 Vertical upward velocity of a rolling-point trochoid

A point at distance $a$ from the axis of a radius-$r$ cylinder rolling downhill at constant axis speed $v$ has $\dot{x}=v[\cos \alpha +(a/r)\cos \theta ]$, $\dot{y}=-v[\sin \alpha +(a/r)\sin \theta ]$. For $0\le \alpha <\pi /2$, the existence of $\dot{x}=0$, $\dot{y}>0$ is equivalent to $a>r$. At $a=r$ the relevant zero-horizontal-velocity point is stationary, so a point within or on the rolling cylinder never has strictly vertical upward motion.