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How do I enter 3 parametric equations for cycloids corresponding to circles with radii 1, 2, and 4. I have tried

ParametricPlot[{{1 (θ - sinθ), (1 - 
 sinθ)}, {2 (θ - sinθ), (1 - 
 sinθ)}, {4 (θ - sinθ), (1 - 
 sinθ)}}, {θ, -2 π, 2 π}]
Michael E2
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Crich
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    All Mathematica commands start with capital letters. ParametricPlot[{ {Sin[theta], Cos[theta]}, 2 {Sin[theta], Cos[theta]}, 4 {Sin[theta], Cos[theta]}}, {theta, -2 Pi, 2 Pi}, ImageSize -> Medium] or ParametricPlot[{ {Cos[theta], Sin[theta]}, 2 {Cos[theta], Sin[theta]}, 4 {Cos[theta], Sin[theta]}}, {theta, -2 Pi, 2 Pi}, ImageSize -> Medium] – Bob Hanlon Nov 18 '14 at 02:56

2 Answers2

8

Just for fun:

f[a_, t_] := a {t - Sin[t], 1 - Cos[t]}
Manipulate[
 ParametricPlot[{f[1, 4 t], f[2, 2 t], f[4, t]}, {t, 0, 4 Pi}, 
  PlotStyle -> {Red, Green, Blue}, 
  Epilog -> {{Orange, Circle[{4 p, 1}, 1], Black, PointSize[0.015], 
     Point[f[1, 4 p]]}, {Orange, Circle[{4 p, 2}, 2], Black, 
     PointSize[0.015], Point[f[2, 2 p]]}, {Orange, 
     Circle[{4 p, 4}, 4], PointSize[0.015], Black, 
     Point[f[4, p]]}}], {p, 0, 4 Pi}]

The following animated gif was made just replacing Manipulate with Table.

enter image description here

ubpdqn
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1

Here is what I believe you are seeking:

ParametricPlot[{{1 (Theta - Sin[Theta]), 
1 (1 - Cos[Theta])}, {2 (Theta - Sin[Theta]), 
2 (1 - Cos[Theta])}, {4 (Theta - Sin[Theta]), 
4 (1 - Cos[Theta])}}, {Theta, -10 Pi, 10 Pi},
AspectRatio -> .5, PlotRange -> {{-8 Pi, 8 Pi}, Automatic}]

The resulting Plot:

enter image description here

bbgodfrey
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