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。 A positive position solution of a 9-bar Pasteur truss is studied by using a combination of D ixon knots and Sy lvester knuckles. First of all, by using the complex vector method, we establish 4 geometric constraint equations for 9-bar Buttress truss and convert them into complex exponential forms. For each of the 3 equations, construct a 6 × 6 D ixon matrix with two variables eliminated and extract two of them After the common factor, the determinant of the matrix is ​​expanded to remove a redundant factor to obtain a binary higher order polynomial equation. The equation is canceled 46 times by using Sy lvester knot elimination formula equation. In the process of returning to the motherland, the other three variables can be directly obtained by using the tangential division method and the Gauss elimination method. Finally, an example is given to prove the feasibility of this algorithm.