Stiff rope

Actually a chain with rigid bodies as the segments.
In reality,a rigidbody cannot exist it would explode when any perturbation happens.
Here,I didn't give it the code of maximum allowed force so it would instead oscillate between frames.

I don't understand the oscillation. When you pick up one of the dots and move it sideways, its neighbors should notice and move with it. Sometimes that happens, but sometimes it starts jittering instead.

That's the problem with a finite time step.
A segment(the lines) should receive force states that's out of phase.(i.e 2 collide 1,after a frame then 3 collide 4,then the errors would be resolved)
Sometimes its in phase and would jitter.(i.e 2 collide 1,and 3 collide 4 after an even number of ticks,then 2 and 3 would jitter.)

Sometimes the rope goes to the origin because it just happened that two hinges occupied the same point and the repelling force doesn't know which direction to go.

Got it. I guess it could be a very tiny finite time step. :~)