You're close to getting it. It took me a while to get my head around too.
Think back to school physics. The direction of the current depends upon the motion of the conductor and the direction of the magnetic field. I'll admit now, I can't remember it either so will refer to current going 'one way' or the 'other'.
Then look here.....
http://www.windstuffnow.com/main/3_phase_basics.htm
Ignore the fact for a moment that it says three phase, but look at the diagrams where it says 1st 2nd and 3rd phase. Imagine them as time frames for the SAME piece of wire.
You can see that as the RED wire, it doesn't cover any magnets and nothing is flowing. An instant later (BLUE wire) the DOWNs of each coil are cutting across the N and the UPs of each coil are cutting across the S, and so current is flowing around that coil.
An instant after that (GREEN) its going off the magnet and the current is begining to fall again.
You can see that if you carry this on, the current will flow in the opposite direction as the DOWNS go across the S and the UPS go across the N magnet faces.
It helps to draw that magnets on a piece of paper and the coil on something transparent and move one slowly across the other. I did this and plotted the current flow, hey presto, a sine wave!
Once you have this bit right, you will see SINGLE phase ac. Most of what you will see on here will be THREE phase, which is just more coils (to put it simply) spaced so that there is always something happening. You can go back now to Ed Lenz's page and read it again, and if you're feeling really brave try the transparency trick and plot that.
http://www.k-wz.de/physik/threephasegenerator.html
Unfortunately, there's no substitute for reading everything you can find, but hopefully this gives you an insight.
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