From where did the ideas that generated the Atlantic Revolutions of the 18th century emerge? What were the consequences of these revolutions at a global level?

Enlightenment ideas from France and Great Britain were the primary influences on the Atlantic Revolutions, which included the American Revolution, the Haitian Revolution, and the French Revolution—all of which occurred within twenty years of each other. John Locke's ideas about the natural rights and liberty of men, as well as notions about property rights, were especially important in the context of the American Revolution. Montesquieu's idea about the separation of powers, as explained in The Spirit of Laws was another important influence in forming American government. 
The American Revolution is believed to have strongly impacted the leaders of the Haitian and French Revolutions. The American colonies had successfully thrown off a much older and greater power, on the basis of self-determination (e.g., no taxation without representation—a notion that did not extend to slaves, of course) and a desire for a democratic government in which everyone would supposedly be given equal access to opportunities to obtain property and participate in government while also being protected from any potential abuses by government. 
Along with Enlightenment ideas that stressed the "natural rights of man," Toussaint L'Ouverture and Dessalines may have believed that if the Americans could overthrow Britain, the Haitians could overthrow the French. The Haitian Revolution began in 1791 and ended in 1804, one year after the Louisiana Purchase. Unfortunately, Haiti's triumph did not last. Over the centuries, the nation has been exploited by greater powers and has fallen to dictators.
The French Revolution took place in 1789. After the Revolution, there was a great deal of interaction between American and French dignitaries. Benjamin Franklin, John Adams, and Thomas Jefferson all spent time in France. The exchange of ideas between the two nations, during the revolutionary period and after, was key in the development of both nations and in the persistence of their democratic ideas.