Editing Screw theory (section)

== History ==
The mathematical framework was developed by Sir [[Robert Stawell Ball]] in 1876 for application in kinematics and [[statics]] of [[mechanism (engineering)|mechanism]]s (rigid body mechanics).<ref name=b1/>

[[Felix Klein]] saw screw theory as an application of [[elliptic geometry]] and his [[Erlangen Program]].<ref>[[Felix Klein]] (1902) (D.H. Delphenich translator)  [http://neo-classical-physics.info/uploads/3/0/6/5/3065888/klein_-_screws.pdf On Sir Robert Ball's Theory of Screws]</ref> He also worked out elliptic geometry, and a fresh view of Euclidean geometry, with the [[Cayley–Klein metric]]. The use of a [[symmetric matrix]] for a [[von Staudt conic]] and metric, applied to screws, has been described by Harvey Lipkin.<ref>Harvey Lipkin (1983) [http://helix.gatech.edu/Papers/1985/LipkinPhdChapter3.pdf Metrical Geometry] {{webarchive|url=https://web.archive.org/web/20160305154047/http://helix.gatech.edu/Papers/1985/LipkinPhdChapter3.pdf |date=2016-03-05 }} from [[Georgia Tech]]</ref> Other prominent contributors include [[Julius Plücker]], [[William Kingdon Clifford|W. K. Clifford]], [[Fedor Menasovich Dimentberg|F. M. Dimentberg]], [[Kenneth H. Hunt]], J. R. Phillips.<ref>[[William Kingdon Clifford|Clifford, William Kingdon]] (1873), "Preliminary Sketch of Biquaternions", Paper XX, ''Mathematical Papers'', p.&nbsp;381.</ref>
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this is discussed under "screw axis"
[[Euler's rotation theorem]] states that any rotation can be described as a rotation about a single axis by a given angle. In general, this is a unique representation (with the exception of zero rotation having an undefined axis and rotation of 180° having an ambiguity in axis direction corresponding to [[gimbal lock]]). Screw theory extends this notion to include translation.
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The homography idea in transformation geometry was advanced by [[Sophus Lie]] more than a century ago. Even earlier, [[William Rowan Hamilton]] displayed the [[versor]] form of unit quaternions as exp(''a r'')= cos ''a'' + ''r'' sin ''a''. The idea is also in [[Euler's formula]] parametrizing the [[unit circle]] in the [[complex plane]].

[[William Kingdon Clifford]] initiated the use of dual quaternions for [[kinematics]], followed by [[Aleksandr Kotelnikov]], [[Eduard Study]] (''Geometrie der Dynamen''), and [[Wilhelm Blaschke]]. However, the point of view of Sophus Lie has recurred.<ref>Xiangke Wang, Dapeng Han, Changbin Yu, and Zhiqiang Zheng (2012) "The geometric structure of unit dual quaternions with application in kinematic control", [[Journal of Mathematical Analysis and Applications]] 389(2):1352 to 64</ref>
In 1940, [[Julian Coolidge]] described the use of dual quaternions for screw displacements on page 261 of ''A History of Geometrical Methods''. He notes the 1885 contribution of [[Arthur Buchheim]].<ref>{{cite journal|author=Buchheim, Arthur |year=1885|jstor=2369176|title=A Memoir on biquaternions|journal= [[American Journal of Mathematics]]|volume= 7|issue=4|pages=293–326|doi=10.2307/2369176}}</ref> Coolidge based his description simply on the tools Hamilton had used for real quaternions.