Belt drives or cable drives can transmit power somewhat more flexibly and, I think, efficiently than shaft drives. A belt or cable doesn’t need enough material to be rigid, just enough to withstand the tension, and it can in theory move arbitrarily fast.
Belt or cable speeds, however, are limited by centrifugal forces around pulleys, which need to have larger radii in order to proportionally reduce the centrifugal forces at a given linear speed — and the area of the pulley increases as the square of its radius. And, of course, at least half the material of the belt is “wasted” in the sense that it’s not carrying any energy, just being returned from the power source to the load under minimal tension.
Suppose that instead of an endless belt we use a straight tension cable, as in a child’s pullstring toy, and instead of transmitting power continuously, we transmit power intermittently. Perhaps 90% of the time, the rope is moving from the load to the source at its maximum safe tension of 1000 N and at 3 m/s, and 10% of the time, it’s moving from the source to the load at 100 N and roughly 30 m/s. Such a rope is transmitting an average power of 2700 W, the equivalent of 12 amps at 230 volts.
0.42 mm² of UHMWPE string can handle 1000 N, assuming 2.4 GPa and no safety factor. Such a string weighs 410 mg/m; 100 m of it weighs 41 g. 100 N accelerates 41 g at 2400 m/s², so it can reach 30 m/s in 12.3 ms. This means you could quite reasonably transmit power in this way with a 10 Hz oscillation in the line, which means the string would move only about 30 cm.
Piano wire also has a yield stress of about 2.5 GPa, although to avoid fatigue you’re supposed to stick to a third of that or so. So a similar amount of piano wire could also transmit a similar load. It would weigh 8 times as much, and it would have more friction, but it wouldn’t be as vulnerable to overheating.
(Hmm, I realize now that the 100 N restoring force is really nothing more than a centripetal force.)
If instead of one cable under tension, you have two, you could maintain continuous power with no intermittency; but, if the power being transmitted doesn’t vary, you could never exceed the power that one cable could transmit at a time, so in a sense the other cable is wasted.
If, instead of two cables, you have three cables, you can have two cables transmitting power at any given time while the third is returning. This allows two-thirds of the mass and volume of your transmission cable to be used for power transmission, while keeping the power transmission perfectly consistent. Furthermore, this can avoid the large accelerations implied in the single-cable skewed triangle I suggested earlier; the speed of the cable that’s about to go into takeup can diminish gradually while the cable that’s just gone into the power cycle can smoothly speed up, maintaining a constant total speed. This is highly desirable, given that the mechanisms driven by the cable can easily weigh much more than the cable, and even 100 m is not very far in some contexts.
It should be emphasized that this kind of three-phase power transmission cannot use the same sinusoidal waveforms used by electrical AC power transmission if two cables are always to be kept in tension.
The three phases can drive a common differential via freewheel clutches.