\(p\  = \ 
      ParametricPlot[{t\  - \ Sin[t], \ 1\  - \ Cos[t]}, \ {t, 0, 4  π}, 
        
	PlotStyle -> RGBColor[1, 0, 0], 
        PlotRange -> {{\(-1\), 13}, {0, 2}}, 
	
        Ticks -> {{0, π, 2  π, 3  π, 4  π}, {0, 1, 2}}]
        \)

Do[Show[p, 
        Graphics[{Circle[{t, 1}, 1],  PointSize[ .02], 
            Point[{t  -  Sin[t],  1  -  Cos[t]}]}], 
        AspectRatio -> Automatic], {t, 0, 4  π}]