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

Is it possible to connect a spinning object to a stationary one without a sliding joint? What else could prevent the connection from twisting, and eventually breaking apart?

Imagine a box with a ball in the middle. Elastic ropes tether the ball to the sides of the box. The ropes are solidly anchored at their ends, there are no sliding joints.

The ball begins to turn, carrying along the rope-ends attached to its surface.

The program Antitwister shows movies of the ball spinning any number times without the ropes breaking.  It can also show the ball spinning while attached to the stationary enclosure by an elastic web that completely encircles the ball.

Motions the Program Can Show

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.
The ball remains stationary.  The elastic moves to twist itself, then to untwist.
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 wheel’s flyer mechanism, which guides the yarn around the spindle, twisting it before it’s wound on the bobbin.

Some Testimonials
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.
Antitwister is a cool program and it’s great fun modifying all the settings to see what happens and mesmerizing to watch it deal with any variable.

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 ?
— Laszlo Tisza
Yes,  see  The Dirac String Trick.

for Windows computers

Program updated 14 Aug 2016:  CPU usage drops to normal when pictures are not being drawn.  Improved Twister/Untwister.  Fixed bug when recording Spinning Wheel in rare situations.  Fixed bug that caused incomplete erasure of movie frames in rare situations.

Text, program and pictures   2015