Rolling discs

Slotted discs, large and small

Take two identical discs and slot them together along diameters so that the discs are perpendicular. There is one separation of centres for which the compound shape has a centre of mass which remains a constant height above the surface of a table. The resulting shape rolls along in a most intriguing way.

Three configurations of rolling ellipses.

Take two identical elliptical discs then it is possible to repeat this construction. Slot them together along major axes so that they are perpendicular. There is a separation of centres for which the centre of mass of the compound shape remains a constant height above the surface of a table.

Rolling pears

Similar shapes can be made in a variety of ways!