Symmetrical Observability of Kinematic Parameters in Symmetrical Parallel Mechanisms

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dc.contributor.authorDurango, S.
dc.contributor.authorRestrepo, D.
dc.contributor.authorRuíz, O.
dc.contributor.authorRestrepo-Giraldo, J.
dc.contributor.authorAchiche, S.
dc.contributor.departmentUniversidad EAFIT. Departamento de Ingeniería Mecánicaspa
dc.contributor.researchgroupLaboratorio CAD/CAM/CAEspa
dc.date.accessioned2016-11-18T22:43:00Z
dc.date.available2016-11-18T22:43:00Z
dc.date.issued2014-05
dc.description.abstractThis article presents an application of symmetry group theory in kinematic identification of parallel mechanisms of nlegs legs -- Kinematic Identification implies the estimation of the actual geometrical parameters (as opposed to nominal ones) of a physical mechanism -- For a symmetric mechanism, KI requires configuring sets of leg positions with symmetrical observability – This article presents as main contributions: (i) a conjecture that allows mapping the symmetries of the mechanism into the active-joint workspace, (ii) a set of necessary conditions to express leg parameters in coordinate systems which allow symmetrical observability, and (iii) a procedure for exploiting symmetries in pose selection for kinematic identification of symmetrical parallel mechanisms -- For the kinematic identification itself, we adopt a divide-and-conquer (DC) identification protocol -discussed by us in another publication- in which each leg of the mechanism is independently identified by using the inverse calibration method -- In this article we emphasize how to exploit the symmetries existent in (nlegs − 1) legs of the parallel mechanism allowing to apply to other legs the symmetry-transformed sample protocol used for the kinematic identification of a reference leg -- The symmetrical observability of sets of leg parameters allows to reduce the costs of the pose selection procedure by a factor of (1/nlegs) compared to a complete DC procedure in which the poses of each leg are selected independently -- The pose selection is carried out only for the reference leg -- For the (nlegs−1) remaining legs the poses are dictated by symmetry operations performed onto the poses of the reference leg -- An application of the symmetrical observability is presented through the simulated kinematic identification of a 3RRR symmetrical parallel mechanismeng
dc.description.sponsorshipPolytechnic School of the University of São PauloSitio webIndicaciones, Associação Brasileira de Métodos Computacionais em Engenharia, International Association for Computational Mechanics, International Congress and Convention Association, Conheça o São Paulo é Tudo de Bom, Embratur, PETROBRASspa
dc.formatapplication/pdfeng
dc.identifier.citation@InProceedings{Durango_Restrepo_Ruiz_Achiche_2012, author = {Durango, S. and Restrepo, D. and Ruiz, O. and Restrepo-Giraldo, J. and Achiche, S.}, title = {Symetrical Observability of Kinematic Parameters in Symmetrical Parallel Mechanisms}, booktitle = {10th World Congress on Computational Mechanics}, pages = {16714}, year = {2012}, editor = {Pimenta, P.M. and Campello, E.M.B.}, address = {Sao Paulo, Brazil}, month = {08-13 July}, OPTpublisher = {ABMEC}, note = {ISBN 978-85-86686-70-2}, abstract={This article presents an application of symmetry groups in symmetrical observability of the kinematic parameters of a mechanism. We use the devised concepts in the particular domain of Kinematic Identification of symmetric parallel mechanisms. KI implies the estimation of the actual geometrical parameters (as opposed to nominal ones) of a physical mechanism and, for a symmetric mechanism it allows configuring sets of leg positions with symmetrical observability. Our investigation takes advantage of this situation and presents the following contributions: (\textit{i}) a conjecture that allows mapping the symmetries of the mechanism into the active-joint workspace, (\textit{ii}) a set of necessary conditions to express leg parameters in coordinate systems which allow symmetrical observability, and (\textit{iii}) a procedure for exploiting symmetries in pose selection for kinematic identification of symmetrical parallel mechanisms. For the kinematic identification itself, we adopt a divide-and-conquer (DC) identification protocol -discussed by us in another publication- in which each leg of the mechanism is independently identified by using the inverse calibration method. In this article we emphasize how to exploit the symmetries existent in ($n_{legs} - 1$) legs of the parallel mechanism allowing to apply to other legs the symmetry-transformed sample protocol used for the kinematic identification of a \textit{reference} leg. The symmetrical observability of sets of leg parameters allows to reduce the costs of the pose selection procedure by a factor of $(1/n_{legs})$ compared to a complete DC procedure in which the poses of each leg are selected independently. The pose selection is carried out only for the reference leg. For the ($n_{legs} - 1$) remaining legs the poses are dictated by symmetry operations performed onto the poses of the reference leg. An application of the symmetrical observability is presented through the simulated kinematic identification of a 3$\underline{R}RR$ symmetrical parallel mechanism. } }spa
dc.identifier.issn2358-0828
dc.identifier.urihttp://hdl.handle.net/10784/9711
dc.language.isoengspa
dc.publisherEditora Edgard Blücher Ltda.
dc.relation.ispartofBlucher Mechanical Engineering Proceedings, vol.1 no.1, pp.254,272, May. 2014spa
dc.rights.accessrightsinfo:eu-repo/semantics/openAccesseng
dc.rights.localAcceso abiertospa
dc.subject.keywordKinematicseng
dc.subject.keywordSymmetryeng
dc.subject.keywordAlgoritmos de calibraciónspa
dc.subject.keywordEcuaciones paramétricasspa
dc.subject.keywordRepresentación paramétricaspa
dc.subject.keywordMecanismo paralelospa
dc.subject.keywordCinemática inversaspa
dc.subject.lembCINEMÁTICAspa
dc.subject.lembSIMETRÍAspa
dc.titleSymmetrical Observability of Kinematic Parameters in Symmetrical Parallel Mechanismseng
dc.typeinfo:eu-repo/semantics/drafteng
dc.typedrafteng
dc.typeinfo:eu-repo/semantics/publishedVersioneng
dc.typepublishedVersioneng
dc.type.localDocumento de conferenciaspa

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