Design of a Novel 3-DoF Serial-Parallel Robotic Wrist: A Symmetric Space Approach

Abstract

For the past forty years, design of robotic wrists in the robot industry has been dominated by a serial kinematics architecture, which parameterizes the end-effector orientation space by Euler angles. Such a design suffers from stationary (or dead-centre) configurations, as well as a weak third axis due to gear train backlash. It was once believed that the study of parallel kinematics mechanisms could result in viable alternatives overcoming the shortcomings of serial wrists. However, this did not happen, probably due to the limited workspace, complex kinematics, and inherent singularities characterizing parallel architectures. In this paper, we propose a novel class of serial-parallel 3-DoF robotic wrists, based on a particular geometry usually found in constant-velocity (CV) shaft couplings. The theory of CV couplings originated with Myard’s study and culminated with Hunt’s work. We have gone one step further, by fully decrypting and completing Hunt’s development using symmetric space theory. The latter allows us to provide an easy-to-follow procedure for synthesizing a unique type of parallel wrists with interconnections. Such novel wrists entail analytic direct and inverse kinematic analyses, and their singularities can be easily identified using the so-called half-angle property, which holds for all symmetric subspaces of the special Euclidean group. By conveniently choosing geometric parameters, the proposed wrists can achieve a singularity-free pointing cone of $180^\circ$, in addition to an unlimited rolling.