The Research of Equal Probability Chaos Sequence Newton Iterative Methods and its Application to Mechanism Synthesis

The discovery of dynamical chaos is one of the main achievements in the modern science and how to expand its application has important significance to the development of modern science. Many questions in natural science and engineering are 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. To improve solving efficiency, the demand to chaos sequences is uniform distribution in every interval. The probability characteristics of three kinds of chaos were investigated. The simulations were work out with Mat lab software. For the first time, a new method to find all solutions based on utilizing equal probability chaos sequences to obtain initial points to find all solutions of the nonlinear questions was proposed and it has higher solving efficiency compared with unequal probability chaos sequences to find all solutions. The numerical example in linkage synthesis shows that the method is correct and effective. And, different equal probability chaos sequences has different solving efficiency, so, for the same kind of question to be solved we can find the best equal probability chaos sequences to be used. This provides a simple realization method for mechanics design.