Mechanical odometers are turned by a flexible cable made from a tightly wound spring. The cable usually spins inside a protective metal tube with a rubber housing. On a bicycle, a little wheel rolling against the bike wheel turns the cable, and the gear ratio on the odometer has to be calibrated to the size of this small wheel. On a car, a gear engages the output shaft of the transmission, turning the cable.
The cable snakes its way up to the instrument panel, where it is connected to the input shaft of the odometer.
This odometer uses a series of three worm gears to achieve its 1690:1 gear reduction. The input shaft drives the first worm, which drives a gear. Each full revolution of the worm only turns the gear one tooth. That gear turns another worm, which turns another gear, which turns the last worm and finally the last gear, which is hooked up to the tenth-of-a-mile indicator.
Each indicator has a row of pegs sticking out of one side, and a single set of two pegs on the other side. When the set of two pegs comes around to the white plastic gears, one of the teeth falls in between the pegs and turns with the indicator until the pegs pass. This gear also engages one of the pegs on the next bigger indicator, turning it a tenth of a revolution.
You can now see why, when your odometer "rolls over" a large number of digits (say from 19,999 to 20,000 miles), the "2" at the far left side of the display may not line up perfectly with the rest of the digits. A tiny amount of gear lash in the white helper gears prevents perfect alignment of all the digits. Usually, the display will have to get to 21,000 miles before the digits line up well again.
You can also see that mechanical odometers like this one are rewindable. When you run the car in reverse, the odometer actually can go backwards -- it's just a gear train. In the movie "Ferris Bueller's Day Off," in the scene where they have the car up on blocks with the wheels spinning in reverse -- that should've worked! In real life, the odometer would've turned back. Another trick is to hook the odometer's cable up to a drill and run it backwards to rewind the miles.
While that does work on older mechanical odometers, it does not work on the new electronic ones, as we will see in the next section...