一种9杆巴氏桁架的位置分析

Displacement Analysis of a Kind of Nine-Link Barranov Truss

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.首先使用结式对4个多项式方程直接消元,得到1个一元52次的多项式方程,再用辗转相除法求其他3个变量,在此过程中发现了6个增根.分析了产生增根的原因并提出了消元过程中避免增根的改进措施,即寻找相关向量之间的关系,在消元过程中降低变量的次数,直接得到一元46次方程.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46.

The vector equations are set up for four loop of one kind of nine-link Barranov truss by complex number vector method, and the four equations are changed into complex exponential number form. Firstly, a 52 degree univariate polynomial equation is deduced by using resultant elimination method. 6 extraneous roots are found during the process to obtain the other 3 variables by using Euclidean algorithm. The production reason of extraneous roots is analyzed and the improved method is proposed, that is the degree of the variables during the elimination process is reduced by searching relations among the vectors, so that a 46 degree univariate polynomial equation can be obtained directly. Finally, it is verified that the analytical solutions number of this kind of Barranov truss is 46 by a numerical example.