CGA-based approach for the inverse displacement of serial-parallel manipulators

This paper presents a CGA-based approach to the inverse displacement of the S-PMs composed of two PMs. Two novel S-PMs including (2-SPR+RPS)+(2-RPS+SPR) and (2-RRS+2-SPS)+(2SPS+PS) S-PMs are taken as cases to illustrate the application of CGA in solving the inverse displacement of S-PMs. For the two S-PMs, according to the geometric property of the structures, by skillfully applying the geometric operations provided by CGA, the vertex coordinates of the middle platform with only one unknown can be obtained. Then, using the distance formula in CGA, one polynomial equation concerned with one unknown can be derived straight forwardly and all solutions can be solved easily. The modeling procedure using CGA has intrinsic geometric intuition and can avoid the complicated algebraic eliminations.