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Get Top View of a 'toroid helix' which rotates around its circular axis?

Posted 4 months ago
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enter image description here enter image description here

Consider a very thin toroid helix which rotates around its circular axis (which passes through individual turns) while it is on a 'friction-full' surface. How would then the top view of the overall motion look like?

(Thin means to neglect elastic compression/elongation effects while helix rolls)

I guess it should be rotating around the center point while the individual turns are rotating around instantaneous circular axis.

An animation would be very much appropriate, kindly somebody come up with that.

(image source - https://i.stack.imgur.com/yLq6t.jpg)

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}]
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