The idea of this class of curves arose during an attempt to resolve an important problem in the doctrine of wheel-work; a statement of the conditions of that problem is thus the natural introduction to the subject.

When the shape of the tooth of one wheel A has been assumed, the shape of the tooth of another wheel B, to work along with it, may be deduced by a very simple graphic process; and when these two wheels are made to turn together, the points of contact describe a certain line or path.