Development of a computer program for dimensional synthesis of a four-bar mechanism that generates a prescribed trajectory

Abstract

This work aims to develop a computational tool for synthesizing a four-bar linkage mechanism that can generate a prescribed path for a point coupler link to follow. The dimensional synthesis of the mechanism involves determining the lengths of each of its links. In this case, two possible configurations are evaluated: crank-rocker and/or double crank. The prescribed path consists of an arbitrary number of points contained in a plane, along with the corresponding rotation degrees of the driver element. Dimensioning the mechanism involves many variables, and it is possible to obtain various configurations that generate paths that are approximately the desired path. Therefore, the synthesis problem arises as an optimization problem in which the objective function seeks to minimize the Euclidean norm between the prescribed points and the points earned. To solve the optimization problem, a user-friendly computer program called SIDIGETRA was developed using the genetic algorithms numerical technique. Design constraints were imposed to obtain an open configuration of the mechanism and to avoid branching defects, order, and Grashof. The program's proper functioning was validated by comparing the results obtained in case studies published in a research article in which the genetic algorithms technique was also applied. The percentage relative errors between the coordinates of the obtained points and prescribed points were calculated and found to be satisfactory. Additionally, the results generated by SIDIGETRA were validated with a visual comparison between the prescribed trajectory and the one obtained by simulating the position analysis of the synthesized mechanism using a commercial software tool designed for this purpose.