Cycloid

Manipulate[Show[
  Table[Graphics[{
     RGBColor[0.8, 0.5, 0.5],
     Disk[{t + tt, 0}, 1],
     PointSize[Medium], Blue,
     Point[{t + tt + Sin[t + tt], Cos[t + tt]}]
     }, PlotRange -> {{-Pi, 3 Pi}, {-1.1, 1.1}}]
   , {tt, -4 Pi, 4 Pi, Pi}]
  ,
  ParametricPlot[{\[Theta] + Sin[\[Theta]],
    Cos[\[Theta]]}, {\[Theta], -Pi, 3 Pi}, Axes -> None]
  ], {t, -Pi, 0}]