Steam “power” began with the Savery and Newcomen engines, but James Watt greatly improved efficiency (and economy) by moving the condensation part of the cycle out of the cylinder.
They did not use the steam to produce power, just atmospheric pressure. The return stroke was gravity powered by the weight of the pump rods extending down the mine.
Watt then devised his linkage, which replaced the chain, to connect the arctuate motion of the end of the beam to the linear motion of the piston rod.
In some respects, Watt stifled the use of steam engines, by strictly enforcing his patents on the condenser, motion, and the crank. Hence the Cornish steam cycle! (There were few rotative engines in Cornwall, using beam engines to carry men and materials to and from the surface).
Even then Watt used low pressure steam, (5 psi) which meant the engines were big, and low powered, because the weight limited speed.
Richard Trevithick, who pioneered steam powered vehicles, was a believer in what he called “strong steam”, at aboiut 40 psi so that a smaller engine, running faster, could deliver as much power as the bigger low pressure engines.
The later development of compound and then triple or quadruple expeansion engines improved both power output and economy.
(If you want to see the largest triple expension engine in Britain, in action, visit The Water Works Museum in Hereford (UK) on a steaming day . It is entirely run by volunteers, so only open on Tuesdays and Sundays, – which is often a steaming day.)
Howard