Abstract: A wire-driven parallel manipulator is a closed-loop mechanism where the moving platform is connected to the base via wires by multitude of independent kinematic chains. The number of moving platform’s degrees of freedoms(DOFs) is defined as the dimension of linearity space which is positively spanned by all the screws of the structure matrix of the manipulator. It is proposed that the singularity with over-mobility of wire-driven parallel manipulators is due to the wrench deficiency of the moving platform because the dimension of the set of wrench decreases. Moreover, the fact that singularities, in addition to the loss of controllability of the moving platform, can also break the continuity of optimal tension distribution, which is a problem particular to singularities in wire-driven parallel manipulators, is stated. And after the analysis of the influence of the gravity of the moving platform on the wrench deficiency taking the manipulator in 1R2T class with 1-2-1 type for example, it is found that the tension distribution of each wire can be reconfigured because of the existence of the gravity even if it can’t eliminate the singularity. Considering the fact that a wire-driven parallel manipulator with the decoupling of every rotational DOFs and the translational DOFs completely controlled is singularity-free, a way to build up singularity-free CRPMs in 1R2T class with 1-2-1 type, RRPMs in 2R3T class with 2-3-2 type is proposed. Using antipodal grasp theorem, a way to build up singularity- free CRPMs in 1R2T class with 2-2 type and 2R3T class with 3-3 type is proposed. Using the theorem of 3-dimension force-closure grasp proposed by Canny, a method to build up singularity-free RRPMs in 3R3T class with 3-3-3 type is presented.

Key words: Parallel manipulator, Singularity with over-mobility, Singularity-free, Wire-driven, Wrench deficiency