Location of the point

Circle rolls on a straight line

Circle rolls outside a fixed circle

Circle rolls inside a fixed circle

On the circumference

Cycloid

Epicycloid

Hypocycloid

Inside the circumference

Curtate Cycloid

Curtate Epicycloid

Curtate Hypocycloid

Outside the circumference

Prolate Cycloid

Prolate Epicycloid

Prolate Hypocycloid