Yes, the magic is possible the way you describe, but if i got you right, and all the so called "cogs" are just some symbols, which let spells to work, then i don't get why they would ever need so many of them. If they can make something to rotate by itself, then what for build gearboxes all over the Winch, if these rotating thingies could have been directly in the point where needed, probably many on one axis, to increase the strength. And if they aren't supposed to rotate at all, then i still fail to see what for put so many of them in small areas all over the winch.
I been always thinking the magic is for the engine and the control descs they have there, with these monitors and stuff.
There are dwarves, blacksmiths and others who maintain the whole mechanism, even if they don't get how the whole thing works, they need to know a little, so that, while they maintain, they know how too. They need to know well how pieces of the mahinery works and so we should be allowed too. Mistery is good, but if it's mistery, because noone really disigned the mahinery, how the NPCs are supposed to say something with sense anyway? We have no way to learn it because of this. Why not while NPCs can and from IC PoV they are the same people as our characters.
As about the shape, i made animation:
http://psgrafika.republika.pl/cogs-l3.swffrom 1st to 10th frame and from 25th to 45th frame, the teeths aren't touching another (don't panic, its not 66% of the time ;P, the animation just slows down at the and and starts slow at the start, couldn't make it regular) Anyway, it turned out the cogs can still rotate quite well. Only because of the "touching of the teeths" which isn't occuring, the cogs work in fact irregurly (to hard for me to animate it well) more than
http://psgrafika.republika.pl/cogs-l1.swf for instance. This means constant speeding and slowing up, which is bad.
I believe that because of the force each cog is causing to another (if they ever were supposed to rotate ;P) and the friction, the teeths tips will get used up and you get a cog more or less of this:
http://psgrafika.republika.pl/cogs.swf shape. And you get big clearance, because the cogs weren't designed this way.
A good alternative for 3D designer is
http://psgrafika.republika.pl/cogs-l1.swf as it saves up some face, put leaves the principle.
It would be suprising if they didn't know in Yliakum, that cogs get used up this way, especially that they didn't invent it like 10 years ago. There is the waterwheel in BD and it's qute old. If it's supposed to move up some simple mahinery, there are needed at least a few cogs. I assume that they figured out since the first implementations, that the cog can't have o sharp teeth tips.
If there was a chain, they would work well with it, but there is none and they look like they should work directly one with another.