基于Dixon结式的一种9杆巴氏桁架位置分析

将Dixon结式运用到基本运动链的位置分析中,完成了一种对称型非平面的9杆巴氏桁架的位置分析的研究,首次给出了这种巴氏桁架解析解的个数.结合矢量法和复数法建立了4个几何约束方程式,使用Dixon结式构造22×22的Dixon矩阵,对两列提取公因式后展开矩阵的行列式得到一元64次多项式方程,回代过程中去掉6组增根后得到58组解.为了对结果进行验证,使用同伦连续法对同一个数字算例进行计算,两种方法得到结果一致,说明这种巴氏桁架的装配构形数目是58.

Direct position analysis of nine-link Barranov truss based on Dixon resultants

The assembly configurations of a kind of non-planar nine-link Barranov truss were analyzed by using Dixon's resultants. Four equations were established for the four loops of the mechanism by using vector method and they were changed into complex exponent numbers form. Dixon method was adopted to construct a 22×22 Dixon matrix and then the greatest common divisor of two columns was extracted. After expanding the determinant of the matrix, a 64 degree univariate polynomial equation was obtained and 6 extraneous roots were canceled in the process of solving the other 3 variables. The same result could be obtained by using homotopy continuations method. A numerical example is given and it verifies that the number of assembly configurations of this kind of Barranov truss is 58.