A unified position analysis of the Dixon and the generalized Peaucellier linkages

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Title: A unified position analysis of the Dixon and the generalized Peaucellier linkages
Author(s): Rojas, N
Dollar, AM
Thomas, F
Item Type: Journal Article
Abstract: This 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.
Publication Date: 24-Aug-2015
Date of Acceptance: 14-Jul-2015
URI: http://hdl.handle.net/10044/1/48938
DOI: https://dx.doi.org/10.1016/j.mechmachtheory.2015.07.008
ISSN: 0094-114X
Publisher: Elsevier
Start Page: 28
End Page: 40
Journal / Book Title: Mechanism and Machine Theory
Volume: 94
Copyright Statement: © 2015 Elsevier Ltd. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Keywords: Design Practice & Management
0913 Mechanical Engineering
Appears in Collections:Faculty of Engineering
Dyson School of Design Engineering

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