Short answers, pulled from the story.
The Antikythera mechanism of Greece stands as one of the earliest known examples of a gear train. This ancient device used multiple gears to track celestial movements with remarkable precision for its time.
Renaissance scientist Georgius Agricola produced illustrations showing gear trains with cylindrical teeth during the 16th century. These drawings documented how engineers were beginning to standardize gear designs for practical machinery.
Input torque applied to gear A transforms into output torque exerted by gear B through the principle of virtual work. If gear A has 10 teeth and gear B has 15 teeth, the system amplifies input torque while reducing speed.
Hunting gear sets feature gear teeth counts that are relatively prime on each interfacing pair so any single tooth on one gear will contact every tooth on the other before repeating the same pairing. This distribution minimizes wear and extends the life of mechanical components significantly.
An intermediate gear which does not drive a shaft performs work is called an idler gear. In a three-gear sequence where gear A meshes with idler I which then meshes with gear B, the overall ratio remains unchanged from direct engagement.
The 2004 Chevrolet Corvette C5 Z06 features a six-speed manual transmission with ratios ranging from 2.97:1 down to 0.56:1. First gear requires the engine to make 2.97 revolutions for every single revolution of the transmission's output shaft.