Model: R07 Point Path for a Rolling Cone on a Plane Surface

The point paths of planar circles rolling on each other generate a class of curves called cylcoids. In the case of conical surfaces rolling on each other, we have spherical cycloids. In model R-7, a cone rolls on a planar surface such that the ratio of diameters of the contact circles is 1:3, thereby generating a three lobe point path in space. This model is a limiting case of models R-3 and R-4. The rolling of cones on each other is important for understanding the motion of helical gear pairs.

Francis Moon 2004-10-25

#### Reference :

- Henderson, Taimina : Experiencing Geometry (ch.21, 2005)
- Reuleaux : Constructor (§215, §216, 1893)

#### Resources :

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