Something like this:
Manipulate[
ParametricPlot3D[
Evaluate[RotationTransform[t, {0, 0, 1}][
RotationTransform[20 t + a, {0, 1, 0}, {1, 0, 0}][{1 + 1/3, 0,
0}]]], {t, 0, 2 Pi}, PlotPoints -> 40,
ColorFunction -> Function[{x, y, z, u}, Hue[20 u]]],
{a, 0, 4 Pi}]