吴方法在平面并联机构位置正解中的应用

Wu's Method for Forward Displacement Analysis of the Planar Parallel Mechanisms

采用吴方法对平面并联机构位置正解问题进行了研究．吴方法是一种求解非线性方程组的数学机械化方法，采用这种方法任何非线性方程组都可以在有限步内得到解决．在给出了吴方法基本原理的基础上，对本问题进行了求解，并将原始方程组转化成为一个三角化的方程组．其中单变量方程的次数为６次，说明平面并联机构可以有６个不同的位姿．最后用数值实例进行了验证，给出了计算结果．吴方法在这一问题中的应用，为求解其它机构学难题提供了新途径．

The forward displacement analysis of the planar parallel mechanisms is studied by using Wu's method.Wu's method is a mechanical mathematics method for solving nonlinear equations.It can solve any nonlinear equations in limited steps.On the base of introducing theory of Wu's method,the problem is solved.The original equations of the problem is changed into triangulated equations in which a single unknown polynomial equation has 6th degree.The result shows that the planar parallel mechanism can have 6 different positions and orientations.In the end,a numerical example is studied.All the solutions for the example are listed.The presented method provides a new way for solving the other difficult mechanism problems.