非平面9杆巴氏桁架的位移分析

将Dixon结式和Sylvester结式结合完成了一种非平面9杆巴氏桁架的位移分析。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Dixon结式法对3个方程式构造一个含有2个变元的6×6 Dixon矩阵，提取其中2行元素的公因式，将新矩阵的行列式展开后得到二元高次多项式方程，该方程与剩下一个方程使用Sylvester结式消去一变元，得到一元高次方程。Sylvester结式消元过程中，消元次序不同，所得一元高次方程的次数也不同，导致了增根的产生，分析了增根产生的原因并提出了改进措施，最终得到一元50次方程。回代过程中，使用辗转相除法和高斯消去法可以直接快速的求出其他3个变元。本文给出了这种巴氏桁架的解析解，并且通过数字算例验证了这种巴氏桁架的解析解数目是50。

Displacement Analysis of Non-Planar Nine-Link Barranov Truss

The displacement analysis of a non-planar nine-link Barranov truss is completed by using Dixon resultants together with Sylvester resultant. Firstly, four geometric loop equations are set up by using vector method in complex number fields. Secondly, three constraint equations are used to construct the Dixon resultants, it is a 6×6 matrix and contains two variables to be eliminated. Extraction of the greatest common divisor（GCD）of two rows of Dixon matrix and computation of its determinant to obtain a new equation are given. This equation together with the forth constraint equation can be used to construct a Sylvester resultant. A high-order univariate polynomial equationis obtained from determinant of Sylvester resultant. During using Sylvester resultant, the different degree of high-order univariate polynomial equation is obtained because the different variable is eliminated, which leads to extraneous roots. The reason of extraneous roots is analysed and the improved method is given. After that a 50 degree univariate polynomial equation can be obtained. Other variables can be computed by euclidean algorithm and Gaussian elimination. The closed form solution of this kind of Barranov truss is obtained. At last a numerical example confirms that analytical solutions of the Barranov truss are 50.