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