Publication
On the constraints violation in forward dynamics of multibody systems
| Summary: | 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. |
|---|---|
| Main Authors: | Marques, Pedro Filipe Lima |
| Other Authors: | Souto, A. Pedro; Flores, Paulo |
| Subject: | 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 |
| Year: | 2017 |
| Country: | Portugal |
| Document type: | article |
| Access type: | open access |
| Associated institution: | Universidade do Minho |
| Language: | English |
| Origin: | RepositóriUM - Universidade do Minho |
| _version_ | 1867439601953538048 |
|---|---|
| author | Marques, Pedro Filipe Lima |
| author2 | Souto, A. Pedro Flores, Paulo |
| author2_role | author author |
| author_facet | Marques, Pedro Filipe Lima Souto, A. Pedro Flores, Paulo |
| author_role | author |
| contributor_name_str_mv | RepositóriUM - Universidade do Minho |
| country_str | PT |
| creators_json_txt | [{\"Person.name\":\"Marques, Pedro Filipe Lima\"},{\"Person.name\":\"Souto, A. Pedro\"},{\"Person.name\":\"Flores, Paulo\"}] |
| datacite.contributors.contributor.contributorName.fl_str_mv | RepositóriUM - Universidade do Minho |
| datacite.creators.creator.creatorName.fl_str_mv | Marques, Pedro Filipe Lima Souto, A. Pedro Flores, Paulo |
| datacite.date.Accepted.fl_str_mv | 2017-04-01T00:00:00Z |
| datacite.date.available.fl_str_mv | 2017-04-06T10:39:45Z |
| datacite.date.embargoed.fl_str_mv | 2017-04-06T10:39:45Z |
| datacite.rights.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| datacite.subjects.subject.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 |
| datacite.titles.title.fl_str_mv | On the constraints violation in forward dynamics of multibody systems |
| dc.contributor.none.fl_str_mv | RepositóriUM - Universidade do Minho |
| dc.creator.none.fl_str_mv | Marques, Pedro Filipe Lima Souto, A. Pedro Flores, Paulo |
| dc.date.Accepted.fl_str_mv | 2017-04-01T00:00:00Z |
| dc.date.available.fl_str_mv | 2017-04-06T10:39:45Z |
| dc.date.embargoed.fl_str_mv | 2017-04-06T10:39:45Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | https://hdl.handle.net/1822/45269 |
| dc.language.none.fl_str_mv | eng |
| dc.publisher.none.fl_str_mv | Springer Verlag |
| dc.rights.none.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| dc.subject.none.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 |
| dc.title.fl_str_mv | On the constraints violation in forward dynamics of multibody systems |
| dc.type.none.fl_str_mv | http://purl.org/coar/resource_type/c_6501 |
| 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. |
| dirty | 0 |
| eu_rights_str_mv | openAccess |
| format | article |
| fulltext.url.fl_str_mv | https://repositorium.uminho.pt/bitstreams/f1316760-cda2-468c-82f6-ef6d3abbf1ab/download |
| id | rum_4e751b30acdc36bcc840c2eedf4c5f4b |
| identifier.url.fl_str_mv | https://hdl.handle.net/1822/45269 |
| instacron_str | repositorium |
| institution | Universidade do Minho |
| instname_str | Universidade do Minho |
| language | eng |
| network_acronym_str | rum |
| network_name_str | RepositóriUM - Universidade do Minho |
| oai_identifier_str | oai:repositorium.uminho.pt:1822/45269 |
| organization_str_mv | urn:organizationAcronym:repositorium |
| person_str_mv | Marques, Pedro Filipe Lima Souto, A. Pedro Flores, Paulo |
| publishDate | 2017 |
| publisher.none.fl_str_mv | Springer Verlag |
| reponame_str | RepositóriUM - Universidade do Minho |
| repository_id_str | urn:repositoryAcronym:rum |
| service_str_mv | urn:repositoryAcronym:rum |
| spelling | engSpringer VerlagporIt 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.application/pdfporOn the constraints violation in forward dynamics of multibody systemsMarques, Pedro Filipe LimaSouto, A. PedroFlores, PauloHostingInstitutionOrganizationalRepositóriUM - Universidade do Minhoe-mailmailto:repositorium@usdb.uminho.ptrepositorium@usdb.uminho.ptISSNIsPartOf1384-5640EISSNIsPartOf1573-272XDOIIsPartOf10.1007/s11044-016-9530-y2017-04-06T10:39:45Z2017-042017-04-01T00:00:00ZHandlehttps://hdl.handle.net/1822/45269http://purl.org/coar/access_right/c_abf2open accessConstraints violationBaumgarte stabilization methodPenalty methodAugmented Lagrangian formulationIndex-1 Lagrangian formulationCoordinate partitioning methodMechanical energyComputational efficiencyForward dynamicsMultibody systemshttp://www.oecd.org/science/inno/38235147.pdfFields of Science and Technology (FOS)Engenharia e Tecnologia::Engenharia Mecânica8295890 bytesliteraturehttp://purl.org/coar/resource_type/c_6501journal articlehttp://purl.org/coar/access_right/c_abf2application/pdffulltexthttps://repositorium.uminho.pt/bitstreams/f1316760-cda2-468c-82f6-ef6d3abbf1ab/download |
| 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 |
| status | SINGLETON |
| subject.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 |
| subject.other.fl_str_mv | Engenharia e Tecnologia::Engenharia Mecânica |
| title | 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_short | On the constraints violation in forward dynamics of multibody systems |
| title_sort | On the constraints violation in forward dynamics of multibody systems |
| 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 |
| topic_facet | 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 |
| url | https://hdl.handle.net/1822/45269 |
| visible | 1 |