Roulettes

Roulettes are curves generated by the rolling contact of one curve or line on another curve or line.  There are various types of roulettes. The most common types of roulettes used in engineering practice are: Cycloids, trochoids, and Involutes. Assume a wheel is rolling along a surface without slipping.     Trace the locus of a point on the wheel.  Depending on the position of the point and the geometry of the surface on which  the wheel rolls , different curves are obtained. Table 1  provides the general classification of roulettes.

Cycloid:  Cycloid is generated by a point on the circumference of a circle rolling along a straight line without slipping.
Epicycloid:  The cycloid is called Epicycloid when the generating circle rolls along the circumference of another circle outside it .
Hypocycloid: Hypocycloid is obtained when the generating circle rolls along the circumference of another circle  but inside it.