Classification of Mechanisms Using graph representation, mechanism structures can be conveniently represented by graphs. The classification problem can be transformed into an enumeration of nonisomorphic graphs for a prescribed number of degrees of freedom, number of loops, number of vertices, and number of edges. The degrees of freedom of a mechanism are governed by Equation (). The number of loops, number of links, and number of joints in a mechanism are related by Euler’s equation, Equation (). The loop mobility criterion is given by Equation (). Since we are primarily interested in nonfractionated closed-loop mechanisms, the vertex degree in the corresponding. | Chapter 6 Classification of Mechanisms Introduction Using graph representation mechanism structures can be conveniently represented by graphs. The classification problem can be transformed into an enumeration of nonisomorphic graphs for a prescribed number of degrees of freedom number of loops number of vertices and number of edges. The degrees of freedom of a mechanism are governed by Equation . The number of loops number of links and number of joints in a mechanism are related by Euler s equation Equation . The loop mobility criterion is given by Equation . Since we are primarily interested in nonfractionated closed-loop mechanisms the vertex degree in the corresponding graphs should be at least equal to two and not more than the total number of loops that is Equation should be satisfied. Furthermore there should be no articulation points or bridges and the mechanism should not contain any partially locked kinematic chain as a subchain. In this chapter we classify mechanisms in accordance with the type of motion followed by the number of degrees of freedom the number of loops the number of links the number of joints and the vertex degree listing. The general procedure for enumeration and classification of mechanisms is as follows. Given the number of degrees of freedom F and the number of independent loops L 1. Solve Equations and for the number of links and the number of joints. 2. Solve Equations and for various link assortments n2 n3 n4 . 3. Identify feasible graphs and their corresponding contracted graphs from the atlases of graphs listed in Appendices C and B or any other available resources such as Read and Wilson 14 . 4. Label the edges of each feasible graph with a given set of desired joint types. This problem may be regarded as a partition of the edges into several parts. Each part represents one type of joint. Two permutations are said to be equivalent if their corresponding labeled graphs are isomorphic. .
