Abstract:

The vector equations are set up for four loop of one kind of nine-link Barranov truss by complex number vector method, and the four equations are changed into complex exponential number form. Firstly, a 52 degree univariate polynomial equation is deduced by using resultant elimination method. 6 extraneous roots are found during the process to obtain the other 3 variables by using Euclidean algorithm. The production reason of extraneous roots is analyzed and the improved method is proposed, that is the degree of the variables during the elimination process is reduced by searching relations among the vectors, so that a 46 degree univariate polynomial equation can be obtained directly. Finally, it is verified that the analytical solutions number of this kind of Barranov truss is 46 by a numerical example.

Key words: Nine-Link Barranov Truss, Displacement Analysis, Resultant Elimination, Euclidean Algorithm