The Industrial Revolution and the world's first factories antedated electricity. How is it possible that a machine shop could run, in an age when you couldn't just plug a machine into a socket?
The answer is, miles of leather (or cotton) belts. Factories had their power source, whether it was a steam engine or a waterwheel, rigged up to drive huge rotating shafts called line shafts. These were suspended overhead and festooned with pulleys. Belts ran from these pulleys down to the factories' machines (or to intermediary pulleys driving another belt), where they drove each machine through another pulley. The line shaft was the powerstrip of the day.
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Machines could be turned "off" by sliding the belt from a fixed pulley onto a loose pulley next to it. By cutting power to the machine, you could then switch the belt onto pulleys of different diameters on the machine, which changed the machine's speed of rotation. In the lower right of both photos below, you can see machines that have pulleys of multiple diameters stacked up against each other.
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Sometimes you had machines that needed to rotate in the opposite direction of the line shaft. There was a simple trick to this: You simply twisted the belt a half turn, making it into a figure eight. You can see one such twisted belt on the right side of the photo below.
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Wondering what it all sounded like? Here's footage of a line-shaft-driven machine shop in Elnora, Indiana:
Fun to watch, but probably not so fun to work within. According to Louis C. Hunter and Lynwood Bryant's "A History of Industrial Power in the U.S., 1780-1930: Vol 3: The Transmission of Power," the line shaft system had plenty of downsides: The layout of machines was dependent on the location of the line shaft rather than efficiency; the systems were noisy, dangerous and dirty; they required frequent lubrication, meaning oil was constantly dripping onto everything.
Then there was the air quality, with the belts constantly shedding and circulating dust—right next to the worker using the machine. When factories finally switched over to electric in the 20th Century, manufacturers not only saw a productivity boost—they also noted "significantly less employee sick time."