Great question. A fanning mill is a winnowing machine. Winnowing is the step of cleaning the grain to separate the considerable chaff, dust, weed seeds and whatnot from what you want to eat. Winnowing is done after the thresher knocks the grains loose from the head. The most basic technology for winnowing is the shallow baskets that can be seen in traditional Chinese paintings of pretty girls tossing the rice harvest up and down in a breeze. This gets old, I'm just here to tell you.
In modern times, the winnowing is done within a large, expensive combine, which moves through the fields cutting the heads off the stalks, threshing, and spitting the clean grain into a bin and the chaff in a stream out the back. Considerable intermediate technology exists between hand threshing with a flail and winnowing with baskets in the breeze and needing a $250,000 combine to harvest 2000 acres of wheat. We just seldom see that level of intermediate technology.
Small threshers can be powered with a tractor or even horses. And a small winnowing machine is a fanning mill. Fanning mills range in size from tabletop models to permanently mounted big honkers. They used to be common on farms, even if the farm had a combine, for cleaning feed, seed crops, and small quantities of edible grains. Fanning mills are still produced and sold, primarily for the seed industry (think flower seed, vegetable seed, bird seed and lawn grass seed.)
In the late 19th century, the A.J. Ferrell company sold many small fanning mills to farmers throughout the country. The Ferrell Clipper consists of a frame, differently sized screens for different kinds of seed, and a small electric motor for shaking the screens. As appropriate technology, it worked so well that the modern Clipper is still sold in tabletop "laboratory" and larger stand alone models. You don't want to ask what a new one costs.
Which is why I went looking for an old one. They are still around, mostly in the Midwest. By the time we got a lot of momentum farming here in the Northwest, there was already a transition to larger farms and larger machines.
Growing grain is the easy part. It's the harvesting, threshing and winnowing that is labor intensive. It's hard to hit the right scale. Even my 16 square foot wheat variety trials, grown in my garden, yielded enough to make processing it by hand a chore. I developed a better sense of what it would take to grow enough grain to actually do something with, such as feed chickens or feed yourself.
People are working on our local appropriate technology infrastructure. Walter Haugen of F.A. Farm uses a leaf shredder for threshing and a box fan for winnowing. Brian Kerkvliet bought a used chipper/shredder and slowed down the gearing to use as a thresher. He also made a winnower from a circular fan, a piece of irrigation pipe and two street Y's. Pretty cool, and a big improvement over hand screens, but without speed control, the Rube Goldberg winnower proved difficult to adjust.
Small scale grain growing is one of those things that is crazy until it isn't. With combines crawling over millions of acres of wheat on the Midwest, why would the small farmer or the even smaller gardener bother with grains? For all the same reasons for growing vegetables locally instead of ceding control over our meals to big growers in California. Because we want to preserve and eat delicious heritage varieties, because monocropping huge expanses of single varieties of grain has regularly led to crop failure in recent history (Southern corn blight, wheat stem rust), because an interest in local eating quickly leads past backyard broccoli to the question of where our energy crops come from, because not all grain varieties are suited to our tricky climate. Because we get 70% of our calories from energy crops and almost none of it comes from Whatcom County and vicinity. Because it's like everything else in reestablishing our local food production; it has to start with the whacko hobbyist.
I found an antique Clipper. They are getting hard to find. We are not the only whacko crazy people taking back their local food sovereignty out there. It has been stripped (only one screen, motor missing) but the frame looks OK in the picture, the motor can be replaced, more screens can be found used or locally fabricated. It's a pig in a poke; the true extent of restoration effort will not be apparent until it gets here from Illinois. It's a start.