Type Synthesis of Multi-Loop Spatial Mechanisms With Three Translational Output Parameters Based on Virtual-Loop Theory and Assur Groups

This paper presents a new approach to synthesize multi-loop mechanisms with three translational displacement parameters based on virtual-loop theory and Assur groups. The approach used kinematic links as a generalized link group added one-by-one to the output link, which further extends the unified link groups in the plane and space. Firstly, the concept of infinitesimal displacement parameters is introduced to describe the displacement parameters. The dependence on the change in the degree of freedom (DOF) and displacement parameters of the output link after adding a 0-DOF generalized link group is established. Then, the link groups with three displacement parameters are synthesized, and the intersection operation rules are given. The single-loop mechanism is synthesized under two circumstances. The 1-, 2-, and 3-DOF dual-loop mechanisms are obtained by adding corresponding generalized link groups. Finally, the multi-loop mechanisms are obtained by adding corresponding generalized link groups. Some novel mechanisms are synthesized to illustrate the effectiveness of the proposed approach.