A structural synthesis method for 3-DOF translational parallel manipulators avoided platform singularities

In this paper, a kind of analytical method, based on the theory of reciprocal screws, is presented for structural synthesis of 3-DOF translation parallel manipulators avoided platform singularities. Because all motion screws and constraints screws form a 6-order spatial screw system, given a system of wrenches of 3-order constraints, the corresponding 3-order motion screws are left. According to this idea, we assume the 3-order constraints are orthogonal, so wherever the platform gone, the order of constraints system will never be decreased. Thus, the singularities are avoided successfully. All feasible limbs that can be used for construction of translation platform avoided singularities are enumerated according to the type of constraints and the number of joints making up the limbs. Further, geometrical conditions for parallel manipulators to possess finite translation motion avoided platform singularities are presented. Several novel mechanisms that satisfy design requirements are sketched as examples.