• CN:11-2187/TH
  • ISSN:0577-6686

›› 2011, Vol. 47 ›› Issue (3): 28-35.

• 论文 • 上一篇    下一篇

绳牵引并联机器人工作空间的判定条件与解析表达

刘欣;仇原鹰;盛英   

  1. 西安电子科技大学电子装备结构教育部重点实验室
  • 发布日期:2011-02-05

Criteria Conditions and Analytic Expression of Workspace of Wire-driven Parallel Manipulators

LIU Xin;QIU Yuanying;SHENG Ying   

  1. Key Laboratory of Electronic Equipment Structure of Ministry of Education, Xidian University
  • Published:2011-02-05

摘要: 研究6自由度完全和冗余约束绳牵引并联机器人力旋量封闭工作空间的性质,给出并证明在不同牵引绳根数下末端执行器位姿属于力旋量封闭工作空间的充要条件,分析满足矢量封闭原理的结构矩阵对应的几何特征。总结6自由度完全和冗余约束绳牵引并联机器人力旋量封闭工作空间的判定定理,即结构矩阵满秩,在结构矩阵中存在列矢量位于6个线性独立列矢量反方向张成的六维凸锥内,且满足相关系数之和大于0。基于以上定理和性质,推导6自由度完全和冗余约束绳牵引并联机器人力旋量封闭工作空间边界的解析表达式,提出力旋量封闭工作空间解析求解方法。数值算例验证了方法有效可行。

关键词: 构型参数, 力旋量封闭工作空间, 绳牵引并联机器人

Abstract: The properties of the wrench-closure workspace of 6 degree-of-freedom completely restrained and redundant restrained wire-driven parallel manipulators are investigated. The necessary and sufficient conditions to test whether a pose of the end-effector driven by an arbitrary number of wires belongs to the wrench-closure workspace of the manipulators are proposed and proved, and the geometric characters of structure matrices satisfying the definition of the wrench-closure are illustrated. A criteria theorem to determine the wrench-closure workspace of the manipulators is concluded. The theorem indicates that the rank of structure matrices of the manipulators should be full, and a column vector existing in structure matrices should be inside the six-dimensional convex polyhedral cone generated by six linearly independent column vectors of structure matrices at their opposite direction, and the sums of the correlative coefficients should be positive. According to the theorem and properties, an analytic expression of the boundary of the wrench-closure workspace is developed for 6 degree-of-freedom completely restrained and redundant restrained wire-driven parallel manipulators. An efficient algorithm that determines the boundary of the wrench-closure workspace is introduced. The numerical examples demonstrate the effectiveness of the proposed algorithm.

Key words: Configuration parameters, Wire-driven parallel manipulator, Wrench-closure workspace

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