Routers aren't made the same as power motors. The HP rating is developed HP and not the same either. A 3HP router may only draw 5-6 amps.
The biggest reason, though is that the bearing system on a router is made for very little side load. If you do what you are planning, there will be a router in the trash next week.
There is also a real possibility of things flying across the room at a high rate of speed.
Don't do it.
Stacy
Go Mike,
Worm gears, and geared reduction systems are to slow normal speed motors down to slow speeds, not to slow fast things down to normal speed. If a gear reduction box was run at 12,000RPM, it would burn up.
When you want something to turn at 100RPM you use a gear box. When you want something that turns at 12,000 RPM to run at 1750RPM, you either reduce it with an 8:1 pulley ratio, or (much better idea) use a different motor. Fan belts don't like 12,000RPM and more than gears do.
Stacy