A Quadratic Form-Based Approach to Identification of Kinematic Chains in Structural Analysis and Synthesis of Mechanisms

Abstract

Abstract Identification of kinematic chains is needed when studying in structural analysis and synthesis of mechanisms. Research on detection of isomorphism in graphs/kinematic chains has a long history. Many algorithms or methods have been proposed. However, these methods have only achieved success in restricted conditions. This paper proposes a new approach using the concept of quadratic form. Graphs/kinematic chains are first represented by their adjacency matrices, the eigenvalues and their eigenvectors corresponding to these adjacency matrices are then calculated. Two graphs are represented by two quadratic expressions. The comparison of two graphs reduces to the comparison of two quadratic expressions. Quadratic expressions are characterized by the eigenvalues and eigenvectors. An algorithm is developed to compare, correspondingly, eigenvalues and eigenvectors of two graphs, known test cases are used to verify the effectiveness of the approach.