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...

Full description

Bibliographic Details
Main Authors: Eric Santiago-Valenten, Edgar Alfredo Portilla-Flores, Efren Mezura-Montes, Eduardo Vega-Alvarado, Maria Barbara Calva-Yanez, Martin Pedroza-Villalba
Format: Article
Language:English
Published: IEEE 2019-01-01
Series:IEEE Access
Subjects:
Online Access:https://ieeexplore.ieee.org/document/8567881/
id doaj-ee8141282999441da2138aeaec6ac155
record_format Article
spelling 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/
work_keys_str_mv AT ericsantiagovalenten agraphtheorybasedmethodfortopologicalanddimensionalrepresentationofplanarmechanismsasacomputationaltoolforengineeringdesign
AT edgaralfredoportillaflores agraphtheorybasedmethodfortopologicalanddimensionalrepresentationofplanarmechanismsasacomputationaltoolforengineeringdesign
AT efrenmezuramontes agraphtheorybasedmethodfortopologicalanddimensionalrepresentationofplanarmechanismsasacomputationaltoolforengineeringdesign
AT eduardovegaalvarado agraphtheorybasedmethodfortopologicalanddimensionalrepresentationofplanarmechanismsasacomputationaltoolforengineeringdesign
AT mariabarbaracalvayanez agraphtheorybasedmethodfortopologicalanddimensionalrepresentationofplanarmechanismsasacomputationaltoolforengineeringdesign
AT martinpedrozavillalba agraphtheorybasedmethodfortopologicalanddimensionalrepresentationofplanarmechanismsasacomputationaltoolforengineeringdesign
AT ericsantiagovalenten graphtheorybasedmethodfortopologicalanddimensionalrepresentationofplanarmechanismsasacomputationaltoolforengineeringdesign
AT edgaralfredoportillaflores graphtheorybasedmethodfortopologicalanddimensionalrepresentationofplanarmechanismsasacomputationaltoolforengineeringdesign
AT efrenmezuramontes graphtheorybasedmethodfortopologicalanddimensionalrepresentationofplanarmechanismsasacomputationaltoolforengineeringdesign
AT eduardovegaalvarado graphtheorybasedmethodfortopologicalanddimensionalrepresentationofplanarmechanismsasacomputationaltoolforengineeringdesign
AT mariabarbaracalvayanez graphtheorybasedmethodfortopologicalanddimensionalrepresentationofplanarmechanismsasacomputationaltoolforengineeringdesign
AT martinpedrozavillalba graphtheorybasedmethodfortopologicalanddimensionalrepresentationofplanarmechanismsasacomputationaltoolforengineeringdesign
_version_ 1724192227513597952