Model: R04 Rolling Cones with Point Paths for 1:3 Diameter Ratio

- imagemovie

The rolling of one circle on another in the plane produces epicycloid and hypocycloid point-paths. In this model, the rolling of non-planar circles is produced by the rolling of one cone inside another cone with a diameter ratio of 1:3. A point on the moving cone traces out a closed spatial curve or point path with three lobes. Similar point paths can be seen in models R- 3, and R-7. Point paths of non-planar rolling circles are important in the design of bevel gears, whose motion is equivalent to that of rolling cones.

Francis Moon 2004-10-25

#### Reference :

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

#### Resources :

- CAD Model : Reuleaux R.04 Rolling Cones with Point Paths for 1:3 Diameter Ratio CAD Model
- Movie : Reuleaux R.04 Rolling Cones with Point Paths for 1:3 Diameter Ratio CAD Movie
- Still Image : Reuleaux R.04 Rolling Cones with Point Paths for 1:3 Diameter Ratio CAD Picture
- Tutorials and Descriptions : R Series: R01-07. Spherical Cycloids and Involutes