Hello!
Thanks for providing a visual reference. This animation is actually pretty simple to recreate, in fact, here it is:
As you mentioned, the spiral part of the carpet follows the same principle of the windmill blades here:
Windmill example: Windmill Blades
The carpet roll was just scaled down proportionally weighting each end to a bone to maintain the correct perspective.
And the carpet below is directly deformed during the animation to simulate its unfolding.
You can download the project to study it here:
spine-carpet.zip
