Roulette (Latin, round, to run, roll) is a method to generate new curves. Curves generated this way are also called roulette. It is the trace of a point (or a line) attached to a curve, while this curve rolls on another curve without slipping. The resulting curve is called a point-roulette or line-roulette respectively. A special class of point-roulette is rolling a circle on a line or another circle. These are known as cycloidal curves. Many of the famous curves, including the ellipse, can be generated this way. (See curve family tree)
Glissette (meaning glide or slide) is the locus of a point or envelope of a line attached to a curve, which slides along two fixed curves. It can be shown that any glissette may also be defined as a roulette. [J. Dennis Lawrence] The most popular example of glissette is the trammel of Archimedes, used to generate astroid and ellipse.
| Fixed Curve c1 | Rolling Curve c2 | Tracing Point | Roulette |
|---|---|---|---|
| any curve | line | on line | involute |
| line | circle | on circum. | cycloid |
| circle | circle | any point | epitrochoid, hypotrochoid |
| parabola | equal parabola | vertex | cissoid of Diocles |
| line | parabola | focus | catenary |
| line | ellipse | focus | elliptic catenary? |
| line | hyperbola | focus | hyperbolic catenary? |
| line | equiangular spiral | any point? | line |
| line | hyperbolic spiral | pole | tractrix |
| line | involute of circle | center | parabola? |
| line | cycloid | center | ellipse? |
See: Websites on Plane Curves, Printed References On Plane Curves.
Robert Yates: Curves and Their Properties.
Wikipedia: Roulette (curve).