In the early 1800s, William Strutt designed a clock based on an epicyclic gear train. There is a good description of it in an edition of the Horological Times. The key elements of the gear train are shown in the following illustration. The frame, escape wheel and driving force are omitted.
To understand how this works, start from the minute arbor. It is attached rigidly to the planet carrier (white). As the carrier revolves, it moves the planet gear (green). The blue gear is one of two sun gears and is fixed to the frame (not shown). The movement of the planet gear has two effects. Firstly, it turns the ring gear (red). At the top, you can just see a small pinion (also green), which would be attached to the escape wheel. This therefore regulates the time. The period of the escapement and the gear ratios are chosen so that the planet carrier rotates once per hour, as required for the minute arbor. The final element is the hour gear (yellow). It is also a sun gear, and is free to rotate on the minute arbor. It has the same diameter but a different number of teeth is different to the fixed sun gear. This is an implementation of Ferguson's mechanical paradox. The rotation of the planet gear causes the free sun to rotate at 1/12th of the rate of planet around the fixed sun, providing the rotation for the hour hand.
The gear ratios work as follows. Let:
- A = teeth on fixed sun gear
- B = teeth on planet pinion
- C = teeth on planet gear
- D = teeth on inner side of ring gear
- E = teeth on outer side of ring gear
- F = teeth on escape pinion
- G = teeth on escape wheel (not shown)
- H = teeth on free (hour) sun gear