On closed-form solutions to the position analysis of Baranov trusses

The exact position analysis of a planar mechanism reduces to compute the roots of its characteristic polynomial. Obtaining this polynomial usually involves, as a first step, obtaining a system of equations derived from the independent kinematic loops of the mechanism. Although conceptually simple, t...

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Detalhes bibliográficos
Autores: Rojas Libreros, Nicolás Enrique, Thomas, Federico|||0000-0001-9341-5528
Formato: artículo
Fecha de publicación:2012
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/17912
Acesso em linha:https://hdl.handle.net/2117/17912
https://dx.doi.org/10.1016/j.mechmachtheory.2011.10.010
Access Level:acceso abierto
Palavra-chave:Kinematics
Position analysis
Baranov trusses
Bilateration
Characteristic polynomial
Cinemàtica
Àrees temàtiques de la UPC::Enginyeria mecànica::Mecànica::Cinemàtica
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spelling On closed-form solutions to the position analysis of Baranov trussesRojas Libreros, Nicolás EnriqueThomas, Federico|||0000-0001-9341-5528KinematicsPosition analysisBaranov trussesBilaterationCharacteristic polynomialCinemàticaÀrees temàtiques de la UPC::Enginyeria mecànica::Mecànica::CinemàticaThe exact position analysis of a planar mechanism reduces to compute the roots of its characteristic polynomial. Obtaining this polynomial usually involves, as a first step, obtaining a system of equations derived from the independent kinematic loops of the mechanism. Although conceptually simple, the use of kinematic loops for deriving characteristic polynomials leads to complex variable eliminations and, in most cases, trigonometric substitutions. As an alternative, a method based on bilateration has recently been shown to permit obtaining the characteristic polynomials of the three-loop Baranov trusses without relying on variable eliminations or trigonometric substitutions. This paper shows how this technique can be applied to solve the position analysis of all catalogued Baranov trusses. The characteristic polynomials of them all have been derived and, as a result, the maximum number of their assembly modes has been obtained. A comprehensive literature survey is also included.20122012-01-0120132013-02-21journal articlehttp://purl.org/coar/resource_type/c_6501AOhttp://purl.org/coar/version/c_b1a7d7d4d402bcceinfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/17912https://dx.doi.org/10.1016/j.mechmachtheory.2011.10.010reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/179122026-05-27T15:37:01Z
dc.title.none.fl_str_mv On closed-form solutions to the position analysis of Baranov trusses
title On closed-form solutions to the position analysis of Baranov trusses
spellingShingle On closed-form solutions to the position analysis of Baranov trusses
Rojas Libreros, Nicolás Enrique
Kinematics
Position analysis
Baranov trusses
Bilateration
Characteristic polynomial
Cinemàtica
Àrees temàtiques de la UPC::Enginyeria mecànica::Mecànica::Cinemàtica
title_short On closed-form solutions to the position analysis of Baranov trusses
title_full On closed-form solutions to the position analysis of Baranov trusses
title_fullStr On closed-form solutions to the position analysis of Baranov trusses
title_full_unstemmed On closed-form solutions to the position analysis of Baranov trusses
title_sort On closed-form solutions to the position analysis of Baranov trusses
dc.creator.none.fl_str_mv Rojas Libreros, Nicolás Enrique
Thomas, Federico|||0000-0001-9341-5528
author Rojas Libreros, Nicolás Enrique
author_facet Rojas Libreros, Nicolás Enrique
Thomas, Federico|||0000-0001-9341-5528
author_role author
author2 Thomas, Federico|||0000-0001-9341-5528
author2_role author
dc.subject.none.fl_str_mv Kinematics
Position analysis
Baranov trusses
Bilateration
Characteristic polynomial
Cinemàtica
Àrees temàtiques de la UPC::Enginyeria mecànica::Mecànica::Cinemàtica
topic Kinematics
Position analysis
Baranov trusses
Bilateration
Characteristic polynomial
Cinemàtica
Àrees temàtiques de la UPC::Enginyeria mecànica::Mecànica::Cinemàtica
description The exact position analysis of a planar mechanism reduces to compute the roots of its characteristic polynomial. Obtaining this polynomial usually involves, as a first step, obtaining a system of equations derived from the independent kinematic loops of the mechanism. Although conceptually simple, the use of kinematic loops for deriving characteristic polynomials leads to complex variable eliminations and, in most cases, trigonometric substitutions. As an alternative, a method based on bilateration has recently been shown to permit obtaining the characteristic polynomials of the three-loop Baranov trusses without relying on variable eliminations or trigonometric substitutions. This paper shows how this technique can be applied to solve the position analysis of all catalogued Baranov trusses. The characteristic polynomials of them all have been derived and, as a result, the maximum number of their assembly modes has been obtained. A comprehensive literature survey is also included.
publishDate 2012
dc.date.none.fl_str_mv 2012
2012-01-01
2013
2013-02-21
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AO
http://purl.org/coar/version/c_b1a7d7d4d402bcce
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/17912
https://dx.doi.org/10.1016/j.mechmachtheory.2011.10.010
url https://hdl.handle.net/2117/17912
https://dx.doi.org/10.1016/j.mechmachtheory.2011.10.010
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.301629

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