Comments on mechanism kinematic chain isomorphism identification using adjacent matrices

A number of theories on the relationship between adjacent matrices of isomorphic mechanism kinematic chains have been investigated. A particular published theory about mechanism kinematic chain isomorphism using adjacent matrices has been revised, after errors in the original theory were discovered. Subsequently, the necessary and sufficient conditions of the eigenvalues and eigenvectors of adjacent matrices for isomorphic kinematic chains have been proven rigorously. A new procedure to identify isomorphic chains has been developed and presented. With this new procedure it is only necessary to compare eigenvalues and several eigenvectors of adjacent matrices of isomorphic kinematic chains to identify the isomorphic chains. Some examples have been provided to demonstrate how to use the theory.