A Graph-Theory-Based Method for Topological and Dimensional Representation of Planar Mechanisms as a Computational Tool for Engineering Design
In this paper, a graph-theory-based approach for representing planar mechanisms is presented, the Santiago Portilla method (SPM). From the corresponding adjacency matrix, SPM generates an extended matrix containing the complete characterization of a planar mechanism, including all the information ab...
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doaj-ee8141282999441da2138aeaec6ac1552021-03-29T22:06:36ZengIEEEIEEE Access2169-35362019-01-01758759610.1109/ACCESS.2018.28855638567881A Graph-Theory-Based Method for Topological and Dimensional Representation of Planar Mechanisms as a Computational Tool for Engineering DesignEric Santiago-Valenten0https://orcid.org/0000-0002-3197-9544Edgar Alfredo Portilla-Flores1https://orcid.org/0000-0002-8951-1346Efren Mezura-Montes2Eduardo Vega-Alvarado3https://orcid.org/0000-0001-9464-7996Maria Barbara Calva-Yanez4https://orcid.org/0000-0003-3500-4880Martin Pedroza-Villalba5https://orcid.org/0000-0001-8208-5244Instituto Politécnico Nacional–CIDETEC–Group of Research and Innovation in Mechatronics–GRIM, México, MéxicoInstituto Politécnico Nacional–CIDETEC–Group of Research and Innovation in Mechatronics–GRIM, México, MéxicoCentro de Investigacíon en Inteligencia Artificial, Universidad Veracruzana, Xalapa, MéxicoInstituto Politécnico Nacional–CIDETEC–Group of Research and Innovation in Mechatronics–GRIM, México, MéxicoInstituto Politécnico Nacional–CIDETEC–Group of Research and Innovation in Mechatronics–GRIM, México, MéxicoInstituto Politécnico Nacional–CIDETEC–Group of Research and Innovation in Mechatronics–GRIM, México, MéxicoIn this paper, a graph-theory-based approach for representing planar mechanisms is presented, the Santiago Portilla method (SPM). From the corresponding adjacency matrix, SPM generates an extended matrix containing the complete characterization of a planar mechanism, including all the information about both topology and geometry. This matrix representation can be used for the optimal design of mechanisms, allowing simultaneously the topological and dimensional synthesis by means of computational tools such as the metaheuristic algorithms. A case study corresponding to the design of a fixed-linear-trajectory tracker mechanism is included in order to test the efficiency of the proposed approach. It was carried out by addressing the design as an optimization problem and solving it with the differential evolution algorithm, representing the individuals in its population by the matrix form generated by the SPM. The results of the case study show that the SPM and its matrix representation constitute a useful and flexible tool for the solution of the real engineering problems involving the design of planar mechanisms.https://ieeexplore.ieee.org/document/8567881/Graph theorytopological designdimensional synthesismatrix representationoptimization |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Eric Santiago-Valenten Edgar Alfredo Portilla-Flores Efren Mezura-Montes Eduardo Vega-Alvarado Maria Barbara Calva-Yanez Martin Pedroza-Villalba |
spellingShingle |
Eric Santiago-Valenten Edgar Alfredo Portilla-Flores Efren Mezura-Montes Eduardo Vega-Alvarado Maria Barbara Calva-Yanez Martin Pedroza-Villalba A Graph-Theory-Based Method for Topological and Dimensional Representation of Planar Mechanisms as a Computational Tool for Engineering Design IEEE Access Graph theory topological design dimensional synthesis matrix representation optimization |
author_facet |
Eric Santiago-Valenten Edgar Alfredo Portilla-Flores Efren Mezura-Montes Eduardo Vega-Alvarado Maria Barbara Calva-Yanez Martin Pedroza-Villalba |
author_sort |
Eric Santiago-Valenten |
title |
A Graph-Theory-Based Method for Topological and Dimensional Representation of Planar Mechanisms as a Computational Tool for Engineering Design |
title_short |
A Graph-Theory-Based Method for Topological and Dimensional Representation of Planar Mechanisms as a Computational Tool for Engineering Design |
title_full |
A Graph-Theory-Based Method for Topological and Dimensional Representation of Planar Mechanisms as a Computational Tool for Engineering Design |
title_fullStr |
A Graph-Theory-Based Method for Topological and Dimensional Representation of Planar Mechanisms as a Computational Tool for Engineering Design |
title_full_unstemmed |
A Graph-Theory-Based Method for Topological and Dimensional Representation of Planar Mechanisms as a Computational Tool for Engineering Design |
title_sort |
graph-theory-based method for topological and dimensional representation of planar mechanisms as a computational tool for engineering design |
publisher |
IEEE |
series |
IEEE Access |
issn |
2169-3536 |
publishDate |
2019-01-01 |
description |
In this paper, a graph-theory-based approach for representing planar mechanisms is presented, the Santiago Portilla method (SPM). From the corresponding adjacency matrix, SPM generates an extended matrix containing the complete characterization of a planar mechanism, including all the information about both topology and geometry. This matrix representation can be used for the optimal design of mechanisms, allowing simultaneously the topological and dimensional synthesis by means of computational tools such as the metaheuristic algorithms. A case study corresponding to the design of a fixed-linear-trajectory tracker mechanism is included in order to test the efficiency of the proposed approach. It was carried out by addressing the design as an optimization problem and solving it with the differential evolution algorithm, representing the individuals in its population by the matrix form generated by the SPM. The results of the case study show that the SPM and its matrix representation constitute a useful and flexible tool for the solution of the real engineering problems involving the design of planar mechanisms. |
topic |
Graph theory topological design dimensional synthesis matrix representation optimization |
url |
https://ieeexplore.ieee.org/document/8567881/ |
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