A planetary gearbox is a gearbox with the input shaft and the output shaft aligned. A planetary gearbox can be used to transfer the biggest torque in the most compact form (referred to as torque density).
The bicycle’s acceleration hub is a great exemplory case of a planet-wheel mechanism: Have you ever wondered ways to get so much power and features in such a small hub? For a three-rate hub, a one-stage planetary gear system can be used, for a five-acceleration hub a 2-stage. Each planet gear system includes a reduction state, a primary coupling and an acceleration mode.
In mathematical terms, the smallest reduction ratio is 3: 1, the largest is 10: 1. At a ratio of significantly less than 3, sunlight gear becomes too large against the planet gears. At a ratio greater than 10 sunlight wheel becomes too small and the torque will drop. The ratios are often absolute i.e. an integer number.
Whoever invented the planetary gearbox isn’t known, but was functionally described simply by Leonardo da Vinci in 1490 and has been used for centuries.