基于吴方法的一种7杆巴氏桁架位移分析研究

Forward Didplacement Analysis of a Seven-link Barravo Truss Based on Wu Method

将吴方法运用到平面基本运动链的位移分析中,完成了一种7杆巴氏桁架的位移分析。结合矢量法和复数法建立3个几何约束方程式,将其扩展为12个多项式方程,同时变量个数由3个增加到12个。这12个方程式中6个为线性方程,剩下6个是简单的非线性方程,并且各多项式的初式中最多有一个变元。使用吴方法经过6次循环得到特征列,其中第一个多项式的最高次数为18次。通过数字实例对结果进行了验证,得到18组无增无漏的解;计算结果表明,与同一巴氏桁架相关的所有Assur组的解的数目是相等的,装配构形完全相同,与我们的预期是一致的。吴方法在这一问题上应用,为求解其他机构学问题提供了新思路。

The Wu Method was applied to the forward displacement analysis of planar basic kinematic chains. A 7-link Barravo truss which is associated with 6-link and 9-joint Assur groups was studied. Three geometric constrain equations were established by using complex number method and vector method and then expanded into 12 polynomial equations. Among the 12 equations, six of them are linear equations and the rest are simple non-linear equations. At the same time the number of variables increases from 3 to 12. The initials of each polynome have at most one variable. Characteristic sets （CS） are obtained through six loops by using Wu method. The 1^st polynomial of the CS obtained is an 18-degree polynomial which is the highest. A numeric example with 18 groups of solutions which have no extraneous roots or miss roots shows that the solutions of Barravo trusses are equal and the configuration of all its associated Assur groups are the same as we expected. The Wu Method presented here provides a new way of thinking to solve other Assur groups or Barravo trusses.