The projector has a vibration problem. The vibration is causing the framing to move down. You can see the vibration when you look in the back of the machine becuase the shutter drive assembely is bouncing on its spring.

When I loosened the shutter to retime the shutter, I turned on the machine and the vibration was gone. When I tightened the shutter the vibration was back.

What do you think?

Your observation would certainly seem to implicate the shutter. Is there any evidence that the shutter has been modified (e.g. cut or bent) in some way? Is there any gap between the hub and shaft which might make it rotate slightly off center? Since it rotates at 1440 rpm, any imbalance could cause vibration.

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If you take the shutter completely off and run the machine for a few seconds you'll see the end of the shaft sort of "dancing" as it spins. If it doesn't then I'd take the shutter and see if it balances. Get a big screwdriver and put it through the hole. Hold the screwdriver perfectly flat and level then give the shutter a spin. Watch how it spins and notice if it spins evenly. Do it two or three more times and see if one side always ends up at the bottom. (Use a marker and put a mark on it so you can tell.) If it does always end up one side down you've probebly got an out of balance shutter.

If not, maybe there is a problem in the shutter shaft, bearings, spline, drive gears or something like that. Are all four of those allen screws that hold the shutter shaft and bearing assembly properly tightened?