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.

Sean Madsen, David von Seggern