Tree Structure Representation and Isomorphism Identification of Assur Groups

Abstract

Isomorphism identification is a necessary part in the kinematic chain and Assur group structure synthesis, and is also the difficult problem in the field of mechanism research. In this paper, a tree structure description and isomorphism identification method for Assur group with multiple-joints and loops has proposed. Firstly, the tree nodes and leaf nodes of the tree structure are expressed by the component values of the group and the degrees of the multiple joint, and the kinematic pair has represented the branches. And then the root and leaf node selection rules of the tree structure had been given and the representation of the unique tree structure had been obtained. The rules of node number arrangement had been proposed, and the node sequence string was obtained in the tree structure chart. Based on this sequence, a new method for determining the isomorphism of groups had been proposed. The practice shows that the method has the advantages of simple principle and less contrast.