|Bottom Center: Dog Driver Plate|
This is a historic item that you are most unlikely to see in current use. Although lathe chucks have been widely available since the civil war, they have historically been fairly expensive. Lathes were sold with a face plate, and machinists either attached their work to a face plate if conducive to that, mounted it on a mandrel, or put the work on centers. The latter two needed some way to turn them, which was readily accomplished with a clamp or a dog. The most usual solution is a Dog.
Dogs were available in all sizes with both a straight tail and a bent tail (shown). The dog slips over the shaft and the set screw is tightened, and the dog tail is inserted in a driver plate for "dog face". The Dog Clamp is similarly installed but has a U Bolt and 2 nuts to tighten instead of a set screw. Dogs are still often used. I would say you are more likely to find a dog clamp in a museum than in a machine shop.