Abstract
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.
Highlights
Mobility identification is a basic problem in linkage analysis and synthesis, which includes branch analysis, sub-branch analysis, the full rotatability problem, and order of motion (Ting, 1989, 1993; Liu and Ting, 1991, 1992)
The first contribution of this paper is to provide a kind of 2 DOF seven-bar spherical parallel manipulator (SPM) with two spherical five-bar loops, which gives another potential choice for industry application
Loop equations are a common tool to analyze the kinematics of planar manipulators, which has been proved in Ting (1993), Ting and Dou (1996), and Wang et al (2010)
Summary
Mobility identification is a basic problem in linkage analysis and synthesis, which includes branch analysis, sub-branch analysis, the full rotatability problem, and order of motion (Ting, 1989, 1993; Liu and Ting, 1991, 1992). Using joint rotation space (JRS; Ting, 2008), the branch graph, which includes all the kinematic information of the 2 DOF seven-bar SPM, is obtained to identify the branches. The second one is first to succeed in identifying singularities and branches of the 2 DOF seven-bar SPM, utilizing the unusual actuated choices and symmetric loop structure. Only containing two five-bar spherical loops, this kind of 2 DOF seven-bar SPM, a symmetric loop manipulator, has several merits, such as easy control, compared to other planar linkages or SPMs. The third one is to use a branch graph to explain the kinetic characteristics of the SPM, which provides geometric insights into understanding the mobility information instead of a complex formula set. 4. Subsequently, two types of branches of the 2 DOF seven-bar SPM are identified according to joint rotation space and branch points in Sect. Conclusions are presented at the end of this paper
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