Enumeration of driving mechanisms in robotics by combinatorial analysis method

Abstract

This research deals with the development of a new method for restricted morphological number enumeration for planar pin-jointed driving mechanisms of mobility 1 and 2. It is based on combinatorial analysis by using the symmetries of kinematic chains. Since the restricting criterion is the position of the robot’s frame, different cases of symmetries are addressed. New expressions for calculating the number of positions of the actuators in a mechanism are presented. These help to reduce the number of chains by avoiding those that are isomorphic with regard to the position of the robot frame. The expressions offer a corrected formulation for counting the number of actuators for planar mechanisms in robotics. Different examples of applications for various planar pin-jointed driving mechanisms of mobility 1 and 2 are presented.