(*Nasser M. Abbasi*) r = 1; backgroundAxes = Plot[0, {x, -Pi, 5 Pi}, PlotRange -> {Automatic, {-r/2, 2 r + .5}}, AspectRatio -> Automatic]; Animate[Show[{backgroundAxes, ListPlot[Table[{x - Sin[x], 1 - Cos[x]}, {x, 0, t, .1}], Joined -> True], Graphics[{PointSize[Large], Red, Point[{t - Sin[t], 1 - Cos[t]}]}], Graphics[Circle[{t, 1}, r]]}], {t, 0, 4 Pi}]