Abstract: Handling multiple-joint and isomorphism identification of planar kinematic chains with multiple-joints is a hard work in the analysis and synthesis of mechanisms. A new approach is suggested to convert the multiple-joints to some parallel simple-joints by using a Pin-link to adjoin all the links on a multiple-joint. The converted adjacent matrix is defined to represent the kinematic chains with multiple-joints. According to some characteristic parameters of the converted adjacent matrix, a new method for isomorphism identification of planar kinematic chains is proposed. Some application examples show that the converted adjacent matrix can conveniently represent planar kinematic chains with multiple-joints, and the Eigen values and eigenvectors of the converted adjacent matrix can be used to identify the isomorphism of planar kinematic chains effectively and efficiently. A new way is provided to the analysis and synthesis of mechanisms with multiple-joints.

Key words: Adjacent matrix, Converting, Isomorphism identification, Kinematic chain, Multiple-joint, dynamic error, dynamic performance, geometry error, multi-leaf collimator, servo feeding performance