I once worked in a business that sharpened reel mowers. The most common were the ganged, pull-behind made by Worthington.
Originally Posted by Mike Burdick
The reel is taken off the mower, mounted on the centers of its shaft and ground. There are two ways to sharpen reels, a cylindrical grind and whatever the other is called. For a cylindrical grind the reel is treated as a cylinder, ground smooth, and then a relief is ground leaving only a very small land. In the other method the relief is ground all the way to the cutting edge, then the reel is lapped to the bedknife by running it backwards with a little valve grinding compound. The bedknife was ground on a separate machine with a vertical spindle and cup wheel, then traversed from end to end. It was noisy dusty work and I don't miss it, though I appreciate knowing how.
"In theory there’s no difference between theory and practice. In practice there’s a lot of difference.” Yogi Berra