关键词: 非平面9杆巴氏桁架, 位移分析, 结式消元法, 辗转相除法, 高斯消去法

Abstract:

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.

Key words: non-planar nine-link Barranov truss, displacement analysis, resultant elimination, Euclidean algorithm,
Gaussian elimination