The Application Of Interval Analysis In The Position Solution Of Nonlinear Mechanism

The research content in this dissertation is an attempt and exploration to bring the interval analysis theory into mechanical design theory. In mechanical design, the solution of some mechanisms will eventually be transformed into very complicated nonlinear equations, such as the spatial linkage mechanisms. However, solving multiple high-order non-linear equations is generally very difficult and hard to get full solutions guaranteed, while interval analysis which is a new branch of mathematics has outstanding advantages in this field. Therefore, the dissertation here presents a new solution method using interval analysis to solve nonlinear mechanism position functions. Different from interval iteration method and other methods, the new interval analysis solution consists of two sections: the interval section and the following point iteration section. Interval section tells out all the sub-intervals which contain unique solution and the point section converges to the approximation of the exact solution in each sub-interval. The new method avoids the complexity of interval iteration method and overcomes the shortcoming that the convergence depends on starting point and is difficult to obtain all the solutions in other iterative methods, which is a innovation in solving method. In addition, a interval method for simplifying initial domain is proposed in the interval section of the position solution for parallel mechanism, which makes the domain chosen not blindly but theoretically and is another innovation in this article. In the dissertation, taking positive position solutions of a 6-DOF parallel mechanism as an example, the whole solving idea and concrete method is expatiated firstly. Then, the programming algorithm is given based on the software Matlab and Intlab. Finally, it is validated using a concrete flat-base solution.