Síntesis óptima de un mecanismo plano para seguimiento de trayectoria utilizando evolución diferencial

Vega-Alvarado, Eduardo; Santiago-Valentín, Eric; Sánchez-Márquez, Álvaro; Solano-Palma, Adrián; Portilla-Flores, Edgar Alfredo; Flores-Pulido, Leticia

doi:10.13053/rcs-72-1-7

Cited by 3 publications

(3 citation statements)

References 7 publications

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“…The kinematics of four-bar mechanisms have been extensively treated; a detailed explanation is found in [ 36 , 37 ]. For analyzing the mechanism position, the closed loop equation can be established as follows:

Applying polar notation to each term of ( 2 ),

Using the equation of Euler on ( 3 ) and separating the real and imaginary parts,

Expressing the equation system ( 4 ) in terms of θ 4 ,

The compact form of Freudenstein's equation is obtained by squaring system ( 5 ) and adding its terms as follows:

where

Then the angle θ 3 can be calculated as a function of the parameters A 1 , B 1 , C 1 , and θ 2 ; this solution is generated by expressing sin⁡ θ 3 and cos⁡ θ 3 in terms of tan⁡( θ 3 /2):

A second-order lineal equation is obtained by substitution on ( 6 ):

From the solution of ( 9 ), the angular position θ 3 is given by ( 10 ):

A similar process is carried out to get θ 4 from ( 4 ) using Freudenstein's equation.…”

Section: Synthesis Of Four-bar Mechanismsmentioning

confidence: 99%

Two-Swim Operators in the Modified Bacterial Foraging Algorithm for the Optimal Synthesis of Four-Bar Mechanisms

Hernández-Ocaña

Pozos-Parra

Mezura-Montes

et al. 2016

Computational Intelligence and Neuroscience

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This paper presents two-swim operators to be added to the chemotaxis process of the modified bacterial foraging optimization algorithm to solve three instances of the synthesis of four-bar planar mechanisms. One swim favors exploration while the second one promotes fine movements in the neighborhood of each bacterium. The combined effect of the new operators looks to increase the production of better solutions during the search. As a consequence, the ability of the algorithm to escape from local optimum solutions is enhanced. The algorithm is tested through four experiments and its results are compared against two BFOA-based algorithms and also against a differential evolution algorithm designed for mechanical design problems. The overall results indicate that the proposed algorithm outperforms other BFOA-based approaches and finds highly competitive mechanisms, with a single set of parameter values and with less evaluations in the first synthesis problem, with respect to those mechanisms obtained by the differential evolution algorithm, which needed a parameter fine-tuning process for each optimization problem.

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Applying polar notation to each term of ( 2 ),

Using the equation of Euler on ( 3 ) and separating the real and imaginary parts,

Expressing the equation system ( 4 ) in terms of θ 4 ,

The compact form of Freudenstein's equation is obtained by squaring system ( 5 ) and adding its terms as follows:

where

Then the angle θ 3 can be calculated as a function of the parameters A 1 , B 1 , C 1 , and θ 2 ; this solution is generated by expressing sin⁡ θ 3 and cos⁡ θ 3 in terms of tan⁡( θ 3 /2):

A second-order lineal equation is obtained by substitution on ( 6 ):

From the solution of ( 9 ), the angular position θ 3 is given by ( 10 ):

A similar process is carried out to get θ 4 from ( 4 ) using Freudenstein's equation.…”

Section: Synthesis Of Four-bar Mechanismsmentioning

confidence: 99%

Two-Swim Operators in the Modified Bacterial Foraging Algorithm for the Optimal Synthesis of Four-Bar Mechanisms

Hernández-Ocaña

Pozos-Parra

Mezura-Montes

et al. 2016

Computational Intelligence and Neuroscience

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“…The kinematics of four-bar mechanisms have been extensively treated, detailed explanations are in [32] and [33]. For analyzing the mechanism position the closed loop equation Fig.…”

Section: A Kinematics Of the Mechanismmentioning

confidence: 99%

A Memetic Algorithm Applied to the Optimal Design of a Planar Mechanism for Trajectory Tracking

et al. 2016

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Memetic algorithms (MA), explored in recent literature, are hybrid metaheuristics formed by the synergistic combination of a population-based global search technique with one or more local search algorithms, which in turn can be exact or stochastic methods. Different versions of MAs have been developed, and although their use was focused originally on combinatorial optimization, nowadays there are memetic developments to solve a wide selection of numerical type problems: with or without constraints, mono or multi objective, static or dynamic, among others. This paper presents the design and application of a novel memetic algorithm, MemMABC, tested in a case study for optimizing the synthesis of a four-bar mechanism that follows a specific linear trajectory. The proposed method is based on the MABC algorithm as a global searcher, with the addition of a modified Random Walk as a local searcher. MABC is a modified version of the Artificial Bee Colony algorithm, adapted to handle design constraints by implementing the feasibility rules of Deb. Four-bar mechanisms are a good example of hard optimization problems, since they are used in a wide variety of industrial applications; simulation results show a high-precision control of the proposed trajectory for the designed mechanism, thus demonstrating that MemMABC can be applied successfully as a tool for solving real-world optimization cases.

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“…Cabrera, et al, realizaron un método para la síntesis óptima de mecanismos trabajando con algoritmos genéticos, utilizaron los problemas de síntesis de mecanismos planos de cuatro barras para probar el método [4]. Eduardo, et al, presentaron la síntesis de un mecanismo de cuatro barras para el seguimiento de una trayectoria lineal de seis puntos, presentó el problema de síntesis como un problema de optimización numérica, utilizó evolución diferencial como parte de la técnica de optimización [5].…”

Section: Introductionunclassified

Sobre la síntesis óptima de mecanismos

Foster-Vázquez

Portillo-Vélez

Vazquez-Santacruz

2019

JSL

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In the engineering design process, it is of particular relevance the problem statement that has to be solved to guarantee an optimal design. There is no general rule for this, and in the particular case of the synthesis of flat mechanisms, the solution strongly depends on the problem statement for the design or mechanism synthesis. The object this paper is presenting one proposal at synthesis problem of a four-bar flat mechanism for cartesian trajectory tracking. The mechanism synthesis problem is stated as a nonlinear optimization problem with non linear constraints. Four different approaches are considered in order to demonstrate the impact of the considered statement of the optimization problem for its solution. The solution of the four optimization problems is obtained by means of numerical calculations using genetic algorithms. The numerical results of the four optimization problem statemens are compared under fair circumstances and they depict the great influence of the initial problem statement for its solution.

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Síntesis óptima de un mecanismo plano para seguimiento de trayectoria utilizando evolución diferencial

Cited by 3 publications

References 7 publications

Two-Swim Operators in the Modified Bacterial Foraging Algorithm for the Optimal Synthesis of Four-Bar Mechanisms

Two-Swim Operators in the Modified Bacterial Foraging Algorithm for the Optimal Synthesis of Four-Bar Mechanisms

A Memetic Algorithm Applied to the Optimal Design of a Planar Mechanism for Trajectory Tracking

Sobre la síntesis óptima de mecanismos

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