How Do Two Rotating Rods Interact?

[haruspex]

I see it like this. A full cycle of the system occurs when rod A performs 1 full rotation and rod B performs 2 full rotations – we’re then back to the originaL start position.

Take point A as the origin so AB lies on the x-axis.

$\theta_A$ is rod A’s direction ($\theta_A = \omega t$) and similarly for rod B, $\theta_B = 2\omega t = 2\theta_A$.

There rods don' intersect for $\pi/2 <\theta_A<3\pi/2$.

But, for example, consider $\theta_A =7\pi/4$. Rod A bisects the 4th quadrant. Rod B points at $7\pi/2$ which is the -y direction. The intersection (point C) is ($l, -l$) so that ABC is a right-angled isosceles triangle.

Is there a mistake in my logic?

No, you are right. It wasn’t as obvious as I thought you were implying, but I didn't follow it through far enough.

 

[eitan77]

Thank you very much to all of you, you helped me a lot!