Get Hypotrochoid essential facts below. View Videos
or join the Hypotrochoid discussion
. Add Hypotrochoid
to your PopFlock.com topic list for future reference or share
this resource on social media.
The red curve is a hypotrochoid drawn as the smaller black circle rolls around inside the larger blue circle (parameters are R
= 5, r
= 3, d
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.
The parametric equations for a hypotrochoid are:
where is the angle formed by the horizontal and the center of the rolling circle (these are not polar equations because is not the polar angle). When measured in radian, takes values from to where LCM is least common multiple.
Special cases include the hypocycloid with d = r is a line or flat ellipse and the ellipse with R = 2r and d > r or d < r (d is not equal to r). (see Tusi couple).
(drawn in red) may be expressed as a special case of the hypotrochoid, with R
); here R
= 10, r
= 5, d
The classic Spirograph toy traces out hypotrochoid and epitrochoid curves.