Workspace and Singularity Analysis of a 2P3RR Planar Parallel Mechanism

Xuzhao Han, Peng Jin, Suolao Li, Wen Liu, Yuanxiong Zhang, Yi Guo
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Abstract

Carried out in-depth research for the parallel mechanism 2P3RR, introduced composition of the mechanism, derived the kinematics formulas which include the positive and the inverse solutions of the position, and the Jacobian matrix of the mechanism is obtained. The parallel mechanism's characteristics such as workspace and singularity are analyzed. The workspace of the mechanism is analyzed by graphic method, and the singularity of Jacobian matrix is used to analyze three singular forms of the mechanism. It can be seen that the positive and inverse kinematics solutions have explicit expressions by solving the parallel mechanism kinematics, the workspace is easy to describe and the singularity of the mechanism can be avoided, which lays a theoretical foundation for the design and development of the mechanism and its application in the field of robots and machine tools.
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2P3RR平面并联机构工作空间及奇异性分析
对并联机构2P3RR进行了深入研究,介绍了该机构的组成,推导了包含位置正解和反解的运动学公式,得到了该机构的雅可比矩阵。分析了并联机构的工作空间和奇异性等特性。用图解法分析了机构的工作空间,利用雅可比矩阵的奇异性分析了机构的三种奇异形式。通过求解并联机构运动学可知,其正逆解具有明确的表达式,工作空间易于描述,避免了机构的奇异性,为该机构的设计开发及其在机器人和机床领域的应用奠定了理论基础。
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