A new method for transforming pin-jointed kinematic chains into geared linkages is introduced. The method utilizes the graph representation in the form of the adjacency matrix and the “degree matrix” , and the powers of these matrices. The method involves first determining the feasible locations for assigning gear pairs in a kinematic chain, followed by determining which of the choices are distinct, and finally, determining the distinct possible ways of assigning the ground link for each distinct “geared kinematic chain” so formed. Because the method is based on matrix manipulations and does not rely on visual inspection, it is easily implemented on a digital computer. The method is applied to an example class of geared mechanism, the single-dof geared seven-bar linkages.