Editing Reuleaux triangle (section)

=== Mechanism design ===
[[File:Luch2 greifer.gif|thumb|upright|left|Film advance mechanism in the Soviet Luch-2 8mm film projector based on a Reuleaux triangle]]
Another class of applications of the Reuleaux triangle involves using it as a part of a [[Linkage (mechanical)|mechanical linkage]] that can convert [[rotation around a fixed axis]]
into [[reciprocating motion]].<ref name="onup">{{citation|title=Old and New Unsolved Problems in Plane Geometry and Number Theory|volume=11|series=Dolciani mathematical expositions|first1=Victor|last1=Klee|author1-link=Victor Klee|first2=S.|last2=Wagon|author2-link=Stan Wagon|publisher=Cambridge University Press|year=1991|isbn=978-0-88385-315-3|page=21|url=https://books.google.com/books?id=tRdoIhHh3moC&pg=PA21}}.</ref> These mechanisms were studied by Franz Reuleaux. With the assistance of the Gustav Voigt company, Reuleaux built approximately 800 models of mechanisms, several of which involved the Reuleaux triangle.<ref name="cornell" /> Reuleaux used these models in his pioneering scientific investigations of their motion.<ref>{{citation|title=Mathematics and the Aesthetic: New Approaches to an Ancient Affinity|series=CMS Books in Mathematics|editor1-first=Nathalie|editor1-last=Sinclair|editor1-link=Nathalie Sinclair|editor2-first=David|editor2-last=Pimm|editor3-first=William|editor3-last=Higginson|publisher=Springer|year=2007|isbn=978-0-387-38145-9|contribution=Experiencing meanings in geometry|first1=David W.|last1=Henderson|first2=Daina|last2=Taimina|author2-link=Daina Taimina|pages=58–83|doi=10.1007/978-0-387-38145-9_4|hdl=1813/2714|hdl-access=free}}. See in particular [https://books.google.com/books?id=GJBKLnkYyi0C&pg=PA81 p. 81].</ref> Although most of the Reuleaux–Voigt models have been lost, 219 of them have been collected at [[Cornell University]], including nine based on the Reuleaux triangle.<ref name="cornell">{{citation|title=The Reuleaux Collection of Kinematic Mechanisms at Cornell University|author1-link=Francis C. Moon|first=Francis C.|last=Moon|date=July 1999|publisher=Cornell University Library|url=https://www.asme.org/wwwasmeorg/media/resourcefiles/aboutasme/who%20we%20are/engineering%20history/landmarks/232-reuleaux-collection-of-kinematic-mechanisms-at-cornell-university.pdf|archive-url=https://web.archive.org/web/20200614022856/https://www.asme.org/wwwasmeorg/media/resourcefiles/aboutasme/who%20we%20are/engineering%20history/landmarks/232-reuleaux-collection-of-kinematic-mechanisms-at-cornell-university.pdf|archive-date=June 14, 2020}}.</ref><ref name="moon241" /> However, the use of Reuleaux triangles in mechanism design predates the work of Reuleaux; for instance, some [[steam engine]]s from as early as 1830 had a [[Cam (mechanism)|cam]] in the shape of a Reuleaux triangle.<ref>{{harvtxt|Moon|2007|page=240}}</ref><ref name="mathtrek">{{citation|first=Ivars|last=Peterson|author-link=Ivars Peterson|title=Rolling with Reuleaux|date=October 19, 1996|work=MathTrek|url=https://www.sciencenews.org/article/rolling-reuleaux|publisher=[[ScienceNews]]}}. Reprinted in {{citation|title=Mathematical Treks: From Surreal Numbers to Magic Circles|series=MAA spectrum|first=Ivars|last=Peterson|author-link=Ivars Peterson|publisher=[[Mathematical Association of America]]|year=2002|isbn=978-0-88385-537-9|pages=141–144|url=https://books.google.com/books?id=4gWSAraVhtAC&pg=PA141}}.</ref>

One application of this principle arises in a [[film projector]]. In this application, it is necessary to advance the film in a jerky, stepwise motion, in which each frame of film stops for a fraction of a second in front of the projector lens, and then much more quickly the film is moved to the next frame. This can be done using a mechanism in which the rotation of a Reuleaux triangle within a square is used to create a motion pattern for an actuator that pulls the film quickly to each new frame and then pauses the film's motion while the frame is projected.<ref>{{harvtxt|Lay|2007}}, [https://books.google.com/books?id=U9eOPjmaH90C&pg=PA83 p.&nbsp;83].</ref>

The rotor of the [[Wankel engine]] is shaped as a curvilinear triangle that is often cited as an example of a Reuleaux triangle.<ref name="icons"/><ref name="howround"/><ref name= "gardner" /><ref name="mathtrek" /> However, its curved sides are somewhat flatter than those of a Reuleaux triangle and so it does not have constant width.<ref>{{harvtxt|Gruber|1983|page=80}}</ref><ref>{{citation | last = Nash | first = David H.
 | date = March 1977
 | doi = 10.1080/0025570x.1977.11976621
 | issue = 2
 | journal = Mathematics Magazine
 | pages = 87–89
 | title = Rotary engine geometry
 | volume = 50}}</ref><ref> {{citation | last1 = Badr | first1 = O.
 | last2 = Naik | first2 = S.
 | last3 = O'Callaghan | first3 = P. W.
 | last4 = Probert | first4 = S. D.
 | doi = 10.1016/0306-2619(91)90063-4
 | issue = 1
 | journal = Applied Energy
 | pages = 59–76
 | title = Rotary Wankel engines as expansion devices in steam Rankine-cycle engines
 | volume = 39
 | year = 1991| bibcode = 1991ApEn...39...59B
 }}.</ref>