吴方法在平面并联机构位置正解中的应用

韩林; 张昱; 梁崇高

吴方法在平面并联机构位置正解中的应用

1.
北京航空航天大学机电工程系
2. 北京邮电大学机电工程系

详细信息

中图分类号: TH 112.1
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- 被引次数: 18
出版历程
- 收稿日期: 1996-12-20
- 网络出版日期: 1998-01-31

Wus Method for Forward Displacement Analysis of the Planar Parallel Mechanisms

1.
Beijing University of Aeronautics and Astronautics,Dept.of Mechanical and Electrical Engineering
2. Beijing University of Posts and Telecommunications,Dept. of Mechanical and Electronic Engineering

摘要

摘要: 采用吴方法对平面并联机构位置正解问题进行了研究.吴方法是一种求解非线性方程组的数学机械化方法,采用这种方法任何非线性方程组都可以在有限步内得到解决.在给出了吴方法基本原理的基础上,对本问题进行了求解,并将原始方程组转化成为一个三角化的方程组.其中单变量方程的次数为6次,说明平面并联机构可以有6个不同的位姿.最后用数值实例进行了验证,给出了计算结果.吴方法在这一问题中的应用,为求解其它机构学难题提供了新途径.
- 机构运动分析 /
- 平面机构 /
- 非线性方程
Abstract: The forward displacement analysis of the planar parallel mechanisms is studied by using Wu's method.Wu's method is a mechanical mathematics method for solving nonlinear equations.It can solve any nonlinear equations in limited steps.On the base of introducing theory of Wu's method,the problem is solved.The original equations of the problem is changed into triangulated equations in which a single unknown polynomial equation has 6th degree.The result shows that the planar parallel mechanism can have 6 different positions and orientations.In the end,a numerical example is studied.All the solutions for the example are listed.The presented method provides a new way for solving the other difficult mechanism problems.
- kinematic analysis of mechanisms /
- plane mechanisms /
- non-linear equations

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参考文献(1)

1. Stewart D.A platform with six degree of freedom.Proc Inst Mech Engrs,1965,180(15): 371~386 2. 吴文俊.几何定理机器证明的基本原理.北京:科学出版社,1984 3. Wu W J.A zero structure theorem for polynomial equation-solving.MM Research Preprings,1987,1: 2~13 4. 吴文俊.吴文俊文集.济南:山东教育出版社,1986 5. Karelin V S.Analytical determinate of kinematic characteristics of the plane 4-th-link structural groups.The theory of machines and mechanisms Proceedings of the 7th World Congress,Spain,1987.155~158 6. Merldt J P.Algebraic-geometry tools for the study of kinematics of parallel manipulators.In:Angeles J.Computational Kinematics.Netherlands: Kluwer academic publishers,1993.183~194

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