Dimension Synthesis Optimization Of Four Bar Linkage Based On Error Feedback Method

With the development of industrial technology,more and more mechanical equipment is developing towards automation and intelligence.The four-bar mechanism gradually play an important role in mechanical engineering.In order to improve the design accuracy of industrial machinery,the scale synthesis problem of four-bar mechanism needs to be solved.However,the current algorithm for solving the four-bar mechanism model still has some shortcomings when dealing with the constraint conditions.When solving the scale synthesis problem of four-bar mechanism,penalty function method is usually used to deal with the constraint conditions.However,there are some disadvantages when the penalty function method copes with the constraints.First,the penalty function method evaluates the solutions outside the constraints,wasting computing resources.Second,solutions outside the constraints do not play a helpful role in the corresponding evolutionary algorithm.Third,for the next generation,solutions outside the constraints may be selected as the parents,and the probability of generating effective offspring is thus reduced.We therefore propose a method to solve the linear constraint problem.The main idea is as follows: in the process of obtaining the optimal solution,if the offspring is not within the bounds of the constraints,the error between the new solution and the constraint boundaries is calculated.The error is then proportionally distributed among the parameters of the model,and a new offspring is obtained within the constraint boundaries.The new offspring then participates in the operation of the optimized evolutionary algorithm in place of the previous offspring.The advantages of this method are as follows: first,it ensures that all offspring satisfy the constraints and save computing resources;second,if the newly generated offspring are better than the previous ones,they can continue to participate in the generation of offspring;third,because all offspring satisfy the constraints,this method ensures that all the function fitness values are valid.In order to verify the performance of the error feedback method,based on the intelligent optimization algorithm,a classical constraint benchmark function and the Markov prediction model about gear transmission are respectively solved.Finally,it is found that this method has good convergence,robustness and other comprehensive performance.Then,the error feedback method is applied to the optimization of the scale synthesis problem of the four-bar linkage.Particle swarm optimization algorithm,differential evolution algorithm and teaching and learning algorithm are used to optimize the four-bar model,and the constraint conditions were processed by error allocation method and penalty function method respectively.Numerical experiments show that the error feedback algorithm has better comprehensive performance than other methods when solving constrained optimization problems.