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dc.contributor.authorRojas Libreros, Nicolás Enrique
dc.contributor.authorDollar, Aaron M.
dc.contributor.authorThomas, Federico
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament d'Enginyeria de Sistemes, Automàtica i Informàtica Industrial
dc.identifier.citationRojas , N.E., Dollar, A., Thomas, F. A unified position analysis of the Dixon and the generalized Peaucellier linkages. "Mechanism and machine theory", 01 Desembre 2015, vol. 94, p. 28-40.
dc.description.abstractThis paper shows how, using elementary Distance Geometry, a closure polynomial of degree 8 for the Dixon linkage can be derived without any trigonometric substitution, variable elimination, or artifice to collapse mirror configurations. The formulation permits the derivation of the geometric conditions required in order for each factor of the leading coefficient of this polynomial to vanish. These conditions either correspond to the case in which the quadrilateral defined by four joints is orthodiagonal, or to the case in which the center of the circle defined by three joints is on the line defined by two other joints. This latter condition remained concealed in previous formulations. Then, particular cases satisfying some of the mentioned geometric conditions are analyzed. Finally, the obtained polynomial is applied to derive the coupler curve of the generalized Peaucellier linkage, a linkage with the same topology as that of the celebrated Peaucellier straight-line linkage but with arbitrary link lengths. It is shown that this curve is 11-circular of degree 22 from which the bicircular quartic curve of the Cayley's scalene cell is derived as a particular case.
dc.format.extent13 p.
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de cossos i polinomis
dc.subject.otherDixon linkage
dc.subject.otherGeneralized Peaucellier linkage
dc.subject.otherCoupler curves
dc.subject.otherPosition analysis
dc.subject.otherDistance Geometry
dc.subject.otherDistance-based kinematics
dc.titleA unified position analysis of the Dixon and the generalized Peaucellier linkages
dc.contributor.groupUniversitat Politècnica de Catalunya. KRD - Cinemàtica i Disseny de Robots
dc.description.peerreviewedPeer Reviewed
dc.rights.accessOpen Access
dc.description.versionPostprint (author's final draft)
local.citation.authorRojas, N.E.; Dollar, A.; Thomas, F.
local.citation.publicationNameMechanism and machine theory

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