On the constraints violation in forward dynamics of multibody systems
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/1822/45269 |
Resumo: | It is known that the dynamic equations of motion for constrained mechanical multibody systems are frequently formulated using the Newton-Euler’s approach, which is augmented with the acceleration constraint equations. This formulation results in the establishment of a mixed set of partial differential and algebraic equations, which are solved in order to predict the dynamic behavior of general multibody systems. The classical resolution of the equations of motion is highly prone to constraints violation because the position and velocity constraint equations are not fulfilled. In this work, a general and comprehensive methodology to eliminate the constraints violation at the position and velocity levels is offered. The basic idea of the described approach is to add corrective terms to the position and velocity vectors with the intent to satisfy the corresponding kinematic constraint equations. These corrective terms are evaluated as function of the Moore-Penrose generalized inverse of the Jacobian matrix and of the kinematic constraint equations. The described methodology is embedded in the standard method to solve the equations of motion based on the technique of Lagrange multipliers. Finally, the effectiveness of the described methodology is demonstrated through the dynamic modeling and simulation of different planar and spatial multibody systems. The outcomes in terms of constraints violation at the position and velocity levels, conservation of the total energy and computational efficiency are analyzed and compared with those obtained with the standard Lagrange multipliers method, the Baumgarte stabilization method, the augmented Lagrangian formulation, the index-1 augmented Lagrangian and the coordinate partitioning method. |
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On the constraints violation in forward dynamics of multibody systemsConstraints violationBaumgarte stabilization methodPenalty methodAugmented Lagrangian formulationIndex-1 Lagrangian formulationCoordinate partitioning methodMechanical energyComputational efficiencyForward dynamicsMultibody systemsEngenharia e Tecnologia::Engenharia MecânicaScience & TechnologyIt is known that the dynamic equations of motion for constrained mechanical multibody systems are frequently formulated using the Newton-Euler’s approach, which is augmented with the acceleration constraint equations. This formulation results in the establishment of a mixed set of partial differential and algebraic equations, which are solved in order to predict the dynamic behavior of general multibody systems. The classical resolution of the equations of motion is highly prone to constraints violation because the position and velocity constraint equations are not fulfilled. In this work, a general and comprehensive methodology to eliminate the constraints violation at the position and velocity levels is offered. The basic idea of the described approach is to add corrective terms to the position and velocity vectors with the intent to satisfy the corresponding kinematic constraint equations. These corrective terms are evaluated as function of the Moore-Penrose generalized inverse of the Jacobian matrix and of the kinematic constraint equations. The described methodology is embedded in the standard method to solve the equations of motion based on the technique of Lagrange multipliers. Finally, the effectiveness of the described methodology is demonstrated through the dynamic modeling and simulation of different planar and spatial multibody systems. The outcomes in terms of constraints violation at the position and velocity levels, conservation of the total energy and computational efficiency are analyzed and compared with those obtained with the standard Lagrange multipliers method, the Baumgarte stabilization method, the augmented Lagrangian formulation, the index-1 augmented Lagrangian and the coordinate partitioning method.The first author expresses his gratitude to the Portuguese Foundation for Science and Technology through the PhD grant (PD/BD/114154/2016). This work has been supported by the Portuguese Foundation for Science and Technology with the reference project UID/EEA/04436/2013, by FEDER funds through the COMPETE 2020 – Programa Operacional Competitividade e Internacionalização (POCI) with the reference project POCI-01-0145-FEDER-006941.info:eu-repo/semantics/publishedVersionSpringer VerlagUniversidade do MinhoMarques, Pedro Filipe LimaSouto, A. PedroFlores, Paulo2017-042017-04-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/45269eng1384-56401573-272X10.1007/s11044-016-9530-yinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-21T12:46:28Zoai:repositorium.sdum.uminho.pt:1822/45269Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:44:27.856999Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
On the constraints violation in forward dynamics of multibody systems |
title |
On the constraints violation in forward dynamics of multibody systems |
spellingShingle |
On the constraints violation in forward dynamics of multibody systems Marques, Pedro Filipe Lima Constraints violation Baumgarte stabilization method Penalty method Augmented Lagrangian formulation Index-1 Lagrangian formulation Coordinate partitioning method Mechanical energy Computational efficiency Forward dynamics Multibody systems Engenharia e Tecnologia::Engenharia Mecânica Science & Technology |
title_short |
On the constraints violation in forward dynamics of multibody systems |
title_full |
On the constraints violation in forward dynamics of multibody systems |
title_fullStr |
On the constraints violation in forward dynamics of multibody systems |
title_full_unstemmed |
On the constraints violation in forward dynamics of multibody systems |
title_sort |
On the constraints violation in forward dynamics of multibody systems |
author |
Marques, Pedro Filipe Lima |
author_facet |
Marques, Pedro Filipe Lima Souto, A. Pedro Flores, Paulo |
author_role |
author |
author2 |
Souto, A. Pedro Flores, Paulo |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Universidade do Minho |
dc.contributor.author.fl_str_mv |
Marques, Pedro Filipe Lima Souto, A. Pedro Flores, Paulo |
dc.subject.por.fl_str_mv |
Constraints violation Baumgarte stabilization method Penalty method Augmented Lagrangian formulation Index-1 Lagrangian formulation Coordinate partitioning method Mechanical energy Computational efficiency Forward dynamics Multibody systems Engenharia e Tecnologia::Engenharia Mecânica Science & Technology |
topic |
Constraints violation Baumgarte stabilization method Penalty method Augmented Lagrangian formulation Index-1 Lagrangian formulation Coordinate partitioning method Mechanical energy Computational efficiency Forward dynamics Multibody systems Engenharia e Tecnologia::Engenharia Mecânica Science & Technology |
description |
It is known that the dynamic equations of motion for constrained mechanical multibody systems are frequently formulated using the Newton-Euler’s approach, which is augmented with the acceleration constraint equations. This formulation results in the establishment of a mixed set of partial differential and algebraic equations, which are solved in order to predict the dynamic behavior of general multibody systems. The classical resolution of the equations of motion is highly prone to constraints violation because the position and velocity constraint equations are not fulfilled. In this work, a general and comprehensive methodology to eliminate the constraints violation at the position and velocity levels is offered. The basic idea of the described approach is to add corrective terms to the position and velocity vectors with the intent to satisfy the corresponding kinematic constraint equations. These corrective terms are evaluated as function of the Moore-Penrose generalized inverse of the Jacobian matrix and of the kinematic constraint equations. The described methodology is embedded in the standard method to solve the equations of motion based on the technique of Lagrange multipliers. Finally, the effectiveness of the described methodology is demonstrated through the dynamic modeling and simulation of different planar and spatial multibody systems. The outcomes in terms of constraints violation at the position and velocity levels, conservation of the total energy and computational efficiency are analyzed and compared with those obtained with the standard Lagrange multipliers method, the Baumgarte stabilization method, the augmented Lagrangian formulation, the index-1 augmented Lagrangian and the coordinate partitioning method. |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017-04 2017-04-01T00:00:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/1822/45269 |
url |
http://hdl.handle.net/1822/45269 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
1384-5640 1573-272X 10.1007/s11044-016-9530-y |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Springer Verlag |
publisher.none.fl_str_mv |
Springer Verlag |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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1799133006129004544 |