一种9杆巴氏桁架的位移分析  

Displacement Analysis of a Nine-Link Barranov Truss

作　　者：王品[1,2] 廖启征[3] 陆震[2] 

机构地区：[1]鲁东大学先进制造与自动化技术重点实验室,烟台264025 [2]北京航空航天大学自动化科学与电气工程学院,北京100191 [3]北京邮电大学自动化学院,北京100876

出　　处：《机械设计与研究》2009年第2期33-36,共4页Machine Design And Research

基　　金：中国博士后科学基金资助项目(20080440295);国家自然科学基金资助项目(50775012);国际科技合作资助项目(2008DFA81280)

摘　　要：将Dixon结式和Sylvester结式结合完成了一种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6×6Dixon矩阵,提取其中2行列元素的公因式,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40次方程。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。首次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40。The displacement analysis of a 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, which is a 6 x 6 matrix and contain two variables to be eliminated. Extract the greatest common divisor of two rows and two columns of Dixon matrix and c, ompute its determinant to obtain a new equation. This equation together with the forth constraint equation can be used to construct a Sylvester resultant. An univariate polynomial equation is obtained from determinant of Sylvester resultant. During using Sylvester resultant, the different degree of 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 40 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 Baranov truss are 40.

关 键 词：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 

分 类 号：TH112.1[机械工程—机械设计及理论]