Feynman defines the following:
We imagine that there are two classes of machines, those that are not reversible, which includes all real machines, and those that are reversible, which of course are actually not attainable no matter how careful we may be in our design of bearings, levers, etc. We suppose, however, that there is such a thing—a reversible machine—which lowers one unit of weight (a pound or any other unit) by one unit of distance, and at the same time lifts a three-unit weight
So to my understanding per this definition, a reversible machine is a machine that can sustain perpetual motion.
We are then introduced with the scenario in Fig. 4-2 which is defined as a reversible machine. One of Feynman's conclusions is that "Now, if 3X exceeds one foot, then we can lower the ball to return the machine to the initial condition, (f), and we can run the apparatus again. Therefore 3X cannot exceed one foot, for if 3X exceeds one foot we can make perpetual motion."
I'm not really understanding what Feynman is trying to point out here, if we assume the correctness of the axiom that this is a reversible machine (that it can lift 3 balls by lowering 1 and vice versa) then it already is technically capable of perpetual motion, i.e we are already in the established hypothetical framework that allows this reversible machine to work. Is he attempting to prove the machine is incapable of perpetual motion while it already is established as capable? What is he trying to get at? What is the sense in that? What was the point then in postulating that this is a reversible machine?