Type Synthesis of Uncoupled Rotational Parallel Mechanisms with Two Degrees of Freedom

A new systematic method for type synthesis of uncoupled rotational parallel mechanisms with two degrees of freedom is presented in order to deal with the strong kinematic coupling of mechanisms obtained by the general method. Based on the actuation wrench screw theory, the mathematic model mapping the inputs and the outputs relationship of the uncoupled rotational parallel manipulators is set up. The relationship between the output motion characteristic of the rotational parallel mechanism and the actuation wrench screws exerted on the moving platform by the actuated joints is also analyzed. The forms of the actuation wrench screws and the corresponding actuated twist screws of the kinematic chains are determined in terms of the condition that the Jacobian matrix of the mechanism is diagonal. Then all possible forms of the non-actuated twist screws are confirmed according to the principle that the actuation wrench screw is reciprocal to all twist screws within a chain except for the actuated one. The steps of