平面曲柄滑块机构函数综合的混沌方法  

Chaos method for function synthesis of planar crank-slider mechanism

作　　者：罗佑新[1] 

机构地区：[1]常德师范学院机械工程系,湖南常德415003

出　　处：《机械设计》2003年第5期27-30,共4页Journal of Machine Design

基　　金：教育部重点科研项目 ( 0 2 10 8) ;湖南省教育厅青年资助项目 ( 0 2B0 36 )

摘　　要：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 ,求解方程的全部实数解。而Julia集的点在Jocobi矩阵行列式值为零的解集的邻域内 ,给定矩阵的行列式值的表达式的一些变量为已知 ,仅只有一个变量未知 ,把它转化为一元非线性方程 ,进而求出其全部解。再确定未给定变量的搜索范围 ,运用粗、精迭代在其邻域内求解即可。运用该算法编写了MATLAB程序 ,对平面曲柄滑块机构的函数综合问题进行了研究 ,得出了Jocobi矩阵的通用表达式 ,从而找到了实现最大精确点时该问题的全部解 ,为实际的平面曲柄滑块机构的设计提供了多种选择方案 。By adopting simple iteration of Newton method, and l et the nonlinear equation be regarded as nonlinear dynamic system, the complete real number solution of equation could be solved by utilizing points of Julia set which leads the system to produce chaos. Points of Julia set are situated in the neighboring region of the disaggregation when the value of Jocobian matrix determinent equals to zero. Some variables in the expression of values for determinent of given matrix were known, except one of the variables was unknown. Complete solutions of the expression are proceed to be found by means of converting the expression into non-linear equation with one variable. After the searching scope of non-specified variables was determined, its solutions can be found in their neighboring regions by the use of coarse and fine iteration. The MATLAB program was compiled by applying this algorithm. A research was carried out on problems of function synthesis for planar crank-slider mechanism, and obtained the general expression of Jocobian matrix,thus sought out complete solutions of that problem when the most precise positions were defined. Multiple schemes of selection were provided for the design of practical planar crank-slider mechanism, and an all new method was provided for mechanism design.

关 键 词：平面曲柄滑块机构 混沌算法 牛顿迭代法 JULIA集 函数综合 

分 类 号：TH112.1[机械工程—机械设计及理论] TH133.5