Interval Iterative Method Based on Liu Chaotic System for Solving Planar Mechanism Synthesis

The problem about mechanism synthesis and approximate synthesis can be converted to nonlinear equations in order to find solutions, but it is very difficult to find all solutions because of the strong coupling of the nonlinear equations. Newton iterative method as an important technique to one dimension and multi-dimension is more sensitive to the initial value and has only a solution obtained. By combining interval Newton iterative method with chaotic sequences and taking chaotic sequences generated in new chaotic system proposed by Liu as the initial values of interval Newton iterative method in the mechanism synthesis problem, all solutions were found. The numerical example in crank-slider mechanism shows the method is correct and effective. The interval iterative method based on chaos can run within the real range, and it provides a new approach for solving mechanism synthesis and other strongly nonlinear equations..