Model: R02 Rolling Cones

The curves traced by the rolling of one cone on another are called spherical cycloids. This model illustrates space curves traced by the rolling of a cone inside another cone with a diameter ratio of 1:3. These curves are similar to the mathematical cycloid curves traced by a plane cylinder rolling on another cylinder. This is Reuleaux's version of 3D graphics. In this model, three curves are traced by three points on the rolling cone. The point on the conical axis traces a circular path, while another traces an elliptically shaped path on a spherical surface. The third path appears to have two cusps and is traced by a point on the circumference of the rolling cone. Rolling cone motion is found in helical gear mechanisms still used in modern automobile transmissions.

Francis Moon 2004-10-25

#### Reference :

- Henderson, Taimina : Experiencing Geometry (ch.21, 2005)

#### Resources :

- Tutorials and Descriptions : R Series: R01-07. Spherical Cycloids and Involutes