Rolling a Polygon on a Circle

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

This Demonstration simulates a regular polygon rolling without slipping around a stationary base circle of radius 1.

[more]

The roulette traced by a point attached to the polygon consists of two different curve types:

1. involute curve sections when an edge of the polygon rolls tangentially over the base circle.

2. circle arcs when a vertex of the polygon makes contact with the base circle.

Varying the circumradius of the rolling polygon changes the circumference ratio between the polygon and the base circle.

A closed curve can be obtained after one revolution around the base circle if the circumference of the -sided regular polygon equals .

By increasing the number of vertices of the polygon, the trace approaches an epitrochoid.

[less]

Contributed by: Erik Mahieu (June 2015)
Open content licensed under CC BY-NC-SA


Snapshots


Details



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send