Sounds like an adjustable tenon cutter. I have my grandfather's. Comes with another tool that sort of looks like one of those little plastic pencil sharpeners that leave shavings all over your school desk, but also fits into a brace. My recollection is it's called a pointer maybe?
That tool puts a chamfer on the end of square or rectangular stock so the tenon cutter has a round area to get centered on. I don't know that Grandpa ever made a chair, but I did watch him repair a wagon wheel where he had to replace a felloe and 3 or 4 spokes. He cranked the round tenons on the ends of the spokes with that cutter in a hurry. As a toddler I was most impressed with the heating of the tire to expand it to get it back on the wheel.
My grandkids wouldn't understand of word I just typed--nor would they care, more's the pity.