Y=Manipulate[
Show[
ParametricPlot[{{A + Sin[x],-1+Cos[x]},{A+Sin[x],-3+Cos[x]}},{x,0,2Pi},
PlotRange->{{-Pi-0.3,Pi+0.3},{0.5,-4.5}},
PlotStyle->{{Gray,Dashed}},
Ticks->{{-Pi,-3Pi/4,-Pi/2,-Pi/4,0,Pi/4,Pi/2,3Pi/4,Pi},{{-1,"1"},{-2,"2"},{-3,"3"},{-4,"4"}}},
GridLines->{{-Pi,-3Pi/4,-Pi/2,-Pi/4,0,Pi/4,Pi/2,3Pi/4,Pi},{0,-1,-2,-3,-4}},
LabelStyle->{Directive[24],FontFamily->"Palatino"},
AspectRatio->Automatic,
ImageSize->Full
],
ParametricPlot[{{A-Sin[x],-1+Cos[x]}},{x,0,A+10^(-10)},
PlotRange->{{-Pi-1.1,Pi+1.1},{0.5,-4.5}},
PlotStyle->{{Red,Solid}}
],
ParametricPlot[{{A+Sin[x],-3+Cos[x]}},{x,0,Pi-A+10^(-10)},
PlotRange->{{-Pi-1.1,Pi+1.1},{0.5,-4.5}},
PlotStyle->{{Red,Solid}}
],
ListPlot[{{A-Sin[A],-1+Cos[A]}},
PlotStyle->{Red,PointSize->0.01}
],
ListPlot[{{A,-1},{A,-3}},
PlotStyle->{Black,PointSize->0.01}
],
ListPlot[{{A+Sin[A],-3-Cos[A]}},
PlotStyle->{Orange,PointSize->0.02}
],
ParametricPlot[{{x-Sin[x],-1+Cos[x]}},{x,-Pi,Pi},
PlotRange->{{-Pi-1.1,Pi+1.1},{0.5,-4.5}},
PlotStyle->{Thick,Blue}
],
ParametricPlot[{{x+Sin[x],-3-Cos[x]}},{x,-Pi,Pi},
PlotRange->{{-Pi-1.1,Pi+1.1},{0.5,-4.5}},
PlotStyle->{Thick,Blue,Dashed}
],
Graphics[{Thick,Blue,Line[{{A-Sin[A],-1+Cos[A]},{A+Sin[A],-3-Cos[A]}}]}],
Graphics[{Thickness[0.003],Darker[Green],Arrowheads[0.02],Arrow[{{A,-1},{A-Sin[A],-1+Cos[A]}}]}],
Graphics[{Thickness[0.003],Purple,Arrowheads[0.02],Arrow[{{A,-3},{A+Sin[A],-3-Cos[A]}}]}],
Graphics[{Thick,Black,Arrowheads[0.02],Arrow[{{-Pi-0.3,0},{Pi+0.3,0}}]}],
Graphics[{Thick,Black,Arrowheads[0.02],Arrow[{{0,0.5},{0,-4.5}}]}]
],
{A,-Pi,Pi,Pi/50}]

Export["TautochronePendulum.cdf",Y,"CDF"]