# 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.

## 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? |