The knowledge of singularity-free regions (SFRs) inside the workspace of a manipulator is helpful in its path-planning and design. To identify such regions analytically, the singularity manifold needs to be determined first. This paper presents the derivation of the gain-type singularity manifold in the task-space of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3$$\end{document}-RPS manipulator, which is further utilised to compute its SFR, in the form of a singularity-free cylinder (SFC), which is free of gain-type singularities. The problem of identifying the longest SFC for a given constant radius and a chosen base circle is posed as a constrained optimisation problem, which reduces to a 21-degree univariate polynomial in the length of the SFC. The formulation is illustrated via a numerical example.
Analytical Determination of the Longest Cylinder Free of Gain-type Singularities Inside the Workspace of a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3$$\end{document}-RPS Spatial Manipulator
Springer Proceedings in Advanced Robotics
International Symposium on Advances in Robot Kinematics ; 2020 ; Ljubljana, Slovenia December 06, 2020 - December 10, 2020
2020-07-18
8 pages
Article/Chapter (Book)
Electronic Resource
English
<inline-formula><alternatives><tex-math>\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3$$\end{document}</tex-math><inline-graphic></inline-graphic></alternatives></inline-formula>-R<underline>P</underline>S manipulator , Gain-type singularity manifold , Singularity-free cylinder , Algebraic elimination Engineering , Robotics and Automation , Computational Intelligence , Robotics , Computational Science and Engineering , Engineering Design