Closed-form displacement analysis of a kind of non-planar nine-link Barranov truss

The displacement analysis of a kind of nonplanar nine-link Barranov truss is completed by using Dixon resultants together with Sylvester resultant. Firstly, four geometric loop equations are set up by using vector method, and then they are changed into complex number form. Secondly, three constraint equations are used to construct the Dixon resultants, which is a 6times6 matrix and contain two variables to be eliminated. Extract the GCD of two columns and two rows of Dixon matrix and compute its determinant to obtain a new equation. This equation together with the forth constraint equation can be used to construct a Sylvester resultant. A 46 degree univariate polynomial equation is obtained from determinant of Sylvester resultant. Other variables can be computed by Euclidean algorithm and Gaussian elimination. At last a numerical example confirms that assembly configurations number of the Barranov truss is 46.