New and efficient method based on Ratti-Wu method for solving forward kinematics problem (FP) of the parallel mechanism

Aim. To our knowledge, there is no paper in the open literature that uses the Ratti-Wu method to solve FP. We now present such a solution. In the full paper, we explain our new and efficient method in detail; in this abstract, we just add some pertinent remarks to listing the two topics of explanation; (1) Ratti-Wu method and symbolic elimination and (2) the mathematical model of FP for 3-6SPS Stewart platform; in topic 1, we point out that the solution of the FP of the parallel mechanism can be changed into a polynomial set to find a zero solution set, which is given by eq.(3) in the full paper; in topic 2, eqs.(4) through (9) are all taken from the open literature except that eq.(9) originally contains what we believe to be some mistakes which are eliminated by us. Thus, a new algorithm is put forward to solve symbolically the FP of the parallel mechanism. Table 1 in the full paper summarizes the results calculated by our new and efficient method and other methods, using Nanna and Waldron's data in pp. 241-242 in Ref.7, a book written by J. Angeles. These results show preliminarily that, compared with other algorithms, our algorithm is evidently much more efficient.