Geometric constraint subsets and subgraphs in the analysis of assemblies and mechanisms

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dc.citation.epage137spa
dc.citation.issue3spa
dc.citation.journalTitleIngeniería y Cienciaeng
dc.citation.journalTitleIngeniería y Cienciaspa
dc.citation.spage103spa
dc.citation.volume2spa
dc.contributor.authorRuíz, Óscar E.
dc.contributor.authorFerreira, Placid M.
dc.contributor.departmentUniversidad EAFIT. Departamento de Ingeniería Mecánicaspa
dc.contributor.researchgroupLaboratorio CAD/CAM/CAEspa
dc.date.accessioned2016-11-18T22:25:09Z
dc.date.available2016-11-18T22:25:09Z
dc.date.issued2006-03
dc.description.abstractGeometric Reasoning ability is central to many applications in CAD/CAM/CAPP environments -- An increasing demand exists for Geometric Reasoning systems which evaluate the feasibility of virtual scenes specified by geometric relations -- Thus, the Geometric Constraint Satisfaction or Scene Feasibility (GCS/SF) problem consists of a basic scenario containing geometric entities, whose context is used to propose constraining relations among still undefined entities -- If the constraint specification is consistent, the answer of the problem is one of finitely or infinitely many solution scenarios satisfying the prescribed constraints -- Otherwise, a diagnostic of inconsistency is expected -- The three main approaches used for this problem are numerical, procedural or operational and mathematical -- Numerical and procedural approaches answer only part of the problem, and are not complete in the sense that a failure to provide an answer does not preclude the existence of one -- The mathematical approach previously presented by the authors describes the problem using a set of polynomial equations -- The common roots to this set of polynomials characterizes the solution space for such a problem -- That work presents the use of Groebner basis techniques for verifying the consistency of the constraints -- It also integrates subgroups of the Special Euclidean Group of Displacements SE(3) in the problem formulation to exploit the structure implied by geometric relations -- Although theoretically sound, these techniques require large amounts of computing resources -- This work proposes Divide-and-Conquer techniques applied to local GCS/SF subproblems to identify strongly constrained clusters of geometric entities -- The identification and preprocessing of these clusters generally reduces the effort required in solving the overall problem -- Cluster identification can be related to identifying short cycles in the Spatial Con straint graph for the GCS/SF problem -- Their preprocessing uses the aforementioned Algebraic Geometry and Group theoretical techniques on the local GCS/SF problems that correspond to these cycles -- Besides improving theefficiency of the solution approach, the Divide-and-Conquer techniques capture the physical essence of the problem -- This is illustrated by applying the discussed techniques to the analysis of the degrees of freedom of mechanismseng
dc.formatapplication/pdfeng
dc.identifier.issn1794-9165
dc.identifier.urihttp://hdl.handle.net/10784/9691
dc.language.isoengeng
dc.publisherUniversidad EAFITspa
dc.relation.ispartofIngeniería y Ciencia, Volume 2, Issue 3, pp. 103-137spa
dc.relation.urihttp://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/489
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rights.localAcceso abiertospa
dc.subject.keywordGeometry, algebraicspa
dc.subject.keywordPolynomialsspa
dc.subject.keywordComputer algorithmsspa
dc.subject.keywordCommutative algebraspa
dc.subject.keywordGeometryeng
dc.subject.keywordalgebraiceng
dc.subject.keywordPolynomialseng
dc.subject.keywordComputer algorithmseng
dc.subject.keywordCommutative algebraeng
dc.subject.keywordRestricciones geométricas.keywor
dc.subject.keywordSistemas CAD/CAM.keywor
dc.subject.keywordBases de Gröbner.keywor
dc.subject.lembPOLINOMIOSspa
dc.subject.lembGEOMETRÍA ALGEBRÁICAspa
dc.subject.lembALGORITMOS (COMPUTADORES)spa
dc.subject.lembÁLGEBRA CONMUTATIVAspa
dc.titleGeometric constraint subsets and subgraphs in the analysis of assemblies and mechanismseng
dc.typeinfo:eu-repo/semantics/articleeng
dc.typearticleeng
dc.typeinfo:eu-repo/semantics/publishedVersioneng
dc.typepublishedVersioneng
dc.type.localArtículospa

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