Research on Position Analysis of a Kind of Nine-Link Barranov Truss

Abstract

The position analysis of a nine-link Barranov truss is finished by using Dixon resultants together with Sylvester resultants. Above all, using vector method in complex plane to construct four constraint equations and transform them into complex exponential form, then three constraint equations are used to construct a 6×6 Dixon matrix, which contains two variables to be eliminated. We extract the greatest common divisor (GCD) of two columns of Dixon matrix and compute its determinant to obtain a new equation. This equation together with the fourth constraint equation can be used to construct a Sylvester resultant. A 50deg univariate polynomial equation is obtained from the determinant of Sylvester resultant. Other variables can be computed by Euclidean algorithm and Gaussian elimination. Lastly, a numerical example confirms that the analytical solution number of the Barranov truss is 50. It is the first time to complete analytical solutions of this kind of Barranov truss.