Animation stays blank during animation

Question

In attempting to answer this question about animating a rolling disk, I constructed a ParametricPlot to Animate. The plot looks fine when not animated, yet while the animation runs the slider moves but there is no plot until the animation stops; after a short delay, the final state of the plot shows up.

How do I ensure the animation shows the elements of the plot?

 mypara[α_] := ParametricPlot[
   {
    {Cos[θ], Sin[θ]},
    {2 Cos[α] + Cos[θ], 
     2 Sin[α] + Sin[θ]}
   },
   {θ, 0, 2 π},
   {r, 1, 2},
   PlotRange -> 3,
   Frame -> False
   ]
 Animate[
   mypara[α],
   {α, 0, 2 π, π/6},
   AnimationRepetitions -> 1
   ]

Answer 1

Another way is just to render the frames first and then use ListAnimate, (BTW I set y0 to -0.1, since its definition is missing)

mypara[\[Alpha]_] := 
  ParametricPlot[{{Cos[\[Theta]], Sin[\[Theta]]}, 
  {2 Cos[\[Alpha]] + Cos[\[Theta]], 2 Sin[\[Alpha]] + Sin[\[Theta]]},
  {r, 0}}, 
  {\[Theta], 0, 2 \[Pi]}, {r, 1, 2}, PlotRange -> 3, Frame -> False]

 list1 = Table[mypara[\[Alpha]], {\[Alpha], 0, 2 \[Pi], \[Pi]/6}]
 ListAnimate[list1, AnimationRepetitions -> 1]