Type synthesis and kinematics analysis of parallel manipulators with equivalent composite universal joints

Several novel parallel manipulators (PMs) with equivalent composite universal joints Ue are synthesized and their kinematics is studied systematically in this paper. First, the 12 novel PMs with Ue are synthesized, and their degrees of freedom are calculated. Second, the structure and merits of the composite limb with Ue for constructing the PMs with Ue are analyzed; the unified formulas are derived for solving the sub-Jacobian matrix, the sub-Hessian matrix, the angular velocity and the angular acceleration of the composite limb with Ue. Third, the formulas are derived for solving the Jacobian matrix and output velocity, the Hessian matrix and output acceleration of the moving platforms of the 10 novel PMs with Ue. Finally, a 5-DoF PM with 2Ue in the 12 synthesized PMs with Ue is illustrated for solving the kinematics of the PMs with Ue; its reachable workspace is constructed for representing merits of the PMs with Ue. The theoretical kinematics solutions are verified by the simulation solution of the simulation mechanism of the 5-DoF PM with 2Ue.