A Comparative Study of Various Methods for Identification of Isomorphism in Kinematic Chains

Abstract

Structural synthesis and analysis of mechanism are very important for the invention and innovation of mechanisms. Structural synthesis of kinematic chains usually involves the creation of a complete list of kinematic chains, followed by an Isomorphism test to discard duplicate chains. A significant unsolved problem in structural synthesis is the guaranteed precise elimination of all Isomorphs. Undetected Isomorphism result in duplicate solutions and an unnecessary effort and falsely identified Isomorphism eliminates possible candidates for new mechanisms. Thus, it is absolutely essential to identify isomorphism from the point of view of time saving and correct synthesis of mechanism kinematic chain. Many methods are available to the kinematicians to detect isomorphism among chains and inversions but each has its own shortcomings. The work presented in this dissertation deals with an approach to critically study some of the existing methods for identification of Isomorphism among kinematic chains and among inversions of given kinematic chain which are then compared with some common examples to select the best method to detect isomorphism in kinematic chain and mechanisms.

The presented work has been divided into two parts. In the first part, all the methods are applied one-by-one for identification of Isomorphism among kinematic chains and among inversions of a given kinematic chain with problems related to one, two and three degree-of-freedom kinematic chains. In the second part, all the methods are compared with their strengths and weaknesses with common examples of six links one degree of freedom Watt and Stephenson Chains to select the best method for identification of Isomorphism among kinematic chains and among inversions of a given kinematic chain. Also, the methods are applied for identification of various structural properties as Degeneration identification, Identification of Type of freedom i.e. Total, Partial and Fractionated degree-of-freedom, in planar kinematic chains of one, two and three degree-of-freedom.