Number Enumeration of Planar Pin-Joined Driving Mechanisms

This paper deals with the development of a new method for the morphological number enumeration for planar pin-jointed driving mechanisms applied in robotic design. The method is based on linkage graph presentation by using geometrical symmetries of kinematic chains and combinatorial analysis. The restricting criteria being the position of: the frame, the end-effector and the actuators (motors) of the robot, different cases of symmetries for planar pin-jointed driving mechanisms of mobility 1 and 2 are addressed. New expressions for calculating the number of different possibilities to position the frame, the end-effector and the actuators in a mechanism are presented, thus reducing the number of the possible solutions by avoiding those that are isomorphic. A further consequence of the present work is the ability for it to be extended to mechanisms with three degrees of mobility and more.