Hypocycloid Involute

$\begin{figure}\begin{center}\BoxedEPSF{HypocycloidInvolute.epsf scaled 700}\end{center}\end{figure}$

$\displaystyle x$	$\textstyle =$	$\displaystyle {a\over a-2b} \left[{(a-b)\cos\phi-b\cos\left({{a-b\over b}\phi}\right)}\right]$
$\displaystyle y$	$\textstyle =$	$\displaystyle {a\over a-2b} \left[{(a-b)\sin\phi+b\sin\left({{a-b\over b}\phi}\right)}\right]$

$\displaystyle x$	$\textstyle =$	$\displaystyle {a-2b\over a} \left[{(a-b)\cos\phi+b\cos\left({{a-b\over b}\phi}\right)}\right]$
$\displaystyle y$	$\textstyle =$	$\displaystyle {a-2b\over a} \left[{(a-b)\sin\phi-b\sin\left({{a-b\over b}\phi}\right)}\right],$

which is another Hypocycloid.