Methodology for the Automatic Generation of Assur Groups from Planar Multi-bar Linkages

Abstract

The theory of Assur groups indicates that the potential Assur groups and linkage types can be obtained by selecting different ground links and driving links of unique kinematic chains. A methodology of automatically generating Assur groups is proposed based on this theory. Aiming at the structure characteristics of Assur groups,an effective and simple method of isomorphism identification of Assur groups is also proposed. This method is also applicable to the isomorphism identification of planar multi-bar kinematic chains. This methodology combines the automatic generation algorithm and computer programming to realize the automatic generation of Assur groups and linkages by using the adjacency matrices and the relevance matrices of the kinematic chains. This methodology makes splitting the Assur groups from planar multi-bar kinematic chains when forming linkages quick and accurate. The automation process has obtained all the 13 Assur groups from four-bar and six-bar and eight-bar kinematic chains and the 153 unique linkage types formed by eight-bar kinematic chains just by isomorphism identification.