Noncircular Roller Drive

In this Demonstration, a roller drive is simulated by two curves rolling along each other without slipping. The curve on the left is the driving roller and turns at a constant angular speed. The curve on the right is the driven roller and turns at an angular speed proportional to the ratio between the radii of both rollers at their contact point.
Controlling the parameters to , you can vary the cumulative angular displacement curve of the driven roller. These parameters can also be used to compute the equivalent polar curves of both rollers.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


For a good article about curves rolling along other curves, see [1].
Take the cumulative angular displacement of the driving roller to be and that of the driven roller to be .
The radius at the mutual contact point of the driving roller is , and that of the driven roller is . These are effectively the polar equations of both curves.
[1] J. Bloom and L. Whitt, "The Geometry of Rolling Curves," The American Mathematical Monthly, 88(6), 1981 pp. 420–426. http://www.jstor.org/discover/10.2307/2321826.
    • 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 © 2018 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+