Kinematic analysis is fundamental for the mechanism synthesis. The kinematic analysis of mechanism is attributed to find the solutions of the nonlinear equations and this process is very difficult. 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, a new method based on utilizing meshed chaos mapping method to obtain locate initial points to find all solutions of the nonlinear questions was proposed. The numerical examples in linkage synthesis and approximate synthesis show that the method is correct and effective.