An automated method for type synthesis of planar linkages based on a constrained subgraph isomorphism detection

We present a method to enumerate and codify all non-isomorphic solutions, for the problem of synthesizing the type of single-DOF linkage mechanisms that satisfy structural requirements for a given kinematic problem. The method is based on the construction of an initial graph taking into account prescribed parts (such as fixations, moving bodies, joints and their interconnections) and the kinematic constraints imposed on them. This initial graph containing structural characteristics of the problem is used as a pattern to search inside a selected atlas of one-DOF mechanism also represented by graphs. A new graph-matrix representation of mechanisms and a mechanism identifier based on the degree code concept was developed to avoid isomorphic occurrences of the initial graph inside each mechanism of the atlas. The same tools were used to enumerate various atlases specialized in a non-isomorphic way from basic kinematic chains. This enumeration takes into account different types of links (rigid, flexible) and joints (revolute, prismatic, flexible, clamped), and proper restrictions were designed to avoid kinematically invalid topologies. The methodology is illustrated with examples for several kinematic tasks.