Classification of Angle-Symmetric 6R Linkage

TL;DR

This paper classifies angle-symmetric 6R linkages, a special overconstrained robotic linkage, into three types based on symmetry and algebraic properties, enhancing understanding of their geometric and kinematic structures.

Contribution

It provides a comprehensive classification of angle-symmetric 6R linkages, including a new type related to cubic motion polynomials, expanding the theoretical framework of overconstrained mechanisms.

Findings

Three types of angle-symmetric 6R linkages identified

Line symmetry as a key classification criterion

Discovery of a new linkage type related to cubic motion polynomials

Abstract

In this paper, we consider a special kind of overconstrained 6R closed linkages which we call angle-symmetric 6R linkages. These are linkages with the property that the rotation angles are equal for each of the three pairs of opposite joints. We give a classification of these linkages. It turns that there are three types. First, we have the linkages with line symmetry. The second type is new. The third type is related to cubic motion polynomials.