<P> Another class of applications of the Reuleaux triangle involves using it as a part of a mechanical linkage that can convert rotation around a fixed axis into reciprocating motion . 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 . Reuleaux used these models in his pioneering scientific investigations of their motion . 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 . However, the use of Reuleaux triangles in mechanism design predates the work of Reuleaux; for instance, some steam engines from as early as 1830 had a cam in the shape of a Reuleaux triangle . </P> <P> 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 . </P> <P> The rotor of the Wankel engine is shaped as a curvilinear triangle that is often cited as an example of a Reuleaux triangle . However, its curved sides are somewhat flatter than those of a Reuleaux triangle and so it does not have constant width . </P> <P> In Gothic architecture, beginning in the late 13th century or early 14th century, the Reuleaux triangle became one of several curvilinear forms frequently used for windows, window tracery, and other architectural decorations . For instance, in English Gothic architecture, this shape was associated with the decorated period, both in its geometric style of 1250--1290 and continuing into its curvilinear style of 1290--1350 . In this context, the shape is more frequently called a spherical triangle, but the more usual mathematical meaning of a spherical triangle is a triangle on the surface of a sphere (a shape also commonly used in architecture as a pendentive). In its use in Gothic church architecture, the three - cornered shape of the Reuleaux triangle may be seen both as a symbol of the Trinity, and as "an act of opposition to the form of the circle". </P>

A shape with three sets of parallel sides