You can grind knives on stones, and the endge will be hollow, in most case. That's how it was traditionaly done. You can see these great pictures of guys in SHeffied lying on their stomachs grinding away on pretty big wheels, driven by line shafts.
The downside is that the stones need to be very true, and kept clean (therefore you need to buy a tool for that), when used agresively they wear quite quickly. And they can fly apart and maim you. Belt sanders start at about 60 bucks, and have none of these problem...
The thing I like about grinding stones is that at standard operating speeds (no expensive variable speed units considered) they don't remove much steel, which means that tools like expensive HSS wood turning chisels last much longer than if sharpened on a fast belt unit. At 1800 rpm, you can use the stone you are cutting on almost as a jig, to roll a perfect cutting edge for the task. Burning isn't a problem with HSS, or one can buy the cool runing stones for the grinder, that wear real quick, but don't get hot. All this is kinda contrary to what one wants in a knife grinder.