Monday, January 17, 2011

On Gear Ratios & Modules etc.

A question about pitch, module and gear ratios came in today so I though I should share this info as it may be useful to others. First some gear nomenclature.

A round gear's Diametrical pitch is defined as its number of teeth divided by its pitch diameter.

Pitch Diameter is NOT the overall outer diameter of the gear, its the diameter of the gear to some point about half way up the gear teeth. Its a small difference from the over all diameter of the gear if we are talking relatively small teeth (like those used by follow focus units) so its not that important to differentiate.

A gears Module(mod) is just the mathematical inverse of the diametrical pitch.

The cine standard is 32 pitch (measured in number of teeth per inch) or 0.8 mod (measured in millimeters per number of teeth)

So, some math specific to the D|Focus:

Pitch = # teeth / Pitch diameter,

D|Gear is ~4" pitch diameter,

# teeth = Pitch * Pitch diameter = 32 teeth per inch * 4 inch = 128 teeth

Module is the inverse of pitch, so Mod = Pitch Diameter / # teeth

However, for whatever reason we measure module in millimeters, not inches. 4" = 101.6mm

# teeth = pitch diameter / Mod = 101.6 mm / 0.8 teeth per mm = 127 teeth

Discrepancy in # teeth in theses 2 calculations is due to inaccurate measurement of pitch diameter (I just measured it with a ruler, could get out my CAD drawings and get an exact measurement, or count # teeth but I'm lazy.)

The drive gear's pitch diameter = 1.5 inch so it has 48 teeth

128 / 48 = 2.667, so the D|Focus + D|Gear as a 2.667 to 1 ratio

So one full, 360 degree rotation of the D|Focus knob will give you a little more than 1/3rd (~135 degrees) the rotation on your lens' focus ring.

There are also some other modules (0.5, 0.6) used on Canon and Fuji broadcast, ENG, 2/3" style cameras.

Types of gears:
The D|Focus, uses 2 general types of gears. The Drive and lens gears are called Spur gears. Pretty much the simplest type of gear. The gearbox used Miter gears which are used to change the direction of motion. Some other follow focuses use helical gears to accomplish this.