How did the search for trade routes to the Orient lead to connections between the Americas, Europe, and West Africa?
The connection originally began with Christopher Columbus' plan to reach Asia by sailing West. Columbus used measurements indicating the Eurasian landmass to be much larger than it actually is; and also measurements indicating that the circumference of the earth was much smaller. Were his measurements correct, Tokyo, Japan would have been in the vicinity of Knoxville, Tennessee. Rather than Asia, he landed in the Caribbean. Whether he knew he was not in Asia is problematic; however he did claim the islands where he landed for Spain.
The Americas were not a wonderful new discovery to the people of Europe; in fact they were largely ignored. It was only much later that the Spanish began to explore in search of gold. Later they determined that the islands in the Caribbean were good for the cultivation of sugar cane, for which there was an insatiable market in Europe. At first, the Spanish enslaved Indians to work on their sugar cane plantations, but they proved poor workers and died frequently. The solution was the importation of slaves from West Africa. Hence was born the connection between the Americas, Africa and Europe, all as a result of Columbus' attempts to reach Asia.
The search for trade routes to the Orient led to the "discovery" of the Americas and to European contact with West Africa. That subsequently led to the horrific contact between Africa and the Americas in the form of the "middle passage" slave trade.
Beginning in 1420, Portuguese ships began exploring down the west coast of Africa. This exploration culminated in Vasco Da Gama's rounding the tip of Africa and sailing to India in 1498. The whole point of this was to allow Portugal to trade with the Orient, but it ended up creating contact between Europe and West Africa.
Of course, Columbus was searching for a way of getting to the Orient by sailing west when he "discovered" the New World. This led to contact between Europe and the Americas. By 1518, the first load of slaves was brought from West Africa directly to the Americas and contact was made between those two continents.
England had established three different types of colonies in North America: royal, proprietary, and charter. Over time, England transformed several of the charter and proprietary colonies into royal colonies and appointed royal governors for them. By the early 1700’s, therefore, the colonial governments shared a similar pattern of governing. One reason the British government allowed its colonies freedom in governing themselves was that England had a long tradition of strong local government. Another reason was that the British government lacked the resources and the bureaucracy to enforce its wishes. Finally, the existing economy and politics of the colonists already served British interests, and the colonists considered themselves loyal subjects of the king.