The derivation of the complete investigation of the shape diversity of Epitrochoids / Epicycloids
An Epitrochoid is a curve (in the picture colored in red).
Epitrochoids are created while a moving wheel (colored in yellow) is scrolling around a fixed wheel
(colored in grey)
The point generating the curve can reside inside the yellow wheel, part of the tread of the wheel
or outside of the wheel (like in the picture).
The animation starts, if the Cursor is over the picture
If you move with the mouse obove an icon in the first row of pictures then an additional circle-shaped surface
will overlay inside the moving wheel.
The circle-shaped surface is a ring. Outside the ring is bordered by points,
which creates epitrochoids with approximate straight-lines.
This border is called the BALL Circle
The inner border of the ring is the point, which creates a circle.
Because this point is identical with the center of the ring, the ring will degenerate into a circular disc.
All points in the degenerated ring create curtate epitrochoids with centers of curvature,
which are inside the ring all the time.