Can the following cycloid equation be transformed into the display form of $y = f (x)$ by eliminating parameters $\phi$?
\begin{equation} \left\{ \begin{array}{**rcl**} x=r(\phi-\sin \phi)& \\ y=r(1-\cos \phi) & \end{array} \right. \end{equation}
I know that it can be easily reduced to the form of $x = f (y)$ and probably there is no explicit elementary function form of $y = f (x)$.
Are there any related theorems that can determine whether a parametric equation can eliminate parameters and express it explicitly?