I don't know how quite they work either.
But here's a thought experiment to help the mind accept that it's not too difficlut:
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A positive displacement pump can be run backwards as a motor.
So by controlling flow through it you control its speed.
That let's you make a very handy device - something that absorbs or delivers torque
at controllable speed.
Connect that to one axle of an automobile differential
and to the other axle, your alternator.
Now drive the input shaft with an engine at some nominal speed
and you can control alternator speed by how much flow you allow through your pump.
That's because a differential gear takes difference between two displacements.
Differential gear was a calculating element before Henry Ford latched onto it. He was a mechanical genius. We forget what an elegant function it really performs.
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Now - if you run a positive displacement pump as a motor, its speed will be in proportion to flow through it.
That means it can be used to measure flow.
In 1930's a boiler fuel oil control system actually used a Model T differential to compute fuel flow. Two positive displacement pumps run as motors, one measuring supply to burners and one measuring return from burners, were geared into the axles but turned in opposite directions. Drive shaft spun at rate proportional to fuel consumed by burners and was used to set airflow to propoer air/fuel ratio..
It was before my time but my mentor remembered it well.
I think it was an old Smoot Controls system. Automatic Controls was not a so well developed field prior to WW2.
Here's an old ad:
https://www.amazon.com/dp/B005DH6KIG/?tag=pfamazon01-20
Anyhow i was reminded of this by the two "displacement units" and differential near top of this link you gave:
http://www.k-makris.gr/AircraftComponents/CSD/C.S.D.htm
and this animation you linked - the swash plate probably controls flow through a positive displacement pump of some sort. Watch it move as you select speeds.
http://17-11-1991.deviantart.com/art/constant-speed-drive-207261432
It's the exact same basic idea as thought experiment above.
Details improve but basic principles are long - lived.
Sorry for long post, but wanted to get you thinking about workings of gears and hydraulic pumps.
Hope this helps. I'll look at your links some more.
THANKS !
old jim