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