It would be a speed governor for a steam engine.The speed governor is connected to the engine wheel (not shown) though a chain and pulley at the base of the governor. The chain spins the governor when the engine wheel turns. When the engine starts to speed up, the governor spins faster, and centrifugal force will force the balls to rise as shown by the lighter outlines in Figure 2. The position of the balls is an indication of the rotational speed. Watt did not invent this device; the device was already in use for other rotating machinery. Watt invented the method to feed this speed signal back to the steam throttle to control the rate steam is admitted to the cylinder.A Brief History of the Steam Engine
It’s a governer to control the speed of the machine.
In simple tearms the balls and attached linkage are attached to the throttle, or valve, or whatever contols power going to the machines power source. Perhaps a steam engine.
As the machine speeds up, because the load has decreased, the balls are swung out away from the vertical shaft, this causes the linkage to reduce the machines power, closes the valve admiting steam to the engine. As the vertical shaft slows down, the balls swing down and more steam is admitted to the engine. There is a set of springs that make it harder or easier for the balls to move out/up. These springs determine the RPM the machine is regulated at.
This was all before electronic/electrical controls.
BTW, the term “running balls out” meant it was running as fast as possible.
There may be additional explainations to the team, but that’s the one I’ve been hearing for 60 years. YMMV.