Closed-form displacement analysis for a nine-link Barranov truss or a eight-link Assur group

The closed-form displacement analysis of one kind of nine-link Barranov trusses which are interrelated to eight kinds of eight-link Assur groups is solved when a rigid quadrangular link is fixed. It is also equivalent to displacement analysis of one kind of eight-link Assur groups. The method used here is vector with complex numbers. Several vector equations are established according to different loops. Then the equations are changed into the form of complex numbers. By algebraic elimination, the problem is reduced to a single unknown equation which is proved to be 48th degree. It shows that this structure of Barranov truss has 48 possible assembly configurations. Moreover, all the Assur groups which interrelate to this nine-link Barranov truss will have the same number of solutions.