The Industrial Revolution was a factor in the uptake of democracy, sure. Just as WWI, WWII and the Cold War were. But it all started in 1776 in the US with the Declaration of Independence and in the 1790s with the French Revolution, which was the inspiration for South America to declare independence from Spain and establish their own democracies with different levels of success. The French Revolution didn't last in France, not at first, but the core concepts are the basis of our current democracy largely in part because the American Revolution kept them alive and spread them.