The annosphere uses relative gearing to turn a seasonal ring once a year while a sundial disk turns once a day. Relative gearing is not common, but it allows for high ratios using very few gears. It produces a relative movement determined by two gear ratios, rather than a simple ratio determined by two gears.
As an example, imagine two gears stacked on top of each other, rotating independently around a common shaft in the center. Let’s say the bottom gear has 100 teeth and the top gear has 99 teeth.
Now imagine that the two gears engage a single smaller driving gear, tall enough to mesh with both of the big gears. The number of teeth on this driver doesn’t matter, but let’s say it has 20 teeth. After the driver turns 5 times, the bottom gear, with 100 teeth, will have turned a single time. However, the top gear, with 99 teeth, will have turned one complete revolution plus a single tooth more.
After a single revolution of the bottom gear, the top gear has moved relative to the bottom gear by one tooth. After the bottom gear revolves 99 times, the top gear with 99 teeth will have revolved once relative to the bottom gear. The two big gears have a relative gear ratio of 99 to 1.
So while the ratio between the 100 tooth and the 20 tooth gear is 5 to 1, and the ratio between the 99 tooth gear and the 20 tooth gear is 4.95 to 1, the ratio between the ratios (5.00 and 4.95) works out to 99 to 1.