[foodevl]

Switching the direction that you're twiddling the bolts would have to change the direction of any movement. But by symmetry, clockwise and counterclockwise twiddling are identical (looking down on the head of each bolt, one is always moving clockwise and one is always moving counterclockwise). So there must be no in/out movement at all.

[ndsipa_pomu]

This is similar to how I guessed the answer - it's a symmetric system, so there's no reason why it would be one direction over the other and so logically there would be no movement.

[aj7]

No there is not that symmetry, because the helix is handed, and the result could depend on the rotation direction with respect to that handedness.

[foodevl]

Relative to the handedness, one bolt is always moving with it, one bolt is always moving against it. Switching direction doesn't change that. So switching direction can't change whether it moves inward or outward.

[rdlw]

Couldn't you transform twiddling one way into twiddling the other way by reflecting through a mirror and turning the bolts 180 degrees end-over-end? If you start with the bolts moving North, the mirroring makes them go South, and turning them around makes them go North again, but now you're twiddling the other way. So the bolts would have to go North no matter which way you twiddle them, so either twiddling is not reversible (which is a repugnant proposition) or they must have a speed of 0.

[colanderman]

Moreover, the problem as posed doesn't specify the direction of twiddling, which kind of gives away the answer.

[fph]

The arrows in the picture specify the direction of twiddling. And the text says "see illustration".