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.
Curve relations by roulette
|Fixed Curve c1||Rolling Curve c2||Tracing Point||Roulette|
|any curve||line||on line||involute|
|circle||circle||any point||epitrochoid, hypotrochoid|
|parabola||equal parabola||vertex||cissoid of Diocles|
|line||equiangular spiral||any point?||line|
|line||involute of circle||center||parabola?|
Related Web Sites
See: Websites on Plane Curves, Plane Curves Books.
Robert Yates: Curves and Their Properties.
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