How to Measure Gears By Mike Meagher

To: "''" <>
Subject: [7x10minilathe] Change Gears (long)


A crude but effective method of determining pitch diameter on spur gears
(like the 7x10 change gears) can be done easily with one measurement.

1. Measure the linear distance between any two corresponding points on two
adjacent teeth, as shown below:

   __ |    __ |
  /  \|   /  \|   (high-tech ASCII graphics best viewed in Courier font)
 /    \__/    \

 (Pick any convenient point, such as one similar point on each tooth crest)

Dimension 'x' is known as the circular pitch, which is equal to the
circumference of the gear pitch circle divided by the number of teeth. The
gear equation is:

  Circular Pitch = Pc = (pitch diameter x pi) / number of teeth

2. Solve for pitch diameter...

  Pitch diameter = (number of teeth x circular pitch) / pi

Diametral Pitch is the number of teeth per inch of the pitch circle

  Diametral Pitch = Pd = number of teeth / pitch diameter

It is a more popular method of gear pitch measure, but is not as
geometrically evident due to the fact that the pitch circle is not visible
on the gears. Without specialized equipment, it would be quite difficult (if
not impossible) for a home machinist to directly measure the pitch diameter
on a gear.

When a gear catalog mentions "pitch," they are referring to diametral pitch.
Fortunately, circular pitch and diametral pitch are related:

  Diametral Pitch x Circular Pitch = Pd x Pc = pi


  Diametral Pitch = Circular Pitch / pi

On an inch gear, the result should be an even number like 10, 12, 24, 32,
48, 72 or 96. Metric gears are another story.

Per AGMA standards (American Gear Manufacturer's Association), circular
pitch and diametral pitch are reserved for the inch system. Metric gears are
specified by "module" instead of pitch, which is the amount of pitch circle
diameter per tooth as measured in millimeters:

  module = m = pitch circle diameter (mm) / number of teeth

While it is the reciprocal of diametral pitch, module is a dimension while
diametral pitch is the number of teeth per inch of the pitch circle

Confused yet? It gets better. Diametral pitch and module are related by a
factor of 25.4:

  Pd x m = 25.4

What this means is that there are very few (if any) directly interchangeable
gears between the inch and metric systems. Like cutting metric threads on
the 7x10, there will be very slight differences between inch and metric
gears, sometimes not very significant. For example, a gear which has a
diametral pitch of 24 (inch system) has a module of 1.0583;  a gear with a
module of 1.0 (metric system) has a diametral pitch of 25.4. Will this
affect anything? The only way to find out is to try out the gear in

Finally getting to the bottom line, if your pitch calculations have you
coming up with a number other than an even number like 24, 32, 48, 72 or 96,
you probably have a metric gear.

A very good basic reference on gears is one of a four-volume catalog from
Stock Drive Products / Sterling Instrument Company. Their "Handbook of
Gears" is also a catalog of inch and metric gears, but the first 150+ pages
deal with gear terminology, gear design parameters and a lot of gear
equations. The book for free for the asking;  Stock Drive Products'
telephone number is (516)328-3300.

I have access to an optical comparator here at work, and I will get some
details on the gears tomorrow morning (30 July 1999). I'll measure the
circular pitch, pressure angle, bore and a few other characteristics on some
gears tomorrow morning and post the results.


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Ty Hoeffer