Mechanism Kinematic Chain Topology Representation And Isomorphism Identification

Isomorphism identification of kinematic chain is key to creative design and type synthesis in a mechanism.Traditional Isomorphism identification easily results in misjudgment and invalidation on the base of matrix identification of topological graph,which has incomplete theory and numerous calculation quantity.Therefore,a comprehensive research into isomorphic identification is needed due to its theoretical significance and application value.Topological graph is composed of vertexes stand for components of a kinematic chain,and sides for kinematic pairs.In the graph,the number of kinematic pair is given to a component with a prime so that a consequent mechanism contained compound hinges is characterized by prime product and sequence described adjacent relations of kinematic chain.This work defines a theorem for isomorphism identification of two mechanisms based on prime product and investigates the topological graph of kinematic chain with compound hinges.In the new topological graph,the vertexes are marked with vertex index and the number of kinematic pair,and the mutually connected components substitutes for all components connected to a compound hinges.Compared with traditional topological graph,this new graph holds the same vertex number and contains complete information of kinematic chains in a mechanism.It turns out that the topological graph is applied to the dynamic modification of adjacency matrix so that it can effectively identify the isomorphism of the kinematic chains with compound hinges.The simple identification is automatically realized with a computational time complexity of polynomial.Furthermore,the software is developed for the isomorphism identification of kinematic chain using object-oriented technology.This software performs the automatic isomorphism identification by invoking the corresponding algorithm to mutually convert between adjacency matrix and topological graph.It provides a new effective tool for the type synthesis of kinematic chains.