Model: R03 Spherical Cycloidal Rolling

The R series embody mathematical principles of rolling cones on cones. In R-3 a brass cone rolls on the outer surface of another cone with diameter rario of 1:3. The spatial curves generated by the rolling of the cone are represented by curved brass rods. In effect the model represents Reuleaux's version of 3D mathematical graphics. In R-3, a point on the rim of the rolling cone generates three lobes in space corresponding to the ratio of the diameters of the cones at the edge. The rolling of a planar circle on another circle generates curves called epicycloids (traced by a point on the circumference). Reuleaux called the curves generated by rolling cones as spherical cycloids. These curves and motions can be found in modern applications 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