In this paper, a new method is proposed for the structural synthesis of a class of redundantly-actuated parallel wrists (RaPWs) with three rotational degrees of freedom of the moving platform and symmetrical structures based on screw theory. First, the new procedure for structural synthesis of RaPWs with closed-loop actuated unit is proposed and the constraint system of the moving platform of RaPWs is analyzed. Then, considering the inclusion relation between the primary constraint system and the limb constraint system, the type of kinematic limb is determined. The synthesis of type-1 and type-2 kinematic limbs is dealt with based on the obtained closed-loop actuated unit and open-loop sub-limb. Next, the RaPWs are synthesized and a number of new RaPWs have been identified. Finally, the condition for proper actuator selections of RaPWs is revealed, and one example is used to perform the validation.
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