• CN:11-2187/TH
  • ISSN:0577-6686

›› 2011, Vol. 47 ›› Issue (13): 35-43.

• 论文 • 上一篇    下一篇



  1. 西安电子科技大学电子装备结构教育部重点实验室;南京电子技术研究所
  • 发布日期:2011-07-05

Analysis on the Static Stiffness of Wire-driven Parallel Manipulators

LIU Xin;QIU Yuanying; SHENG Ying   

  1. Key Lab of Electronic Equipment Structure of Ministry of Education, Xidian University Nanjing Research Institute of Electronics Technology
  • Published:2011-07-05

摘要: 基于微分变换和线几何理论,建立包含关节弹性变形以及绳拉力等因素的绳牵引并联机器人的刚度模型,推导刚度矩阵的数学表达式。模型不仅考虑驱动单元、绳的弹性变形对机构刚度的影响,而且考虑机构在广义外力作用下由末端执行器微分运动所引起的结构矩阵的变化。通过线矢量的引入,分步求导模型中结构矩阵对末端执行器位姿变分的三维Hessian矩阵。模型表明,绳牵引并联机器人的系统刚度由两部分组成,其中一部分主要取决于绳的几何布置、末端执行器的位姿、驱动支链的物理特性;另一部分表达为结构矩阵相对末端执行器位姿的变分-Hessian矩阵与绳拉力矢量的乘积。大射电望远镜5 m缩尺模型数值仿真与试验结果的对比验证了该方法的正确有效。

关键词: Hessian矩阵, 刚度, 绳牵引并联机器人, 微分变换, 线几何

Abstract: Based on differential transform and linear geometry theory, a stiffness model of wire-driven parallel manipulators is established, including the elastic deformation of joints and wire tension. And a mathematical expression of the stiffness matrix is developed. Not only the influence of elastic deformation of the drive units and wires on the mechanism stiffness, but also the change of the structure matrix due to the movement of end-effectors under the action of generalized external force are considered in the stiffness model. The structure matrix derivative with respect to the position and orientation of the end-effectors, namely three dimension Hessian matrix is obtained by introducing linear vector. The model shows that the stiffness matrix of wire-driven parallel manipulators consists of two parts, one of which depends mainly on the geometric distribution of the wires, the position and orientation of the end-effectors, and the physical property of the driven links, while the other is a product of the Hessian matrix and the wire tension vector. The simulation and experiments of a five-meter scaled model of large spherical radio telescope verify the accuracy and effectiveness of the proposed method.

Key words: Differential transform, Hessian matrix, Line geometry, Stiffness, Wire-driven parallel manipulator