BIZOMAT MAKEOS · Gears
Inch Involute Spline Measurement Between or Over Pins
For an inch involute spline (ANSI B92.1) with a known actual space width or tooth thickness, what is the measurement between two pins for the internal spline, or over two pins for the external spline, with the standard pin size?
Two-pin measurement of inch involute splines by the handbook’s formulas: pitch diameter D = N ÷ P and base diameter Db = D cos φD; for internal splines inv φi = s ÷ D + inv φD − di ÷ Db and Mi = Db sec φi − di (even teeth) or Db cos(90° ÷ N) sec φi − di (odd teeth) with di = 1.7280 ÷ P (30° and 37.5°) or 1.9200 ÷ P (45°); for external splines inv φe = t ÷ D + inv φD + de ÷ Db − π ÷ N and Me = Db sec φe + de (even) or Db cos(90° ÷ N) sec φe + de (odd) with de = 1.9200 ÷ P, the pressure angle at the pin centre found from its involute.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Spline measured | choice | Whether you measure an internal spline between pins or an external spline over pins. |
| Diametral pitch P | 1/in | Diametral pitch of the spline, the first number of the pitch fraction (e.g. 3 for 3/6). |
| Number of teeth N | teeth | Number of teeth of the spline. |
| Pressure angle | choice | Standard pressure angle of the spline. |
| Actual space width s (internal) or tooth thickness t (external) | in | Actual space width (internal) or tooth thickness (external) at the pitch circle that the measurement is for. |
| Pin diameter (0 = the standard pin) | in | Diameter of the pins used, or 0 for the standard pin size. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Spline measured
- What it is
- Whether the spline is internal and measured between pins, or external and over pins.
- Units and format
- Choose one of 2 options from the list: Internal spline, between pins; External spline, over pins.
- Example
- The form opens with “Internal spline, between pins” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Chooses the between-pins or over-pins formula and the standard pin.
- Get it right
- Internal splines are in the hub; external splines are on the shaft.
What this means: Diametral pitch P
- What it is
- Teeth per inch of pitch diameter, the first number of the spline pitch.
- Units and format
- Enter a number in 1/in: threads per inch. The form accepts 0.000001 1/in to 128 1/in. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 1/in as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the pitch diameter and the standard pin size.
- Get it right
- For a 3/6 pitch spline enter 3; the second number sets the tooth depth.
What this means: Number of teeth N
- What it is
- Count of teeth or spaces around the spline.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 6 teeth to 200 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the pitch diameter and the odd-tooth correction.
- Get it right
- Odd numbers of teeth use the cos(90° ÷ N) correction.
What this means: Pressure angle
- What it is
- Standard pressure angle of the involute spline teeth.
- Units and format
- Choose one of 3 options from the list: 30°; 37.5°; 45°.
- Example
- The form opens with “30°” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Sets the base diameter and the standard internal pin.
- Get it right
- Read it from the drawing or the spline designation: 30°, 37.5° or 45°.
What this means: Actual space width s (internal) or tooth thickn…
- What it is
- Arc width of the space (internal) or tooth (external) at the pitch circle to be measured.
- Units and format
- Enter a number in in: inches. The form accepts 0.000001 in to 20 in. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.52677 in as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A wider space or thicker tooth moves the pins and changes the reading.
- Get it right
- Use the maximum or minimum actual value from the spline standard to get the measurement limits.
What this means: Pin diameter (0 = the standard pin)
- What it is
- Diameter of the gauge pins used in the measurement.
- Units and format
- Enter a number in in: inches. The form accepts 0 in to 5 in. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 in as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Larger pins sit further out on the flanks.
- Get it right
- Enter 0 to use the standard pin, 1.728 ÷ P or 1.920 ÷ P.
Method and formulas
- D = N ÷ P; Db = D cos φD; inv φ = tan φ − φ.
- Internal: inv φi = s ÷ D + inv φD − di ÷ Db; Mi = Db sec φi − di (even N) or Db cos(90° ÷ N) sec φi − di (odd N); standard di = 1.7280 ÷ P (30°, 37.5°) or 1.9200 ÷ P (45°).
- External: inv φe = t ÷ D + inv φD + de ÷ Db − π ÷ N; Me = Db sec φe + de (even N) or Db cos(90° ÷ N) sec φe + de (odd N); standard de = 1.9200 ÷ P.
- The angle is found from its involute by Newton iteration instead of the involute tables.
- Example: the measurement between pins is 5.8351 in.
Limitations
- The measurement checks the actual space width or tooth thickness only; it does not show the fit, which depends on the effective dimensions.
- Pins must touch the flanks on the involute; check that the pin contact lies between the form and major (or minor) diameters.
- For the maximum and minimum measurements, enter the limits of the actual space width or tooth thickness from the standard.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Inspect the actual space width of an internal spline with pins
- Inspect the actual tooth thickness of an external spline over pins
- Set the pin measurement limits from the space width or tooth thickness limits
Who it is for
- Quality inspectors
- Gear machinists
- Toolmakers
What you get
- Pitch and base diameters
- Pin diameter used
- Pressure angle at the pin centre
- Measurement between or over pins
Interpreting the result
- A larger space width moves the pins outward, so the internal measurement between pins falls.
- A thicker external tooth raises the measurement over pins.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2271–2272. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Useful alongside · BIZOMAT original book
Measuring and specifying a gear
What it covers: Check tooth thickness with span measurement, identify an unknown gear from its tooth count and diameter, and write the data a gear drawing needs.
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Open the Inch Involute Spline Measurement Between or Over Pins calculator