An Automated Method for Type Synthesis of Planar Linkages based on a Constrained Subgraph Isomorphism Detection

MARTÍN PUCHETA; ALBERTO CARDONA

MULTIBODY SYSTEM DYNAMICS

Springer

Año: 2007 vol. 18 p. 233 - 258

1384-5640

We present a method to enumerate and codify all non-isomorphic solutions, forthe problem of synthesizing the type of single-DOF linkage mechanisms that satisfy structuralrequirements for a given kinematic problem. The method is based on the constructionof 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 initialgraph containing structural characteristics of the problem is used as a pattern to search insidea selected atlas of one-DOF mechanism also represented by graphs. A new graph-matrixrepresentation of mechanisms and a mechanism identifier based on the degree code conceptwas developed to avoid isomorphic occurrences of the initial graph inside each mechanismof the atlas. The same tools were used to enumerate various atlases specialized in a nonisomorphicway from basic kinematic chains. This enumeration takes into account differenttypes of links (rigid, flexible) and joints (revolute, prismatic, flexible, clamped), and properrestrictions were designed to avoid kinematically invalid topologies. The methodology isillustrated with examples for several kinematic tasks.