Roulette

Description

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.

History

Formula

Properties

Curve relations by roulette

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?

Related Web Sites

See: Websites on Plane Curves, Printed References On Plane Curves.

Robert Yates: Curves and Their Properties.

Roulette (curve).

Graphing Calculator

2006-05