关键词: 9杆巴氏桁架, 位移分析, 共形几何代数, 脱离坐标系, 一步消元

Abstract:

Based on conformal geometry algebra, a novel geometric modeling and computing method for the displacement analysis of a nine-link Baranov truss is proposed. Under the frame of conformal geometric algebra, in terms of the representations of the basic geometric elements such as point, sphere, surface, and point pair and the area sign of the triangle, two constraint equations are formulated by the intersection, dissection, and dual operation. Then, a 54th-degree univariate equation without extraneous roots and root loss is derived by one-step resultant elimination. The advantage of the proposed method lies in that the derivation of two constraint equations are free of coordinate and the elimination procedure is simplified due to the reduction of the number of constraint equations. Finally, a numerical example is given to validate the correctness of the method. The proposed method provides a new sight for the theoretical solution of the displacement analysis for other nine-link Baranov trusses.

Key words: nine-link Baranov truss, displacement analysis, conformal geometric algebra, free of coordinate system, one-step elimination