

When the black circle with radius 1 rolls on the outside of the blue
circle with radius 2 the fixed red point on the small circle traces
out an arc of the epicycloid E_{2} and when it rolls
on the inside the blue circle it traces out an arc of the hypocycloid
H_{2} (a diameter). The two arcs form the curve
A_{1}.

When the circle with radius 1 rolls on the outside of the circle with
radius 4 the fixed green point on the small circle traces out arcs of
the epicycloid E_{4} and when it rolls on the inside
it traces out arcs of hypocycloid H_{4}. The four arcs
form the curve A_{2}.



When the blue circle with radius 2 rolls inside the black circle with
radius 4 the moving red curve A_{1} is enveloped by
the green curve A_{2}.






The construction above is lifted to horizontal
planes z = constant.

The blue circle is rolled a distance proportional to the height
z. Observe that the blue circles no longer are above each other.

By rotating the picture in each horizontal plane the blue circles can
be positioned over each other such as to form a blue cylinder inside a
black cylinder.

The motion generated by letting the blue cylinder roll inside the
black cylinder is in each horzontal plane the same as before.






A series of pump chambers are formed and they move upwards as rigid
bodies under the motion generated by the letting the blue cylinder
roll inside the black cylinder.
