Abstract:

The problem of synthesizing a planar 4-bar linkage with given two fixed pivots such that the coupler curve passes through five given points is considered with the Groebner-Sylevester hybrid approach. Firstly, the closed-form equations of the single point are constructed. Next, the reduced Groebner basis under degree lexicographic ordering for the closed-form equations is obtained using computer algebra. Selecting 23 Groebner bases from 89 ones, a 23×23 Sylvester’s matrix can be constructed. A 36th degree univariate equation is obtained directly from the determinate of the matrix. The same result can be obtained with continuation method. A numerical example is given and it verifies that the problem has at most 36 solutions in the complex field.

Key words: path synthesis, mechanisms synthesis, Groebner basis, Sylvester resultant