Optimal synthesis of mechanisms with genetic algorithms

TLDR: The main advantages of the solution methods of optimal synthesis of planar mechanisms are its simplicity of implementation and its fast convergence to optimal solution, with no need of deep knowledge of the searching space.

About: This article is published in Mechanism and Machine Theory.The article was published on 2002-10-01 and is currently open access. It has received 311 citations till now. The article focuses on the topics: Genetic algorithm & Evolutionary algorithm.

Figures

Table 2 Final mechanism of case 3 from several optimization methods

Fig. 8. Path tracked by the solutions to case 3 from different methods along with target points. ( ): exact gradient method; (––): KK algorithm; ( ): proposed method; (– – –): central difference; ( ): target points.

Table 1 Final mechanism of case 2 from several optimization methods

Fig. 7. Solution of case 2 from the different optimization methods. (––): KK algorithm; ( ): proposed method; ( ): target points.

Fig. 4. Scheme of the entire algorithm for the synthesis of mechanisms.

Fig. 1. Piecewise multipoint crossover for reproduction.

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Pii: s0094-114x(02)00051-4" ?

This paper deals with solution methods of optimal synthesis of planar mechanisms. 

Q2. What is the benefit of the algorithm?

In this method, which offers the benefit of being easy and simple to implement, an algorithm is presented to optimize the position error between the target points selected by the designer for the coupler point and the points reached by the resulting mechanism, subject to different constraints. 

Q3. What is the solution for the population size of 100?

The best solution was found for a population size of 100, where probabilities for crossover and mutation are 0.6 and 0.1 respectively, and the factor F of the disturbing vector ofthe selection equals 0.4. 

Q4. What is the description of the algorithm?

It was observed that the algorithm shows fast convergence to the optimal result and very low error of adjustment to target points. 

Q5. How long did the algorithm run on a 486 PC?

Regarding the algorithm proposed in this paper, the computation time was 2.86 s for case 2 and 3.25 s for case 3, against 16.98 s and 37.03 s of the genetic algorithm KK that runs on a 486 PC at 33 MHz. 

Q6. What is the main reason why the synthesis of mechanisms has been so successful?

The great increase in computer power has permitted the recent development of routines that apply numerical methods to the minimization of a goal function. 

Q7. What are the references on the subject?

References on the subject also exist by [7–9], solving the synthesis problem by using precision points to be reached by the coupler point of the mechanism, but these methods restrict the number of precision points in order to allow the solution of the mathematical system to be closed, and show problems caused by the wrong sequence of the precision points followed. 

Q8. How many iterations are shown in Fig. 5?

The evolution of the goal function along the iterations are shown in Fig. 5, where it is shown that the position error is reduced 99.99% in only 100 iterations. 

Q9. What is the effect of the gain of input angles between adjacent positions of the mechanism?

It was also observed that the gain of input angles between adjacent positions of the mechanism is very directly related to the distance between adjacent target points. 

Q10. What is the expression for the position of the coupler of the designed mechanism?

This expression for the position of the coupler of the designed mechanism is used in Eq. (6) to develop the first part of the goal function.