Hyper-chaotic mapping Newton iterative method to mechanism synthesis - Youxin, Luo (Strojniški vestnik, 2008)
The synthesis and approximate synthesis problems for planar mechanism can be transformed into a system of multivariable polynomial equations or general nonlinear equations. Newton iterative method is an important technique to one dimensional and multidimensional variables and iterative process exhibits sensitive dependence on initial guess point. Based on utilizing multi-start point technique and hyper-chaotic mapping (Hénon hyper-chaotic system) as initial points of Newton iterative method, an innovative new method to find all solutions of general nonlinear equations in kinematics quickly and effectively was proposed. The computing step and method was given. The numerical examples in linkage synthesis and approximate synthesis show that the method is correct and effective.
Keywords: kaotični sistemi; mehanizmi spajanja; sinteza mehanizmov; nelinearne enačbe