Kinematic condition analysis of three-DOF pure translational parallel manipulators

Several 3-DOF pure translational parallel manipulators have been reported recently. However, kinematic conditions of such translational parallel manipulators have not been studied deeply. Most previously reported translational parallel manipulators were analyzed by considering constraints on the motion of an independent leg. In addition to the constraints of independent legs, the effect of the constraints on an overall mechanism are analyzed in this paper. The overall kinematic constraints are explained by introducing the restriction of motion, which is a constraint that prohibits a manipulator from moving in a certain region or direction, instantaneously. By introducing it, kinematic constraints can be embedded explicitly in the formulation of rate kinematics, and by analyzing it, constraints for a desired motion can be found. This paper derives constraints for pure translational motion in a systematic way. Necessary and sufficient conditions are suggested and several translational parallel manipulators with their kinematic features are provided.