A slight 2

dimensional extension of the

cycloid. See also

cyclohedron for an extension of the cycloid into

three dimensions.

The curtate cycloid is defined to be a cycloid measured at a point

*outside* the generating

circle:

,.onOK@@@@@HQme.,
,.szF'` `'Tux.,
,z'` `'c,
,x'` `'w,
.u'` `'n.
dy qb
/7 VA
4y \D
,I' `U,
dp qb
,j' `t,
AV VA
69 96--a--* (x,y) <-- example point of measure,
VA AV distance "a" from the edge of the circle.
`t, ,j'
qb dp
`I, ,U'
\D 4y
VA /7
qb dy
`'n. .u'`
`'w, ,x'`
`'c, ,z'`
`'Tux., ,.szF'`
`'TTOK@@@@@HQTT'`

Let (x,y) be a point of the

curtate cycloid, where the generating circle has radius

**r**, and the shortest distance from (x,y) to the edge of the circle is

**a** at all

angles

**t**. Then,

`
x=`**r***(**t**-sin(**t**))-**a***sin(**t**)

and

y=**r***(1-cos(**t**))-**a***cos(**t**)