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Internally Geared hubs are quite a marvel of engineering. They use multiple complex systems to initiate tan enclosed shifting mechanism. They are being included here because they use some similar designs of parts to the freecoaster. They also are often called “coaster-brakes” when they actually are not.
An internally geared hub engages when rolling backward, can shift smoothly (even when not moving), and can have a back pedal brake. The original patent for a 3-speed internally geared hub was filed in 1903 by Sturmy Archer. They have been making these hubs ever since.
Here are a few diagrams and pictures of each. As I find more resources, I will post them up here.

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