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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.
A simple Newton iterative method is used to iterate the nonlinear equations and consider the nonlinear equations as nonlinear dynamical systems. By using the points of the Julia set that make the system produce chaos, all the real solutions of the equations are solved, while the points of Julia set are in the determinant of the determinant of Jocobi matrix In the neighborhood of the solution set with zero, some variables of the expression for the determinant value of a given matrix are known, only one variable is unknown, and it is transformed into a unary nonlinear equation, and then the univariate nonlinear equation Then all the solutions are obtained in the neighborhood of a given variable, and the search range of the variable is determined according to the whole solution of the unary nonlinear equation, the rough and refined iterative method is used to solve all the position solutions. MATLAB Program, a general solution to the problem of all position of 6-SPS mechanism of a general robot is studied. The general expression of Jocobi matrix is obtained, and all the positive solutions of the Jocobi matrix are obtained, which provides a completely new solution to the problem of positive position of the 6-SPS mechanism Methods.