Design and analysis of a novel parallel manipulator for pick-and-place applications

This paper presents a novel 4 degree-of-freedom Schönflies-motion parallel manipulator, which is an upgraded design of a 3 degree-of-freedom planar parallel manipulator. The manipulator consists of three identical RRPaR\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal {RRP}}}_{a}{{\mathcal {R}}}$$\end{document} (R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {R}}$$\end{document}: a revolute joint, Pa\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal {P}}}_{a}$$\end{document}: a planar parallelogram) and one RRRRR\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {RRRRR}}$$\end{document} subchain. The three actuated joints, the first revolute joints, of RRPaR\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal {RRP}}}_{a}{{\mathcal {R}}}$$\end{document} subchains are designed to have a common rotation axis, and the actuated joint (the second R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {R}}$$\end{document} joint) axis of the RRRRR\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {RRRRR}}$$\end{document} subchain is perpendicular to the common rotation axis. This architecture contributes large rotationally-symmetric workspace and unlimited rotational capability of the end-effector. The fundamental demerit of typical parallel manipulators, limited workspace, is completely removed. In this paper, the loop-closure equations are derived. The inverse and forward kinematics and singularity analysis are discussed. An algebraic derivation of the dextrous workspace is presented.