Five precision point-path synthesis of planar four-bar linkage using algebraic method

Abstract

The problem of synthesizing a planar four-bar linkage with two given fixed pivots such that the coupler curve passes through five given points is considered with the Groebner-Sylvester hybrid approach. First, closedform equations of a single point are constructed. The reduced Groebner basis in degree lexicographic ordering for the closed-form equations is then obtained using computer algebra. A 23 6 23 Sylvester's matrix can be constructed by selecting 23 out of 89 Groebner bases. A 36th degree univariate equation is obtained directly from the determinate of the matrix. The same result can be obtained with a continuation method. A numerical example is given and verifies that the problem has at most 36 solutions in the complex field.

Synthesis of an NR Robot With Four-Bar Constraining Modules

“…See Huang et al (2008) [10] for recent work on path synthesis for four-bar linkages. The use of four-bar linkage modules to constrain an nR serial chain extends the work by Soh and McCarthy [6,7], who use RR links to constrain nR serial chains.…”

Study of Differential Evolution Variants in the Dimensional Synthesis of Four-Bar Grashof-Type Mechanisms

“…The last one is the topic related to our work. It is worth mentioning that the dimensional synthesis of a simple mechanism such as a four-bar mechanism is not a trivial task and can essentially be performed by graphical [19], algebraic [20], analytic [19], or optimization [21] methods. The first three methods are helpful for synthesizing four-bar mechanisms when the trajectories (paths) are relatively simple.…”

“…10] T , c2 = [17.66, 15.142] T , c3 = [11.736, 17.878] T , c4 = [5, 16.928] T , c5 = [0.60307, 12.736] T , c6 = [0.60307, 7.2638] T , c7 = [5, 3.0718] T , c8 = [11.736, 2.1215] T , c9 = [17.66, 4.8577] T , c10 =[20,10] …”