关键词: 9杆巴氏桁架, Dixon结式, Sylvester结式, 位移分析, 辗转相除法

Abstract: Dixon resultant and Sylvester resultant are adopted to complete the displacement analysis of a kind of nine-link Barranov truss with 2 coupled degree. Above all, vector method with complex number is used to construct four constraint equations and change them to complex number exponential form. Secondly, Dixon resultant for three constraint equations is used to construct a 6×6 Dixon matrix which eliminates two variables and compute the determinant of Dixon matrix to obtain a new equation. Then Sylvester resultant for the remainder constraint equation and the new equation is used to obtain a 52 order uni-variate polynomial closed form equation. The closed form equation is solved and the other variable is obtained by using Euclidean algorithm. Other two variables can be computed by Gaussian elimination. It is the first time to complete the dis-placement analysis of this kind of Barranov truss. A numerical example confirms that the algorithm is valid and the assembly configurations of the real number solutions are given. It shows that the maximum assembly configurations number of this kind of Barranov truss is 52.

Key words: Euclidean algorithm, Displacement analysis, Dixon resultants, Nine-link Barranov truss, Sylvester resultants