Structural Analysis of Twelve Link Kinematic Chain Using Graph Theory

Structural analysis plays a crucial role during the designing of mechanism. Structural analysis of kinematic chain deals with connection among the members of kinematic chain and its mobility. In the present work efforts has been made to provide adequate solution of structural analysis of kinematic chain by considering the example of twelve link mechanism. With the help of graph theory the structure of the kinematic chain is shown by its kinematic graph in which the links shows the vertices and the joints shows the edges. The kinematic graph is then represented by incidence matrix or adjacency matrix. This matrix shows the connection between the links. Then a simple method is applied on the matrix to determine the coefficient of characteristic polynomial equation. Finally for mobility analytic test is performed to find whether kinematic chain possess total, fractioned, or partial degree of freedom.