# Hypotrochoid (parametric equation Y- coordinate)

## Description

A hypotrochoid is a roulette traced by a point attached to a circle of radius r rolling around the inside of a fixed circle of radius R, where the point is a distance d from the center of the interior circle. Special cases include the hypocycloid with d = r and the ellipse with R = 2r. The classic Spirograph toy traces out hypotrochoid and epitrochoid curves.

Related formulas## Variables

y_{x} | Y-coordinate (m) |

R | Radius of the fixed circle (m) |

r | Radius of the circle rolling around the inside of the fixed circle (m) |

θ | The angle formed by the horizontal and the center of the rolling circle (radians) |

d | The distance from the center of the interior circle (m) |