Its called a REEL MOWER commonly used on golf courses, specifically on the greens. Reel mowers allow for a more calculated cut, they are actually the best lawn mower to mow any lawn with but they are so expensive most people cant afford them to mow their lawn.

Golf courses use them because they need to keep the greens cut very VERY VERY low to allow for a fast ball speed too high of a cut and the golf balls wont roll .

I make a living every day working on these awesome mowers. I would recommend buying one if you can afford the high price