Egon, way back there 50-52 years ago when I was doing tire repairs, I'd never heard of a tire machine. We did have a little manual device for breaking the bead on ordinary car and pickup tires, but for trucks and tractors, we had a sledge hammer that was, in fact, a hammer on one side and much like a very very blunt chisel on the other side. It took a little practice initially, but you soon learned to swing the big sucker so that broad chisel blade hit the rubber right at the rim and slipped in between the rubber of the tire and steel of the rim (there was no such thing as aluminum or alloy wheels). And you just worked your way around the rim until the bead broke loose, then you turned the wheel over and did the other side. And yes, I did split rim and split ring wheels when we'd never heard of cages. Of course we had heard of people being killed by those things, so when I put one together, initially I'd put just enough air to straighten the tube without the valve core, then let that air out so the tube could relax and be straight in the tire. Then install the valve core, apply air a little at a time, and tap on the rim all the way around to be sure that split rim or ring was properly seated. We'd do that a half dozen times before getting up to the operating pressure. But then we wised up a bit and would raise the car lift, put the truck tire under there and let the lift down almost onto the tire. And I was lucky enough to never have one explode or give me any trouble.
Of course, the last one of that type I had to work on was in July, 1972, in Canada, enroute to Alaska, when twice I had to work on one of the tires/wheels on my 1971 3/4 ton Chevy pickup which still had bias ply tube type tires and split ring wheels.