Control of the optimum synthesis process of a four-bar linkage whose point on the working member generates the given path

Abstract

This paper presents the optimum synthesis of a four-bar linkage in which the coupler point performs a path composed of rectilinear segments and a circular arc. The Grashof four-bar linkage whose geometry provides minimum deviations from the given problem for certain parts of the crank cycle is chosen. The motion of the coupler point of the four-bar linkage is controlled within the given values of allowed deviations so that it is always in the prescribed environment of the given point on the observed segment. The synthesis process tends to bring only those path segments that are beyond the boundaries within the prescribed boundary deviations. During the synthesis, allowed deviations change from the initial maximum values to the given minimum ones. Groups of mechanisms realising satisfactory approximation to the desired motion can be obtained by the method of controlled decrease of allowed deviations with the application of the Differential Evolution (DE) algorithm.