北京航空航天大学学报 ›› 2009, Vol. 35 ›› Issue (1): 48-51.

• 论文 • 上一篇    下一篇

Stewart台体并联机器人位置正解

庄育锋1, 黄昔光2, 廖启征1   

  1. 1. 北京邮电大学 自动化学院, 北京 100876;
    2. 北方工业大学 机电工程学院, 北京 100041
  • 收稿日期:2008-01-25 出版日期:2009-01-31 发布日期:2010-09-16
  • 作者简介:庄育锋(1972-),男,上海人,讲师,zhuangyf@bupt.edu.cn.
  • 基金资助:

    国家973资助项目(2004CB318000);国家自然科学基金资助项目(50475161);国家863计划资助项目(2007AA04Z211)

Direct kinematics of Stewart mechanism robot

Zhuang Yufeng1, Huang Xiguang2, Liao Qizheng1   

  1. 1. School of Automation, Beijing University of Posts and Telecommunications, Beijing 100876, China;
    2. School of Mechanical and Electrical Engineering, North China University of Technology, Beijing 100041, China
  • Received:2008-01-25 Online:2009-01-31 Published:2010-09-16

摘要: 为获得Stewart台体并联机器人位置正解的解析解,使用分次字典序Groebner基和Sylvester结式相结合的代数方法对该问题进行研究.利用计算代数中的分次字典序Groebner基算法,计算该机器人位置正解封闭数学模型的分次字典序Groebner基;从得出的51个基中选取20个基,构造20阶Sylvester结式,分析符号形式方程组的变量次数,可以直接得出该机器人位置正解一元高次方程的次数为40且最多有40组解的结论,其结果与前人的完全一致,但结式的尺寸却小得多.为了对结果进行验证,使用同伦连续法对同一个数字算例进行计算,两种方法得到结果一致.为并联机构位置正解的研究提供了一种新的有效算法.

Abstract: The Groebner-Sylevester hybrid approach was presented to obtain the closed-form solutions of the direct kinematics of the Stewart mechanism robot. The reduced Groebner basis under degree lexicographic ordering for the closed-form equations was presented based on computer algebra method. And 20 Groebner basis were picked out from the 51 Groebner basis. Then a 20×20 dimensional Sylvester-s matrix was constructed, which is relatively small in size. And a 40th degree univariate equation was presented from the determinate of the matrix by analyzing the numbers of the variables in the equations. To verify the proposed algorithm, a same numerical example was calculated based on the continuation method as well as the the proposed algorithm. It shows that the proposed algorithm calculates simply and rapidly to lead to the univariate equation. The results both by using the continuation method and based on the proposed algorithm are same. Then a novel and practical algorithm to solve the direct kinematics of the parallel mechanism robot was presented.

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