The Hierapolis sawmill is believed to be a Roman water-powered stone sawmill at Hierapolis, Asia Minor (modern-day Turkey). Dating to the second half of the 3rd century AD, the sawmill is considered the earliest known machine to combine a crank with a connecting rod, although neither clear ancient scripts nor engineering drawings were yet found to support this theory.
Some archaeologists believe that the watermill is evidenced by a raised relief on the sarcophagus of a certain Marcus Aurelius Ammianos, a local miller. On the pediment a waterwheel fed by a mill race is shown powering via a gear train two frame saws cutting rectangular blocks by the way of connecting rods and, through mechanical necessity, cranks (see diagram). The accompanying inscription is in Greek and attributes the mechanism to Ammianos' "skills with wheels".
Hierapolis sawmill Wikipedia
Further Roman crank and connecting rod mechanisms, without gear train, are archaeologically attested for the 6th century AD water-powered stone sawmills at Gerasa, Jordan, and Ephesus, Turkey. A fourth sawmill possibly existed at Augusta Raurica, Switzerland, where a metal crankshaft from the 2nd century AD has been excavated.
Literary references to water-powered marble saws in Trier, now Germany, can be found in Ausonius' late 4th century AD poem Mosella. About the same time, they also seem to be indicated by the Christian saint Gregory of Nyssa from Anatolia, demonstrating a diversified use of water-power in many parts of the Roman Empire.
The three supposed finds push back the date of the invention of the crank and connecting rod mechanism by a full millennium; for the first time, all essential components of the much later steam engine were assembled by one technological culture:
With the crank and connecting rod system, all elements for constructing a steam engine (invented in 1712) — Hero's aeolipile (generating steam power), the cylinder and piston (in metal force pumps), non-return valves (in water pumps), gearing (in water mills and clocks) — were known in Roman times.