Optimum synthesis of path generating four-bar mechanisms using differential evolution and a modified error function

This paper proposes a new error function that can be used for optimum synthesis of path generating mechanisms. The proposed error function is formulated in a way that makes it suitable for use in applications when the primary requirement is that the synthesized path should match closely with the prescribed path. The proposed error function is used in the optimum synthesis of four-bar mechanisms. The method of differential evolution is used to carry out the optimization. Results for three path synthesis problems are presented. Results obtained by using the proposed error function are compared with those obtained by using the commonly used cumulative squares of Euclidean distance error function, on the basis of the values of transverse and longitudinal errors between the prescribed and synthesized paths. The usefulness of the proposed error function is established on the basis of the comparative results.

► We propose a modified error function for optimum path synthesis of mechanisms.
► We present comparative results for the proposed and commonly used error functions.
► Use of the modified error function decreases transverse error.
► Use of the modified error function increases longitudinal error.
► The proposed error function provides an alternative to the designer.