Identification of Isomorphism and Distinct Mechanisms Using Square Adjacency Matrix

For obtaining the structurally distinct mechanisms of the kinematic chains, link disposition matrix, flow matrix and row matrix of adjacency matrix are used. These methods shows either a lack of uniqueness or it consumes a lot of time. Determination of distinct mechanism using flow matrix is very long process. Therefore to overcome this problem we are trying to develop a computationally efficient method for generalizing the planer kinematic chains having same number of links but different kinematic pairs to determining the distinct mechanisms from the given kinematic chains which is called Squared Adjacency Matrix [SAM] In the present work the graph theory is applied in the modelling of kinematic chains and mechanisms. A new matrix is obtained from the kinematic graph of the kinematic chains, called Squared Adjacency Matrix. Fixing the links of 1 links kinematic chain, 1 mechanisms are generated. Similarly other links are fixed and other mechanisms are obtained. Some of them are equivalent and others are different. If the corresponding row and column entries of the square adjacency matrix are changed to a11 = 1 and remaining elements are zero as turn in turn, n square adjacency matrices are obtained and it is representation of n mechanisms. Therefore the new structural invariants are obtained from n square adjacency matrices. These invariants are identical for structurally equivalent mechanisms and distinct for distinct mechanisms. Therefore number of distinct mechanisms can be obtained from the given kinematic chain. The proposed method is applied to determine the distinct mechanisms of single degree of freedom, six links, eight links and ten links kinematic chains