9杆巴氏桁架的位置分析

以非平面基本运动链(9杆巴氏桁架)为研究对象,对其数学模型和消元过程进行了研究。使用复数向量法对9杆巴氏桁架4个回路建立几何关系,列出矢量方程组并转化成为复指数形式。使用Sylvester结式对4个多项式方程依次两两消元,得到一个一元50次的多项式方程,求解后使用辗转相除法求其他3个变量,完成位置分析。最后通过一个算例,验证了这种巴氏桁架的解析解的数目为50。

Displacement Analysis of a Nine-link Barranov Truss

The mathematics model and elliminiation process of the non-planar basic movement chain(nine-bar Barranov truss) is studied.The vector equations are set up for four loops of the nine-link Barranov truss by complex number vector method,and the four equations are changed into complex exponential number form.A 50 degree univariate polynomial equation is deduced by using resultant elimination method.The other 3 variables are obtained by using Euclidean algorithm.Finally,it is verified that the number of analytical solutions of this kind of Barranov truss is 50 by a numerical example.