Assorted musings
The mention of steam pumps brought to mind the reciprocating pumps of the Worthington Simpson kind.
These used what I would call a form of gab gear to operate the steam valve to reverse the motion of the power piston.
(In a similar way to quickly flinging the reversing lever from forward to reverse, and back again, on a steam locomotive. )
Beam engines of the Cornish type used the steam power to raise the pump rods. The majority of the pumping was done by the weight of the massive wooden pit gear driving the pump plunger down. Until Trevithick, steam pressures were of the order of only 5 psi. He advocated using "Strong Steam" at 40 psi.
The valves ("nozzles" ) were controlled by tappets, which could be moved, on rods connected to the beam, and so directed steam to upper or lower side of the piston to cause the beam to reciprocate.
The beam engines at Coleham Head, in Shrewsbury pumped 112 and 114 gallons at each stroke. These engines were rotative, and had flywheels some 11 feet in diameter.. Normally, they ran at 11 rpm. At 16 rpm they were reputed to shake the building!
The flywheel basically stores kinetic energy to provide momentum to carry the crankshaft through the points where the piston is producing little or no rotative power, and by absorbing energy during the power strokes serves to damp out the power surges and deliver a more even delivery of torque. In effect it decreases angular acceleration during the power stroke, but increases it during idle strokes.
It does not do this totally effectively. Witness the torsional oscillations at the free end of a crankshaft, when an engine is under load, although torsional flexibility of the crankshaft effects the magnitude of the vibration.
The hammer blow referred to in connection with steam locomotives, most obvious in two cylinder locomotives, is the result of the secondary forces resulting from balancing the primary forces. (piston, connecting rod, and crankpin ) Multi cylinder locomotives, particularly four cylinder, with divided drive, used the forces generated by one pair of cylinders to counteract those produced by the other pair.
Attempts to minimise hammer blow on two cylinder locomotives had the side effect of producing a fore and aft oscillation, which was most prevalent in the first coach of the train.surge.
Possibly, connecting the piston rod to a pendulum would cause enough energy to be stored to run the egine through the inner and outer dead centre positions.
Howard