Cycloids and Trochoids of an Elliptic Base Curve

Trochoids and cycloids are glisettes: curves generated when a closed curve rolls inside or outside a fixed base curve.
In this Demonstration, the rolling curve is a circle, which rolls without slipping on an elliptic base curve; the generated curve is called a hypotrochoid or an epitrochoid, according to whether the circle rolls on the inside or the outside of the ellipse. The generator point (or pole) that draws the curve is at a variable distance from the center of the rolling circle. If is equal to the circle radius, the trochoids become cycloids.
The circle radius is computed such that the circle performs an integer number of revolutions around itself while completing a loop around the ellipse. The number of cusps formed in the completed curve is for a hypotrochoid and for an epitrochoid.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2017 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+