X=Manipulate[
Show[ParametricPlot[{{A-Sin[x],-1+Cos[x]}},{x,0,2 π},
PlotRange->{{-1,2 π+1},{0.5`,-2.5`}},
PlotStyle->{{Gray,Dashed}},
Ticks->{{0,(π/4),(π/2),((3 π)/4),π,((5 π)/4),((3 π)/2),((7 π)/4),2 π},{{-1,"1"},{-2,"2"}}},
GridLines->{{0,(π/4),(π/2),((3 π)/4),π,((5 π)/4),((3 π)/2),((7 π)/4),2 π},{0,-1,-2}},
LabelStyle-> {Directive[24],FontFamily->"Palatino"},AspectRatio->Automatic,ImageSize->Full],
ParametricPlot[{{A-Sin[x],-1+Cos[x]}},{x,0,A+(1/(10^5))},
PlotRange->{{-1,2 π+1},{0.5`,-2.5`}},
PlotStyle->{{Red,Solid}}],
ParametricPlot[{{x-Sin[x],-1+Cos[x]}},{x,0,A+(1/(10^5))},
PlotRange->{{-1,2 π+1},{0.5`,-2.5`}},
PlotStyle->{Thick,Blue}],
Graphics[{Thickness[0.003`],Darker[Green],Arrowheads[0.02`],Arrow[{{A,-1},{A-Sin[A],-1+Cos[A]}}]}],
Graphics[{Thick,Black,Arrowheads[0.02`],Arrow[{{-1.1`,0},{2 π+1,0}}]}],
Graphics[{Thick,Black,Arrowheads[0.02`],Arrow[{{0,0.5`},{0,-2.5`}}]}],
Graphics[Text[Style["x/r",Directive[18],FontFamily->"Palatino"],{2Pi+0.9,0.15}]],
Graphics[Text[Style["y/r",Directive[18],FontFamily->"Palatino"],{0.2,-2.4}]]
],{A,0,2Pi,Pi/50}
]

Export["Cycloid.cdf",X,"CDF"]