Model: R01 Spherical Cycloid for a Plate Rolling on a Cone.

Models R-1 to R-7 are mathematical in nature and present geometric curves in space generated by the rolling of plates and cones on other cones. The rolling of a circle on a plane generates a curve called a cycloid. The curves represented in these models are called spherical cycloids by Reuleaux. Mechanisms based on rolling cones include bevel gear pairs that are used in many applications including automotive components. In model R-1, a circular plate rolls on a conical surface. The plate is fixed at the apex of the cone by a spherical joint. As the plate rolls a point on the edge, marked by a red line, generates a closed space curve that is constructed out of brass or bronze. A similar model with a plate and a cone is R-6.

Francis Moon 2004-11-04

#### Reference :

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

#### Resources :

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