中文摘要：

使用Sylvester结式消元法完成了一种9杆巴氏桁架的位置分析。首先使用矢量法和复数法建立4个几何约束方程式，再使用Sylvester结式消元法对4个方程式分3步消元，得到一个一元44次的多项式方程，在使用辗转相除法求解其他3个变量的过程中发现了4个增根。分析了增根产生的原因并提出了消元过程中去掉增根的方法，直接得到一元40次方程。最后通过一个数字算例，验证了这种巴氏桁架的解析解数目是40。

英文摘要：

The position analysis of a kind of nine-link Barranov truss is completed by using Sylvester resultants. First, four geometric loop equations are set up by using vector method in complex number fields. Then, four constraint equations are used to construct a Sylvester resultant by three steps and a 44-order univariate polynomial equation is obtained. Euclidean algorithm is used to solve other 3 variables, but the process shows that there are 4 extraneous roots in the 44-order univariate polynomial equation. The reason of extraneous roots is analysed and an improved method is given. Finally, a 40-order univariate polynomial equation is obtained. A numerical example is given and it verifies that the number of analytical solutions of the Barranov truss are 40.