Model: L01 Positive Return Mechanism with Curved Triangle

In this mechanism, rotary motion of a crank (in the back) turns the equilateral curved triangle. The curved triangle is a figure of constant width and its motion causes the slider to oscillate back and forth through contact with two parallel guides. At either the left or right extremes of this motion there is a period of finite dwell or rest of the slider. Such a mechanism is called in modern texts on mechanisms a positive return cam—i.e. the curved triangle is the cam and it acts to move the slider in both directions.

The pure version of the curved triangle in parallel guides is also represented in the Reuleaux-Voigt models B-2, B-3, B-4. The curved triangle cam was used in early 19th century steam engines to activate a control value as in a Woolf engine. It was noted in a number of early kinematics books such as Willis (1841,1870). One reference cites Euler as one who studied its geometric properties.

In modern mathematical texts the constant width curved triangle has been called the Reuleaux triangle—not because he invented it—but because Reuleaux was the first to generalize the curved triangle to other curves of constant width.

This model also contains the centrodes of the cam-slider engraved on a glass slide. In a beautiful demonstration of the idea that all planar motions can be represented by pure rolling, Reuleaux’s model shows that the motion is equivalent to rolling of a duangle on a curved triangle (i.e. the centrodes).

Francis Moon 2001-00-00

#### Reference :

- Reuleaux, Kennedy : Kinematics of Machinery (p. 116, Art. 22., 1876)
- Henderson, Taimina : Experiencing Geometry (ch.21, 2005)
- Willis : Principles of Mechanism (Fig. 154, 1870 Edition, 1841)

#### Resources :

- Tutorials and Descriptions : Reuleaux Triangle