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工程设计学报
Chinese Journal of Engineering Design  2003, Vol. 10 Issue (2): 70-74    DOI:
    
Finding all solutions to forward displacement analysis problem of
6-SPS parallel robot mechanism with chaos-iteration method
 LUO  You-Xin, LI  Da-Zhi
Department of M echanical Engineering，Changde Teachers University，Changde 415003，China
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Abstract  A numerical method was found，taking the iteration of Newton method as a nonlinear dynamitic system in which Julia sets leads to chaos．Those points of Julia set was in the neighborhood of those points where belong to the determinant of satisfies Jacobian matrix was equal to zero．Jacobian matrix equation was changed in a nonlinear equation with one variable by giving the other variable’s value and the variable scope of the nongiven variable was confirmed，then all solutions of the equation with one variable were found．All values were given in the neighborhood of those points to given variables and the scope for the nongiven variable by the solution wasconfirmed， then all solutions of wanting problems were determ ined by rude and fine iteration method． The finding all solutions to forward displacement analysis problem of 6-SPS parallelrobot mechanism was solved by this method，general expression of Jacobian with Newton iteration was obtained，and thus all solutions for this problem were determined． This provides a simple and new realization method for robot mechanics design.

Key words： parallel robot mechanism       forward displacement analysis      chaos algorithm       Newtoniteration      matlab programming language      Julia set     
Published: 28 April 2003
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LUO You-Xin
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Cite this article:

LUO You-Xin, LI Da-Zhi. Finding all solutions to forward displacement analysis problem of
6-SPS parallel robot mechanism with chaos-iteration method. Chinese Journal of Engineering Design, 2003, 10(2): 70-74.

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https://www.zjujournals.com/gcsjxb/     OR     https://www.zjujournals.com/gcsjxb/Y2003/V10/I2/70


求一般6-SPS并联机器人机构的全部位置
正解的混沌迭代方法

采用简单的牛顿迭代法迭代，并将非线性方程视为非线性的动力学系统，利用使系统产生混沌的Julia集
的点求解方程的全部实数解，而Julia集的点在Jocobi矩阵行列式的值为零的解集的邻域内，给定矩阵的行列式的
值的表达式的一些变量为已知，仅有一个变量未知，把它转化为一元非线性方程，进而求出一元非线性方程全部
解． 再在给定变量的邻域内取定给定变量，根据一元非线性方程的全部解以确定该变量的搜索范围，运用粗、精迭
代法求解全部位置解．运用该算法编写了MATLAB程序，对一般机器人6-SPS机构的全部位置正解问题进行了
研究，得出了Jocobi矩阵的通用表达式，从而得到了其全部位置正解，为实际的6-SPS机构的位置正解问题提供了
全新的方法．

关键词： 并联机器人机构,  位置正解,  混沌算法,  牛顿迭代法,  Matlab程序,  Julia集 
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