known as self-motion. This article presents two different approaches to analyze the potential for large motion at a singular configuration: (1) A necessary (but not sufficient) condition for self-motion is derived that assumes that the manipulator has perfect precision; (2) The unconstrained motion is analyzed based on finite clearance in the joints. Numerical results are presented and compared.