Forward displacement analysis of the general 6–6 Stewart mechanism using Gröbner bases

A new algorithm for the solution of the forward displacement analysis of the general 6–6 Stewart mechanism is presented in this paper. Gröbner basis theory is used and the problem of the forward displacement is reduced to a 40th-degree polynomial equation in a single unknown from a constructed 13 × 13 Sylvester’s matrix which is relatively small in the size, from which 40 different locations of the moving platform can be derived. Numerical examples confirm the efficiency of the procedure.