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Cycloid Curves

​
revolutions
2
ratio
2.
The curve traced out by a point on the rim of a circle rolling along a straight line is called a cycloid. Let the radius of the circle be
a
. Allowing the tracing point to be either within or without the circle at a distance
b
from the center generates "curtate" or "prolate" cycloids, respectively. The variable
ratio
is
b/a
, limited to the range [0, 2]. For
ratio=0
, the result is a straight horizontal line. For
0<ratio<1
, the curve is a curtate cycloid. For
ratio=1
, it is an ordinary cycloid. For
1<ratio≤2
, it is a prolate cycloid. Note that
ratio>2
is allowable but not used here.
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