基于Sylvester结式的9杆巴氏桁架位置分析  

Position Analysis of Nine-link Barranov Truss Based on Sylvester Resultant

作　　者：王品[1,2] 王昕彦[1] 陆震[2] 廖启征[3] 

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,北京100083 [3]北京邮电大学自动化学院,北京100876

出　　处：《机械科学与技术》2009年第11期1460-1463,共4页Mechanical Science and Technology for Aerospace Engineering

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

摘　　要：使用Sylvester结式消元法完成了一种9杆巴氏桁架的位置分析。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Sylvester结式消元法对4个方程式分3步消元,得到一个一元44次的多项式方程,在使用辗转相除法求解其他3个变量的过程中发现了4个增根。分析了增根产生的原因并提出了消元过程中去掉增根的方法,直接得到一元40次方程。最后通过一个数字算例,验证了这种巴氏桁架的解析解数目是40。The position analysis of a kind of nine-link Barranov truss is completed by using Sylvester resultants. First, four geometric loop equations are set up by using vector method in complex number fields. Then, four constraint equations are used to construct a Sylvester resultant by three steps and a 44-order univariate polynomial equation is obtained. Euclidean algorithm is used to solve other 3 variables, but the process shows that there are 4 extraneous roots in the 44-order univariate polynomial equation. The reason of extraneous roots is analysed and an improved method is given. Finally, a 40-order univariate polynomial equation is obtained. A numerical example is given and it verifies that the number of analytical solutions of the Barranov truss are 40.

关 键 词：9杆巴氏桁架 位置分析 Sylvester结式消元法 辗转相除法 

分 类 号：TH113.2[机械工程—机械设计及理论]