9杆巴氏桁架的位移分析  

DISPLACEMENT ANALYSIS OF NINE-LINK BARRANOV TRUSS

作　　者：王品[1] 廖启征[1] 庄育锋[1] 魏世民[1] 

机构地区：[1]北京邮电大学自动化学院,北京100876

出　　处：《机械工程学报》2007年第7期11-15,共5页Journal of Mechanical Engineering

基　　金：国家重点基础研究发展计划(973计划;2004CB318000);国家自然科学基金(50475161);教育部科学技术研究(104043);高等学校博士学科点专项科研基金(20050013006)资助项目。

摘　　要：将Dixon结式和Sylvester结式结合完成耦合度为2的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,并将其转化成复指数形式,再使用Dixon结式对其中3个方程式构造一个消去两个变元的6×6Dixon矩阵。将矩阵的行列式展开后得到二元高次多项式方程,该方程与剩下一个含有两个变元的方程使用Sylvester结式消去其中任一变元后,得到一元52次封闭方程。求解封闭方程后,使用辗转相除法求出另外一个变元。回代过程中,使用高斯消去法求出剩余的两个变元。首次给出了这种巴氏桁架的解析解,并且通过数字算例进行验证算法的可行性,同时给出实数解所对应的装配构型图。结果表明:这种巴氏桁架的装配构型数目最大是52。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 univariate 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 displacement 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.

关 键 词：9杆巴氏桁架 位移分析 Dixon结式 Sylvester结式 辗转相除法 

分 类 号：TH113.2[机械工程—机械设计及理论]