Spinning 3-Dimensional Graphics

  ParametricPlot3D[
    {Sin[2t], Cos[5t], t, {Hue[.75], Thickness[.01]}}, 
    {t,0, 2*Pi}, BoxRatios -> {1, 1, 1}, 
    ViewPoint -> {2, 3, 0}, Background -> Hue[.07]],

can be spun (around the z-axis)by

  Table[
    ParametricPlot3D[{Sin[2t], Cos[5t], t, {Hue[.75], Thickness[.01]}}, 
      {t,0, 2*Pi}, BoxRatios -> {1, 1, 1}, 
      ViewPoint -> {2*Cos[Theta], 3*Sin[Theta], 0}, 
      Background -> Hue[.07],SphericalRegion -> True],
  {Theta, 0, 2*Pi, 2*Pi/35}]

(The modifier SphericalRegion->True helps to render each graph in the table in a consistent fashion.) The resulting animation looks like:

One can also spin the curve by using the command SpinShow. To use this command it is first necessary to load the Animation graphics package by

   <<Graphics`Animation`

Then enter

  gg = ParametricPlot3D[
         {Sin[2t], Cos[5t], t, {Hue[.75], Thickness[.01]}}, 
         {t, 0, 2*Pi}, BoxRatios -> {1, 1, 1}, 
         ViewPoint -> {2, 3, 0}, Background -> Hue[.07]]

  SpinShow[gg, Frames -> 35, SpinRange -> {0 Degree, 360 Degree},
    SpinTilt->{10 Degree, 15 Degree}]