Dimensional Synthesis of a Six-bar Shaper Mechanism with the Genetic Algorithm Optimization Approach

Abstract

—This paper provides an approach based on the genetic algorithm for the dimensional synthesis of a six-bar mechanism for a shaper machine. The main purpose of the optimization algorithm is to maintain the velocity of the mechanism’s slider constant within a specified range of the rotational motion of the input link. Therefore, first, an objective function is defined for the slider. Then, the velocity function of the slider is calculated using a set of mathematical relationships and the mechanism’s kinematic constraints. In order for this function to reach the objective function, a cost function is defined. This cost function is minimized, and the output approaches the objective function by selecting the appropriate parameters for the mechanism. To this end, four accuracy points are selected within a specific range of motion of the input link. Subsequently, the distances between the points on the velocity function of the slider and the predetermined function are calculated at these four points. The goal is to minimize these four distances. Hence, a cost function is defined in the form of the squares of the sums of these distances and is minimized using the genetic algorithm. Therefore, this cost function is used to minimize the error between the desired points and the points generated by the mechanism and can be affected by factors such as the lengths of the links, the transmission angles, the Grashof condition, and the mechanism type. In the genetic algorithm, the population, crossover, or mutation determines the accuracy of the results. The purpose of this research is to find the optimal dimensions of the links in order to minimize the error between the ideal and actual slider velocity functions. Ultimately, a numerical example is provided where the optimal dimensions are suggested by the optimization algorithm.