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  1. Let there be two squares (or rectangles, but say its squares for simplicity).
  2. These squares are attached to an axis (bellow, marked red) around which they can rotate.
  3. For simplicity, let's say they are on a corner.

Theorem:

When rotating simultaneously, continuously and at the same speed, there should exist a pair of points (or probably multiple pairs) on the surface of each square, which will stay at the constant distance from each other during a part of rotation, meaning each of the squares will have rotated the same angle (i.e. 45, 90, 120, 180 deg).

Experimentation in a CAD program: enter image description here

  1. We can connect a beam (pic1 - blue line) between the two points and they will successfully rotate (around axes marked red) together and maintain distance (rigid beam). But then they will rotate at different speeds!
  2. If we connect elsewhere, rotation speed changes, test point pairs in the picture - violet, yellow, green.
  3. This suggests that there exists two points where the distance AND the rotation speed BOTH stay constant (pic 1).
  4. If the points are correct, angles of both rotations should be equal at all times even with the fixed beam between the points (pic 2)

enter image description here

Question: how to correctly identify these pairs?

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  • $\begingroup$ are you saying that the gray squares rotate around the red points? ... what do the orange squares represent? $\endgroup$
    – jsotola
    Mar 24 at 21:17
  • $\begingroup$ But they rotate at different speeds ... what does that mean? $\endgroup$
    – jsotola
    Mar 24 at 21:22
  • $\begingroup$ @jsotola orange are just some left over planes. Didn't know how to hide them $\endgroup$
    – Danielius
    Mar 27 at 22:38
  • $\begingroup$ It means what is said... If you connect them, you cannot rotate them at the same speed, there appears some kind of function of an non linearity... I will adjust the grammar of that sentence $\endgroup$
    – Danielius
    Mar 27 at 22:40
  • $\begingroup$ that means that the distance between tbe points varies $\endgroup$
    – jsotola
    Mar 27 at 22:46

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