Optimal Synthesis of Mechanisms by using an EDA based on the Normal distribution

Sergio Ivván Valdez Peña, Arturo Hernández Aguirre, Salvador Botello Rionda, Eusebio E. Hernández-Martínez


The problem of synthesis of mechanisms is to find the adequate dimensions in the elements in order to perform a given task. The task is defined by a set of points named: precision points. The problem is defined as minimizing the distance among the precision points and the actual position of the mechanism, the decision variables are the elements dimensions, the position and rotation of the relative coordinate system and two parameters related with the initial position and velocity. The proposal of this work is an algorithm for automatized synthesis of mechanisms. We use an Estimation of Distribution Algorithm (EDA), to approximate the optimum, by sampling and estimating a Normal multivariate probability distribution. Each sample is a candidate solution (a candidate mechanism), then we measure the difference between the precision points and the actual positions of the mechanism, the best candidate solutions are used to update the probability distribution, and the process is repeated until convergence is reached. We apply the proposed method for the synthesis of a Four-bar planar mechanism with closed chain. The obtained results are near-optimal designs that are better than others reported in the literature. The proposed method is a competitive alternative for the automatized synthesis of mechanism. We obtain high quality results when compare our approach with other reported in the literature. Additionally, the proposal presents other interesting features: the number of precision points can be increased without the need of increasing the dimension of the search space, in addition, the algorithm can be used for optimizing any mechanism. The results suggest that EDAs can successfully approach this kind of problems, hence, future work contemplate to use the same strategy for tackling more complex problems, possibly involving control parameters, or intending to design singularity-free closed kinematic chains.


Synthesis of mechanisms; Evolutionary techniques; Estimation for distribution algorithms; optimization


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DOI: https://doi.org/10.21640/ns.v6i11.65


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