Detection Of Isomorphism Among Kinematic Chains Using Link-Joint-Loop Adjacency

Abstract

An important aspect in the field of mechanical engineering is to deal with the transmission of motion to meet the specific requirement. For fulfilling this need various mechanical elements such as linkages, levers, gear-trains, eccentrics, cams, etc. are commonly adopted. Hence, the structural analysis of kinematic chains and synthesis of linkages becomes a major area of study in mechanical engineering. At the conceptual stage of design, it is always required to select the best possible kinematic chain for the specified task. Hence, it becomes necessary to do the structural analysis and synthesis of all the possible distinct kinematic chains available with specified number of links and degrees of freedom. Basically, the results of structural synthesis ends with the generation of distinct kinematic chains but it does not lead to logical conclusion unless the capabilities of the structures are explored. How accurately a kinematic chain is generated with specified number of links and degree of freedom depends upon how accurately the chain is tested for isomorphism. Past researchers had developed some methods to test a kinematic chain for isomorphism but many of these methods fail at some stage or the other. Many of the methods that are reported to test for isomorphism and to identify distinct inversions in structural analysis are either based on link-link adjacency, link-joint adjacency or link-loop adjacency. But all the three important features of kinematic chains viz. link-joint-loop have not been considered for the exact structural assessment. Keeping this in view, quantitative methods are being developed which includes link-joint-loop adjacency to detect isomorphism among kinematic chains. The developed method for testing isomorphism also reveals other characteristics of kinematic chain and deliver results in many aspects e.g. efficiency, reliability, computational time, etc. Since, all the three features of kinematic chains viz. link-joint-loop are considered to analyze the structural aspect and its relation to function; the expected outcome will reveal some kinematic characteristics of the chain with high degree of reliability and efficiency for application in planar manipulators from the viewpoint of workspace.