Structural synthesis of parallel manipulators with coupling sub-chains

A conventional parallel manipulator uses serial kinematic chains or the legs to support a single moving platform. The movement of the platform may be further constrained by adding interconnections among its legs to form the so-called coupling sub-chains. The introduction of coupling sub-chains to the kinematic structures of parallel manipulators, while allowing for improved performance and functionality, presents also significant challenges in the structural synthesis of the resulting manipulators. This paper presents a systematic method for the structural synthesis of parallel manipulators with coupling sub-chains. The contracted graphs in connection with Euler's equation are constructed based on permutation and combination, and the isomorphism is identified. Then, fractionation and simplification process of the contracted graph of the resulting manipulators are analyzed. In the second half of the paper, a screw theory based method for constraint synthesis of kinematic chains is developed to synthesize various legs and coupling sub-chains. Examples were provided to demonstrate the efficacy of the advocated method.