On the optimum synthesis of a four-bar linkage using differential evolution and method of variable controlled deviations

Abstract

The synthesis of a four-bar linkage in which the coupler point performs approximately rectilinear motion is presented in this paper. The Grashof four-bar linkage whose geometries allow minimum deviations from the problem given for different parts of the crank cycle has been chosen. The motion of the mechanism crank point located in the prescribed environment of the given point on the observed segment is followed within the prescribed values of allowed deviation. Allowed deviations change during the optimisation process from the given maximum values to the given minimum ones. Very high accuracy for motion along a straight line at a large number of given points has been achieved by using the method of variable controlled deviations and by applying differential evolution algorithm (DE). The mechanism obtained is not symmetrical and the ratios of lengths between individual members of the mechanism are not normalised.