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dc.contributor.authorRojas Libreros, Nicolás Enrique
dc.contributor.authorThomas, Federico
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament d'Enginyeria de Sistemes, Automàtica i Informàtica Industrial
dc.identifier.citationRojas, N.; Thomas, F. A robust forward kinematics analysis of 3-RPR planar platforms. A: International Symposium on Advances in Robot Kinematics. "Advances in Robot Kinematics: motion in man and machine". Piran-Portorož: Springer Verlag, 2010, p. 23-32.
dc.description.abstractThe standard forward kinematics analysis of 3-RPR planar parallel platforms boils down to computing the roots of a sextic polynomial. There are many different ways to obtain this polynomial but all of them include exceptions for which the formulation is not valid. Unfortunately, near these exceptions the corresponding polynomial exhibits numerical instabilities. In this paper, we provide a way around this inconvenience by translating the forward kinematics problem to be solved into an equivalent problem fully stated in terms of distances. Using constructive geometric arguments, an alternative sextic —which is not linked to a particular reference frame— is straightforwardly obtained without the need of variable eliminations nor tangent-half-angle substitutions. The presented formulation is valid, without any modification, for any planar 3-RPR parallel platform, including the special architectures and configurations —which ultimately lead to numerical instabilities— that cannot be directly handled by previous formulations.
dc.format.extent10 p.
dc.publisherSpringer Verlag
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.subjectÀrees temàtiques de la UPC::Informàtica::Robòtica
dc.subject.lcshRobots -- Kinematics
dc.subject.otherRobot kinematics
dc.subject.other3-RPR parallel robots
dc.subject.otherCoordinate-free formulations
dc.subject.otherCayley-Menger determinants
dc.subject.otherNumerical stability
dc.titleA robust forward kinematics analysis of 3-RPR planar platforms
dc.typeConference report
dc.subject.lemacRobots -- Cinemàtica
dc.contributor.groupUniversitat Politècnica de Catalunya. ROBiri - Grup de Robòtica de l'IRI
dc.rights.accessOpen Access
dc.description.versionPostprint (author’s final draft)
upcommons.citation.authorRojas, N.; Thomas, F.
upcommons.citation.contributorInternational Symposium on Advances in Robot Kinematics
upcommons.citation.publicationNameAdvances in Robot Kinematics: motion in man and machine

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