<< Algorithms
How a Spinning Object
Can Remain Connected to
a Stationary One

Imagine a ball in the middle of the room suspended in the air by six elastic cords. Call them ropes. Each rope is glued to the ball at one rope-end and to a wall, the ceiling, or floor at the other. The ropes are all straight and untwisted.

Then the ball starts turning around on its vertical axis. The rope-ends attached to the ballís surface go around with it while the rope-ends attached to the room remain stationary. The ropes become tangled and twisted.

The ball turns around exactly once and pauses. During this pause you can try to untangle the ropes but you wonít succeed.

Then the ball continues turning around, in the same direction, and stops after a second turn. Surprise, now you can untangle the ropes so they are all straight and untwisted, as they were at the beginning.

The ropes can be manipulated while the ball turns so the ball spins without pause forever yet the ropes never tangle and twist beyond a certain amount. This can be done with any number of ropes, six was just to be definite.

The computer program Antitwister shows movies of this motion.  It can also show the ball spinning while attached to the room by an elastic web that completely encircles the ball.

Some of the Motions the Program Can Show

Direct Antitwister
The elastic never wraps around or twists beyond 360°.
The elastic is straight and untwisted every two turns of the ball.
Adams Antitwister
Here the elastic is never straight and untwisted, its twist is always 180°.
A pole rope moves in an especially simple way:  it bends but never twists, it keeps its shape, and remains in a vertical plane.  This plane rotates at exactly half the speed of the ball.
Dirac String Trick
First the ball turns twice around, the elastic passively following.  Then the ball stops, and remains stationary while the elastic moves to untwist itself.
Rotation of a Rotation
The ball remains stationary.  A 360° twist of the elastic in one direction turns over to a 360° twist in the other direction, and back again.  The rotation of a rotation.
Dirac Flip
First the ball turns once around, the elastic passively following, and stops.  Then the elastic moves to reverse the twist as in the preceding motion.  The ball then turns once more, the elastic passively following, and the twist is undone.
Spinning Wheel
Twister rather than Antitwister.  The elastic twists ceaselessly as the ball remains stationary.  (The motion, unlike that of the other motions, is not periodic.)
A pole rope moves like the yarn in a spinning wheelís flyer mechanism, which guides the yarn in a way to make it twist as itís wound on the bobbin.

I set up and ran Antitwister.  I have to tell you that I am truly stunned and amazed.  The continuous web images are especially intriguing.  I had never seen the Adams machine, where the ball spins at exactly twice the rate of the orbiting rope.
— M. S.
Antitwister is a cool program and itís great fun modifying all the settings to see what happens and mesmerizing to watch it deal with any variable.
— A. T.

Thank you for sending me your fascinating program.  I never tried anything like it and I am delighted that I can do it.

Do you have something more theoretical to explain the background ?
— LŠszlů Tisza
Yes,  see  The Dirac String Trick.
See also the  U.S. patent for a mechanism  invented by Dale A. Adams.

(upgraded  11 June 2024)
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