My 2 cents worth, for what that's worth:
The "variac" is an "auto-transformer". You may use a lower voltage than rated, however you may NOT USE A HIGHER voltage.(at 60 Hz AC) I doubt you would ever face that problem, with exceptions of course. The bottom line: you can safely connect to 120 VAC, just remember that current (amps, I, KVA) does not double. It is the limiting factor. If connected to 120 volts, the output would be ~140 volts max at rated current. That would give you a safe output of 0-100%=0-120volts for use with a grinder or other "sewing machine motor". I HAVE seen an induction motor used with a lamp dimmer as a speed control, but it was an industrial application and only "sorta-kinda" worked. OK for the application but not recommended.
Your clutch problem is a whole different issue. The determining factor there involves the manufacturer's spec sheet. I can only say for sure that DC would far and away do a better job than AC. A good strong DC field would be much more desirable for a clutch. (chuck) Use a full wave bridge and a good strong capacitor. A 1000MFD cap will suffice for 1 amp at power line frequency. With AC, you would get "zero crossing" at 120 times per second. Beyond that, you get into electrical theory serious and I don't have the 10 years or so to make you into an electrical engineer.
Oh, and by the way, when my name gets posted with this entry; you can add BSEE1974 in your mind. I posted an artical a few years back on the subject. But as a newbie I don't think the moderator will allow a link. Maybe later...
Try www(dot)hudsontelcom(dot)com and home shop electrics for a general overview of the subject.