Cycloid[t_] := Module[ {C, D}, 
C ={{Thick, Black}, Circle[ {t, 1}, 1]};
D ={{Red, Thick}, Disk[ {t - Sin[t], 1 - Cos[t]}, 0.1]};
Return[Graphics[{C, D}]];
];

P = ParametricPlot[ {t - Sin[t], 1 - Cos[t]} , {t,-Pi, 4Pi}, AspectRatio -> Automatic,  ImageSize -> 500];
Manipulate[ Show[P, Cycloid[t]], {t, 0, 4 Pi}]