What factors contributed to the success of the voyages between the 15th and 18th centuries?
One factor is that cartography improved during the Renaissance as trade increased between Asia and Western Europe. The riches of Asia gave the Europeans more incentives to find the fastest way to get there, and the fall of Constantinople in 1453 meant the land route was primarily closed. Renaissance cartographers looked at the methods of the ancient Greeks and Romans as well as Arab sailors in order to plan their trips and design their ships and sails, as ship designs took great leaps forward during this time as well.
Another factor is the rise of the nation-state and the joint-stock company. Sending out sailing vessels to Asia was quite risky, and it was not uncommon to lose everything in these ventures due to storms or pirates. Nation-states such as Spain were able to pay adventurers like Christopher Columbus from Italian city-states to sail to what would hopefully be Asia. The kingdoms of the Medieval period did not have this amount of capital on hand. Also, the joint-stock company of England made it possible for venture capitalists to fund their own voyages, such as the one which established Jamestown. The Dutch, great seafarers and traders in their own right, pioneered the use of maritime insurance, which increased the number of people willing to risk capital in order to gain a reward.