An automated method for type synthesis of planar linkages based on a constrained subgraph isomorphism detection (Q2458276)

The paper proposes a method to obtain a linkage mechanism design for the kinematic problem. This method suggests a systematic procedure of topological alternative evaluation, which is based on combinatorial analysis and graph theory and is developed to search and codify the non-isomorphic solutions of the problem. Firstly, an ``initial graph'' is constructed taking into account system requirements -- structural, functional, etc. It is obtained by endowing each link by a vector and each kinematic pair by an edge. This graph has matrix representation. Secondly, an atlas of kinematic chains with simple joints, using a graph representation for each of them, is given. To avoid isomorphisms, a ``type adjacency matrix'' is introduced, which is based on the degree code characterizing an alternative mechanism. The approach is illustrated with examples for several kinematic tasks. The method is used as a part of a complete synthesis of rigid and flexible mechanisms implemented in the context of a finite element program.