一种9杆巴氏桁架的位置正解  

Direct position analysis of a 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：《清华大学学报（自然科学版）》2006年第8期1373-1376,共4页Journal of Tsinghua University(Science and Technology)

基　　金：国家"九七三"重点基础研究项目(2004CB318000);国家自然科学基金资助项目(50475161);2004年教育部科学技术研究重点项目(104043);高等学校博士学科点资助项目(20050013006)

摘　　要：使用D ixon结式和Sy lvester结式相结合的方法研究了一种9杆巴氏桁架的位置正解。首先,用复数向量法对9杆巴氏桁架建立4个几何约束方程式并转化为复指数形式,对其中3个方程式构造一个消去两个变元的6×6 D ixon矩阵,提取其中两列的公因式后,将矩阵的行列式展开去掉一个多余的因式得到二元高次多项式方程,该方程与第4个约束方程使用Sy lvester结式消去其中任一变元后,得到一元46次方程。回代过程中,使用辗转相除法和G auss消去法可以直接求出其他3个变元。最后通过一个算例,证实了这种算法的可行性。The direct position analysis of a nine-link Barranov truss was analyzed by using the Dixon resultant together With the Sylvester resultant. Four geometric loop equations were constructed using the vector method and translated into complex exponential form. Then, three constraint equations were used to construct the Dixon resultant, which is a 6 ×6 matrix with two variables to be eliminated. Extracting two column＇s GCD and calculating the determinant of the Dixon matrix, a new equation is obtained after canceling a redundant factor. The new equation was combined with the 4th geometric equation to construct the Sylvester resultant which is a 46 degree univariate polynomial equation. Other variables were computed using the Euclidean algorithm and Gaussian Elimination. A numerical example verifies that this closed form solution for the Barranov truss is correct.

关 键 词：9杆巴氏桁架 位置正解 Dixon结式 Sylvester结式 辗转相除法 

分 类 号：TH112.1[机械工程—机械设计及理论]