Structural synthesis and analysis of serial–parallel hybrid mechanisms with spatial multi-loop kinematic chains

This paper presents a novel method of structural synthesis and analysis of serial–parallel hybrid mechanisms with spatial multi-loop kinematic chains based on the displacement group theory. The topological arrangements of serial–parallel hybrid mechanisms can be developed by the Assur group transformation and fractal method to obtain the multi-loop forms of subchains and platforms. In the light of the results of topological arrangements, a method of Spatial Multi-loop Detachment is presented to analyze the output displacement subsets and mobility of spatial multi-loop mechanisms. In particular, the problem of output relations with non-spanning tree netted form is solved by the detachment method. Meanwhile, a proposition about intersection of displacement subsets of multi-loop paths can be obtained. Based on the results of Spatial Multi-loop Detachment of topological arrangements, the configuration card of displacement subsets of subchains is developed to accomplish the allocation of displacement subsets and design of specific structure of spatial multi-loop subchains. At last, three novel serial–parallel hybrid mechanisms are synthesized to demonstrate the applicability of the presented method.