The concept of Hamming number technique and its application to detect isomorphism among kinematic chains has been already reported [A. C. Rao and D. Varada Raju, Mechanism and Machine Theory 26, 55-75 (1991)]. This concept has great potential and can be used further to reveal certain properties such as degeneration and type of freedom which will be helpful during the synthesis of single and multi degree or freedom kinematic chains. Also, the concept of symmetry in kinematic chains is introduced and its utility in detecting isomorphism among chains, and in rating them is illustrated. Writing of the Hamming matrix directly to save time and effort, for a chain, is explained. (C) 1997 Elsevier Science Ltd.