(1)
 
(2)

is given by
(3)
 
(4)

As can be seen in the above figure, the involute is simply a shifted copy of the original cycloid, so the cycloid is its own involute!
(1)
 
(2)

is given by
(3)
 
(4)

As can be seen in the above figure, the involute is simply a shifted copy of the original cycloid, so the cycloid is its own involute!
Weisstein, Eric W. "Cycloid Involute." From MathWorldA Wolfram Web Resource. https://mathworld.wolfram.com/CycloidInvolute.html