File(s) not publicly available
A unified position analysis of the Dixon and the generalized peaucellier linkages
journal contribution
posted on 2023-06-09, 00:27 authored by Nicolas Rojas, Aaron M Dollar, Federico ThomasThis 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.
History
Publication status
- Published
Journal
Mechanism and Machine TheoryISSN
0094-114XPublisher
ElsevierVolume
94Page range
28-40Department affiliated with
- Engineering and Design Publications
Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2016-03-07Usage metrics
Categories
No categories selectedKeywords
Licence
Exports
RefWorks
BibTeX
Ref. manager
Endnote
DataCite
NLM
DC