There are many different types of gears that you may encounter when building stuff. This serves as a living document to outline the different types of gears and the parameters that are used to specify the size and dimensions of gears.
Spur gears
Spur gears are the most common type of gear we think of when we think of a gear. A spur gear is the simplest type of gear, consisting of a cylinder or disk with teeth. The teeth (ideally) are not straight-sided, and they mesh together to rotate adjacent gears.
The above shows a gear with 8 teeth; N = 8.
The common parameters you see when defining a gear are:
Number of Teeth, N
The number of teeth in the gear.
Pitch diameter, D
The diameter of the gear. More accurately, this is the diameter you would want to use if instead of a gear you used a straight cylinder abutting another cylinder. (Because the teeth stick out and penetrates into the adjacent gear, the pitch diameter of a gear does not actually represent the diameter of the gear.)
Circular pitch, p
The distance between two teeth on a gear, measured along the pitch circle.
Diametral pitch, DP (or sometimes P)
The ratio of the number of teeth to the pitch diameter. This is a far more convenient unit, as it allows you to quickly determine the diameter of a gear: if you have a gear with a DP of 32 per inch, and the gear has 16 teeth, then you know the pitch diameter is 1/2 inch (N/DP).
Because this is such a useful metric (because it allows you to quickly figure out the pitch diameter of a gear from the number of teeth, and thus, position the gear centers with the correct distance), this is the most common metric you will see.
The four values above are related to each other through the following equations:
- DP = N/D = π/p
The pressure angle, which is the angle between the tooth face and the gear wheel. The subject of the specific shape of each tooth on a gear can be a very complicated topic, but suffice it to say the selection of a pressure angle affects the performance of gears in a wide variety of weird and wonderful ways; see the link for more information.
The important thing to remember here:
When matching gears, adjacent gears must have the same pressure angle and the same diametral pitch. Further, the ratio of the number of teeth determine how fast or slow adjacent gears move.
The Hacking Den 