Pedal sometimes getting stuck Back story

During this weekend we went on a trip with rented bikes, and observed the following problem on one of them: the left pedal would sometimes not spin on the shaft (i.e. it remained in the same position, no matter, how the shaft was turned, whereas the normal functioning would be that it is always "horizontal", i.e. it changes its angle relative to the shaft, when the shaft moves -- so that you can keep your foot horizontal too). This is of course very unpleasant and could be even dangerous. (The pedal could be made to spin, by applying much more force on it than normally.)
As I said, the problem was intermittent: sometimes the pedal was spinning normally, then it would get stuck for sometime, then it would get unstuck and spin again, without any apparent reason.

We could not find a way to remove (and then put back) the pedal either, but I'm not sure it would have helped (we also thought of lubricating it, but did not do it in the end). 

Questions


How are pedals attached and spinning on the shaft?

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I'm guessing that they are not directly spinning on the shaft, because then they would unscrew (or tighten) as they spin. So I think there must be a rod, which is tightened on the shaft, and a bearing around that, and then the pedal spins on this bearing. Is this correct?


If this is correct then the issue must have been with the bearings and removing and putting back the pedal wouldn't have helped. Am I correct?
The correct solution would have been probably to lubricate the bearings, but how can you do it? Can you take it apart and then assemble it again so precisely that it still works afterwards?
A pedal is made of two major components. 


The pedal body, which is where your foot presses.  This part rotates around the pedal axle once per crank revolution.  It does not rotate with respect to the ground or your foot.
The pedal axle, which supports the body and threads into the crank arm.  The axle does not rotate with respect to the crank arm, but does rotate wrt to the ground and to your foot.
Sundries like bearings or bushings to reduce friction.




This is a modern pedal cutaway to show the axle (sometimes called a spindle or shaft.)  The pedal body should turn freely on the axle with minimal finger pressure.  A good shove of the body should make it spin around from 1 to 10 times.   Modern cheap plasticky pedals may only move a part of a turn.

Your hire bike probably had seized bearings in one pedal, making the body locked to the axle.  The quick fix is to add light lubricant in both sides if possible.  If that doesn't fix it, the hire shop should have quickly swapped out the pedal with a spare.   If they were plastic pedals then sometimes they crack in weird possibly hard to see places, but locking the bearings is a common consequence of damage.

Causes - bikes ridden in the wet/salt/grit/sand and put away dirty.  No bearing system likes dirt.   A good clean and relube can save a lot of pedals, but some are just too-far gone.