A method for position analysis of a kind of nine-link Barranov truss

This paper studies the position analysis of a kind of nine-link Barranov truss. Firstly, vector method is used to derive four geometric constraint equations, which are subsequently transformed into complex exponent form by Euler's complex number formula. Three of these constraint equations are picked to construct the Dixon resultant, a 6 × 6 matrix of two variables. Expanding the determinant of this matrix yields an additional equation which is then combined with the forth constraint equation to construct a Sylvester resultant matrix. The determinant of this matrix yields a univariate polynomial of order 56. Solving this polynomial, we obtain all solutions to the suppressed variable. The solutions of other variables can be computed by Euclidean algorithm and Gaussian elimination. A numerical example is provided to verify the result. It is the first time that this kind of Barranov truss is solved analytically.