It was some fun little idea I had when working on a project but for some strange reason I didn't get it to work.
Rotation is all wrong, linking/parent the knot to the rope didn't work. I tried with time remapping the frames from the animation.
So I left it out, but now I'm wondering what I forgot to do.
The Beam effect coupled with some displacement should be decent for the rope. To have one end of the rope attached to the circle, an Expression to link the End Position of the Beam effect to a Null's Position Property should work. BUT first, copy and paste the circle's Mask Path property to the Null's Position.
You can KF the Mask Path and then copy its KFs to the Null's Position to get a more interesting effect. There is no need to rotate the circle. A Ramp and/or animated Vegas effect should help to provide the illusion that the circle is rotating.
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Or you can try Plexus - if you use Lights as points, you can get a line to move in 3d space between the two Lights/Points, Link and position one light to the character running, link a Null to this Light, position it as the center of the lasso loop and link the second Light to it, positioning to be on a circle (either a 2d layer with a circle graphic positioned in 3d space, or use Particular on a different layer using the same Light as a generator together with the "ipod streak" technique to create a true volumetric 3d loop). If you rotate the loop centered Null on it's y axis you should get what you need (add a x or z axis variation to simulate the wobble)