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When the black circle with radius 1 rolls on the outside of the blue
circle with radius 6 the fixed red point on the small circle traces
out an arc of the epi-cycloid E6 and when it rolls
on the inside the blue circle it traces out an arc of the hypo-cycloid
H6. The six arcs form the curve
A3.
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When the circle with radius 1 rolls on the outside of the circle with
radius 8 the fixed green point on the small circle traces out arcs of
the epi-cycloid E8 and when it rolls on the inside
it traces out arcs of hypo-cycloid H8. The eight arcs
form the curve A4.
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When the blue circle with radius 6 rolls inside the black circle with
radius 8 the moving red curve A3 is enveloped by
the green curve A4.
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The construction above is lifted to horizontal
planes z = constant.
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The blue circle is rolled a distance proportional to the height
z. Observe that the blue circles no longer are above each other.
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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.
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The motion generated by letting the blue cylinder roll inside the
black cylinder is in each horzontal plane the same as before.
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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.
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