Risu the Troll
If you made it curve, the drill action wouldn't work properly though, because the end of the blade would swing too far out. Unless I'm totally misinterpreting the instructions.
Wouldn't friction in the hilt just make the hilt heat up?
Well, honestly, there'd be no point in having a spinning katana, anyway, as a majority of the motions/moves used in traditional swordfighting would not be conducive to a drilling motion, not to mention negate the beauty of a katana's ability to make a perfectly clean cut/slice. With this in mind, one would assume that a spinning katana would be a purely fantasy-based weapon. However, without the characteristic curve, a katana ceases to appear as such, and becomes a standard-looking single-edged sword.
That aside, it is an interesting idea for a weapon.