Full Idea
The modern idea of explaining with mechanisms became current in the 17th century when Galileo articulated a geometrico-mechanical form of explanation based on Archimedes' simple machines. This became the 'mechanical philosophy'.
Gist of Idea
Galileo introduced geometrico-mechanical explanation, based on Archimedes
Source
report of Galileo Galilei (Il Saggiatore ('The Assayer') [1623]) by Machamer,P/Darden,L/Craver,C - Thinking About Mechanisms 5.2
Book Reference
-: 'Philosophy of Science' [-], p.15
A Reaction
So is Archimedes the source? I would say that mechanical explanation is just commonsense, and is predominant in all human thinking, even in tiny infants.