# [✓] Plot the circles within a Manipulate?

GROUPS:
 Consider the following code: hypocycloid[tend] := Module[{a = 4, b = 1, x, y, p}, x[t_, p_] := b (a/b - 1) Cos[t] + b p Cos[(a/b - 1) t]; y[t_, p_] := b (a/b - 1) Sin[t] - b p Sin[(a/b - 1) t]; ParametricPlot[{x[t, 1], y[t, 1]}, {t, 0, tend}, PlotStyle -> {Red, Thick}, Ticks -> None, ImageSize -> 225, Epilog -> {Thick, Blue, Circle[{0, 0}, a], Black, Circle[{x[tend, 0], y[tend, 0]}, b], Red, PointSize[Large], Point[{x[tend, 1], y[tend, 1]}], Black, Line[{{x[tend, 0], y[tend, 0]}, {x[tend, 1], y[tend, 1]}}]}, PlotRange -> (1 + 1/20) {-a, a}]]; Manipulate[Quiet@hypocycloid[tend], {tend, .0001, 2*Pi}] 
 Marco Thiel 3 Votes It does work if you define your functions properly: hypocycloid[tend_] := Module[{a = 4, b = 1, x, y, p}, x[t_, p_] := b (a/b - 1) Cos[t] + b p Cos[(a/b - 1) t]; y[t_, p_] := b (a/b - 1) Sin[t] - b p Sin[(a/b - 1) t]; ParametricPlot[{x[t, 1], y[t, 1]}, {t, 0, tend}, PlotStyle -> {Red, Thick}, Ticks -> None, ImageSize -> 225, Epilog -> {Thick, Blue, Circle[{0, 0}, a], Black, Circle[{x[tend, 0], y[tend, 0]}, b], Red, PointSize[Large], Point[{x[tend, 1], y[tend, 1]}], Black, Line[{{x[tend, 0], y[tend, 0]}, {x[tend, 1], y[tend, 1]}}]}, PlotRange -> (1 + 1/20) {-a, a}]]; Then Manipulate[Quiet@hypocycloid[tend], {tend, .0001, 2*Pi}] does work.Cheers,Marco