geometry - Plotting an epicycloid

I am fairly new to Mathematica, and I cannot figure out how to plot an epicycloid. I have plotted some neat looking things in my attempts, but I still can't make one. I am not looking to make an animation; I just want the plot of an epicycloid.

Would I use PolarPlot or ParametricPlot? How do I get a static picture of an epicycloid?

Answer

I recreated the animation on Wikipedia:

enter image description here

Here is the Manipulate version:

R = 3; r = 1;

fx[θ_, a_: 1] := (R + r) Cos[θ] - a r Cos[(R + r) θ/r];
fy[θ_, a_: 1] := (R + r) Sin[θ] - a r Sin[(R + r) θ/r];

gridlines = Table[{x, GrayLevel[0.9]}, {x, -6, 6, 0.5}];


plot[max_] := ParametricPlot[
  {fx[θ], fy[θ]}, {θ, 0, max},
  PlotStyle -> {Red, Thick},
  Epilog -> {
    Thick,
    Blue, Circle[{0, 0}, R],
    Black, Circle[{fx[max, 0], fy[max, 0]}, r],
    Red, PointSize[Large], Point[{fx[max], fy[max]}],
    Black, Line[{{fx[max, 0], fy[max, 0]}, {fx[max], fy[max]}}]

    },
  GridLines -> {gridlines, gridlines},
  PlotRange -> {-6, 6}
  ]
Manipulate[plot[max], {max, 0.01, 2 Pi}]

Comments

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