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)