Structural synthesis and variation analysis of a family of 6-DOF parallel mechanisms with three limbs

This paper presents the structural synthesis and variation of a family of six degrees of freedom (DoF) parallel mechanisms with three limbs, based on screw theory and group theory. Firstly the preliminaries of screw theory and group theory are briefly introduced; three corollaries and a geometric approach are presented to solve the reciprocity and correlation between screws. Then a general procedure is developed for the structural synthesis of parallel mechanisms. A family of 6-DoF parallel mechanisms with structure of 3-RXPX (X, alternative of R-, U- or S-pair) are proposed according to the developed procedure. The structural variation methods based on screw reconstruction and displacement manifold variation are proposed for the extension of the constructed mechanisms. Two examples corresponding to the two proposed variation methods show that the structural variation methods are valid to expand the number of the synthesized parallel mechanisms.