Identification Of Distinct Inversions In A Kinematic Chain Using Link-Joint-Loop Adjacency

Abstract

Every machine needs a suitable mechanism to impart motion and transmit power. Hence, it becomes necessary to study the various aspects of a mechanism in terms of synthesis and structural analysis of kinematic chain. In past few decades, a lot of researchers had put their efforts in identifying distinct kinematic chain with a given degree of freedom, tested them for isomorphism and identified the distinct number of mechanisms (inversions) that can be obtained by fixing a link in a particular kinematic chain. All those methods are solely dependent on the study and analysis of two basic factors of any kinematic chain i.e links and joints. However, the presence of loops and its effect in driving a mechanism is somehow neglected. The complete analysis of the structure of a kinematic chain depends on the study of all the three factors i.e. links, joints and loops. This paper approaches with a new method based on matrix composition to identify the accurate number of distinct mechanisms which can be obtained in a particular kinematic chain. The method adopted is quite simple and reliable as it considers the presence of loop among the kinematic chain along with the links and the joints hence uses link-joint-loop adjacency.