牛顿混沌迭代方法及四杆导引机构综合应用举例

机构学问题的数学模型常可化为多元非线性方程组，一般求解多元非线性方程组需要初始值，而初始值的选择是相当困难的。同伦方法不需初始值就能求出全部解，为求解这一问题提供了可行的方法，但需要培写专用的程序，且计算量比较大。该文结合MATLAB7．1高级程序设计语言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，利用使得系统产生混沌的Julia集的点求解方程的全实数解，而Julia集的点集用二周期逆像函数求得，再在其邻城内求解即可。运用该算法培写了MATLAB程序，并以平面四杆刚体导引机构综合问题为例进行了运算，找到了实现最大精确点时该问题的全部解，为实际机构的设计提供了多种选择方案，为机构学设计提供了一种迭代新算法。

Comprehensive application instance citation of Newton chaos iteration approach and four-bar guiding mechanism

The mathematical model of mechanism problems can usually be transformed into multi-variable non-linear equation sets. Generally the initial value is needed for solving the multi-variable non-linear equation sets, yet it is quite difficult to choose an initial value. The homology continuation algorithm could find out all solutions without needing the initial value, thus provided a feasible method for solving this problem, but it needs to compile a special purposed program and with a rather big amount of computation. Combined with high grade programming design language MATLAB7.1 and using simple Newton iteration method to make iteration and let the non-linear equation be looked upon as a non-linear dynamics system, this paper utilizes the points of Julia set, which makes the system to produce chaos, to solve all real numbered solution of the equation, whereas the point set of Julia set was obtained within its neighbor field by employing two periodic backward image function. The MATLAB program was compiled by the employment of this algorithm, and taking the comprehensive problem of planar four-bar rigid-body guiding mechanism as an example to carrying out the operation. All solutions of this problem, while the point of maximum accuracy has been achieved, were found out, thus provided multiple selectable schemes for the design of actual mechanism and also provided a kind of new iteration algorithm for mechanism design.