Sub-chain symmetry approach for morphological choice of planar mechanisms in robotics

This paper deals with the morphological confined choice for kinematic mechanisms in robotics. It is based on sub-chain symmetries of structures taking into account the position of the frame and of the end-effector of the robot. Pairs of groups of mutually symmetrical mechanisms are detected. Thus, eliminating the symmetrical ones confines the number of possible configurations. Different cases of symmetries have been studied. Expressions for the calculation of the number of frames and end-effectors are presented. They enable the reduction of the number of structures by avoiding those that are isomorphic. The rules for choosing the position of the frame and end-effector are imposed. The influence of the prismatic joints is also evoked. Following this, examples for applications for various planar pin-jointed kinematic structures are presented, enabling the field of research to be restricted to the possible solutions.