Cranks were known in Roman times. The knowledge wasn't lost in the Middle Ages, because the crank was an essential part of the crossbow. Yet, it took centuries before the crank came to minting. The invention is usually credited to an Augsburg silver smith, Marx Schwab. However, metalworking machines driven with cranks were already in use in the silver mines of the Harz.
Schwab's merit is perhaps that he made a machine that would actually work for longer periods, using the correct trade-offs of thickness of plate and precision of parts. This came to the attention of Charles de Marillac, French ambassador to the free city. Marillac went into secret negotiations with Schwab, who was code-named "Chevalier de Saint-Sépulchre". A top-secret mission, consisting of the intendant (minister of finance and Marillac's brother) and François Guilhem, director of the Lyon mint, went to Augsburg to buy the equipment. Guilhem was dead set against it, foreshadowing two centuries of opposition against machines in all mints. He was replaced by an engineer, Aubin Olivier. The transaction was concluded and the machines shipped to Paris before an envoy from Charles V arrived in Augsburg. Meanwhie, Aubin Olivier had learned how to work the machines. The first mechanized mint was set up on the Ile de la Cité in Paris, using water power.
The new mint operated at full capacity from 1551 to 1554. The cost of the mint were higher than expected and the opposition of the minter's guild was venomous. Mint master Marillac was accused of fraud, the cour des monnaies decided the new mint could only make medals, top staff was promoted away. However, what killed the mint was the succession of the mentally weak Charles IX in 1559, who considered himself an accomplished old-fashioned minter.
This scenario was repeated in other mints, only the names of the actors changed. The main problem was probably that the machines could not yet be made with enough precision, so they broke down often, which would explain the higher cost. As technical knowledge improved over the next 100 years, the screw press proved unstoppable. No amount of guild power could reason with the beautiful, well struck, round coins of mechanized mints.
The illustration is again from Diderot. At the time the screw press had become commonplace. Note that the boy is still there, feeding planchets into the machine, but there are now four minters.
Peter