Assur Group Inferred Structural Synthesis for Planar Mechanisms

Abstract

In order to obtain a comprehensive list of possible mechanisms with various choices of both R and P pairs and mechanism inversion of planar mechanisms, a new structural synthesis method is developed by integrating Assur groups (AGs) as elements in the newly developed groupbased adjacency matrix. This extended adjacency matrix is proposed with the diagonal elements representing three fundamental elements as the frame link, driving link, AG and augmented AG (AAG) if metamorphic mechanisms are to be synthesized. The offdiagonal elements provide information on group combination and connection forms of the above three fundamental elements and that on the associated kinematic pairs. Based on the extended adjacency matrix, all assembly modes for the given AGs can be established and isomorphism mechanisms can be identified at the same time. Considering all types of the AGs in the extended adjacency matrix, group permutation and combination are used and connection forms are generated including variation of the driving link and mechanism inversion. The structural synthesis is then extending to generating a comprehensive list of types of mechanisms and illustrated by the synthesis for class II 6bar planar mechanisms with both R and P pairs, generating a list of 588 types of mechanisms that are derived for the first time. The paper further applies the approach to metamorphic mechanisms, and obtained five connection forms of the 7bar 2DOF metamorphic mechanisms.