Franklin was curious as to how far he was traveling by carriage, in his role as postmaster, for his travels between Philadelphia and Boston.
While the concept of the odometer dates back to ancient times, Franklin did create his own version. The concept was to attach the device near the wheels of a carriage, determine the circumferance of the wheel and the number of revolutions required to travel a mile, and have the device register the distance traveled.
The Institute News (June-July 1949) describing the action of an odometer
When actuated from a carriage wheel having a circumference of thirteen and one-fifth feet, a mile was registered in each four hundred revolutions. If wired to the top of the front axle at the right hand side it was easily set in operation by a nub-type projection on a hub or spoke and the dials were readily visible to both driver and rider." This odometer consists of a series of cogs and wheels that measure distance as noted above. On top of the works is a flat metal plate that has a series of three circles. The left circle has a T above it and has numbers from 10 to 1 running counterclockwise around the circle (10 is in the noon position). The circle is white with black Arabic numerals. The center circle is slightly larger than the side circles and it has the numbers 100 to 10, in increments of 10, running counterclockwise around the circle (100 is in the noon position). The circle is white with red Arabic numerals. The right circle has an H above it and has numbers from 10 to 1 running clockwise around the circle (10 is at the noon position). The circle is white with black Arabic numerals. At the center of the central circle is a brass arrow; the one on the left is completely missing and the one on the right is only a flat disk.
Source: Benjamin Franklin Tercentenary