Singularity and branch identification of a 2 degree-of-freedom (DOF) seven-bar spherical parallel manipulator

Abstract

Spherical parallel manipulators (SPMs) have a great potential for industrial applications of robot wrists, camera-orientating devices, and even sensors because of their special structure. However, increasing with the number of links, the kinematics analysis of the complex SPMs is formidable. The main contribution of this paper is to present a kind of 2 degree-of-freedom (DOF) seven-bar SPM containing two five-bar spherical loops, which has the advantages of high reaction speed, accuracy rating, and rigidity. And based on the unusual actuated choices and symmetrical loop structure, an approach is provided to identify singularities and branches of this kind of 2 DOF seven-bar SPM according to three following steps. Firstly, loop equations of the two five-bar spherical loops, which include all the kinematic characteristics of this SPM, are established with joint rotation and side rotation. Secondly, branch graphs are obtained by Maple based on the discriminants of loop equations and the concept of joint rotation space (JRS). Then, singularities are directly determined by the singular boundaries of the branch graphs, and branches are easily identified by the overlapping areas of JRS of two five-bar spherical loops. Finally, this paper distinguishes two types of branches of this SPM according to whether branch points exist to decouple the kinematics, which can be used for different performance applications. The proposed method is visual and offers geometric insights into understanding the formation of mobility using branch graphs. At the end of this paper, two examples are employed to illustrate the proposed method.