Critical Study of Existing Methods And Development of A New Method To Test Isomorphism of Kinematic Chains

Abstract

Design is one of the core activities of any engineering field. Design of mechanical newlinesystems requires development of mechanisms and machines. Mechanisms form an integral newlinepart of machines. Synthesis and analysis of mechanisms, therefore, play an important role in newlinethe design of machines. Some of the challenges faced by the designers during synthesis of newlinemechanisms are: newline1. Enumeration or synthesis of non-isomorphic structures known as kinematic chains newlinefrom which mechanisms are derived. newline2. Detection of isomorphism among kinematic chains. newline3. Rigid sub-chain detection and newline4. Structural analysis of kinematic chains to investigate newlinea. Distinct inversion that can be obtained from a kinematic chain newlineb. Mobility type identification and newlinec. Structure based performance assessment prior to dimensional synthesis newlinePresent study is an attempt to provide efficient solutions to some of these problems. newlineReliability of chain generation depends upon the reliability of the method used to test newlineisomorphism. Almost all methods reported hitherto fail at some stage or the other. A critical newlinereview of the existing methods was carried out in order to know the reasons of their failure or newlinelimitations. A comprehensive comparison of the methods from the viewpoint of their newlinereliability, computation time, and other advantages and disadvantages lacking in the literature newlineis one the objectives of the present work. newlineDetection of isomorphism of kinematic chains is still an actively pursued problem and newlineefficient algorithms are required to be developed to substantiate fully automated process of newlinemechanism design. A new method Link Invariant Set has been developed applying the newlinetechniques of graph theory to detect isomorphism among kinematic chains and are presented newlinein this work. newlineGeneration of planar linkages (kinematic chains) with more number of links is a huge newlinetask. The accuracy of isolating distinct mechanisms that can be derived from innumerable newlinenumber of chains generated depends upon precise identification of identical links of a newline