关键词: Sylvester消元, 并联机构, 矢量消元, 位置正解

Abstract: A new algebraic elimination algorithm for the forward displacement analysis of a general 6-4 in-parallel platform (6-4SPS) is presented. A 6-4SPS structure is changed into an equivalent 2RPS-2SPS structure and a mathematical modeling is established based on the trilateration formula containing a few number of Cayley-Menger determinants derived by using barycentric coordinates; five basic constraint equations with five variables are obtained from eight equations with eight variables by introducing vector loop relationships and substitution variables; the equation containing two variables is derived from the four equations containing other three variables by the vector elimination; a 32th-degree polynomial equation in a single variable is derived from a 10×10 Sylvester resultant which is constructed from the equation by vector elimination and the last of the five. A numerical example is given to confirm the results, whose solutions agree with the original equations without extraneous roots.

Key words: Forward displacement analysis, In-parallel platform, Sylvester resultant, Vector elimination