A circle of radius r is rolling on a parametric "base" curve B(t).
A spoke of length R is connected to the center of the
circle, and a pencil attached to the end of the spoke traces a resulting curve.
Note that the situations where the circle would get "stuck" in the base curve
(e.g., due to the radius of curvature of B(t) becoming smaller than r) are not recognized.
A physical interpretation of the resulting curve could be based on considering the 2D
picture to be a projection of a "thin" 3D picture.
base curve 
parameter values 
Line: B(t) = ( 2 pi t, 0 )

r=1, R=1 (cycloid) 
r=1, R=2 (prolate cycloid) 
r=1, R=0.5 (curtate cycloid) 
Circle: B(t) = ( 3 cos(2 pi t), 3 sin(2 pi t) )

r=1, R=1, inside (hypocycloid) 
r=1, R=0.5, inside 
r=1, R=1.5, inside 
r=1, R=1, outside (epicycloid) 
r=1, R=0.5, outside 
r=1, R=1.5, outside 
Parabola: B(t) = ( t, t^{2}  5 )

r=1, R=1, inside 
r=0.9, R=1.5, inside 
r=0.5, R=1.5, inside 
r=1, R=1, outside 
r=1, R=1.5, outside 
r=1, R=0.5, outside 
