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

yxY-coordinate (m)
RRadius of the fixed circle (m)
rRadius of the circle rolling around the inside of the fixed circle (m)
θThe angle formed by the horizontal and the center of the rolling circle (radians)
dThe distance from the center of the interior circle (m)