Chaos Nested Intervals Method to Solve Nonlinear Equations and Planar Crank-Slide Mechanism Synthesis

The problem of planar crank-slide mechanism synthesis is transformed into nonlinear equations to be found, Newton iterative method is an important technique to one dimensional and multidimensional variables and iterative process exhibits sensitive dependence on initial guess point. For the first time, based on the study of statistic property of Logistic mapping, a new method to find all solutions of the nonlinear equations based on utilizing chaos nested intervals of Logistic mapping to obtain locate initial points is proposed. The numerical example shows that the method is effective. This provides a simple realization method for mechanics design.