BIZOMAT MAKEOS · Power Transmission
Open Belt Drive Geometry
What speed, wrap and pitch length follow from this pulley layout?
Calculate ideal speed ratio and exact geometric belt pitch length for two circular pulleys in an open drive.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Driver pitch diameter | mm | Effective pitch diameter, not pulley outside diameter. |
| Driven pitch diameter | mm | Effective pitch diameter on the output shaft. |
| Centre distance | mm | Distance between the parallel shaft axes. |
| Driver speed | rpm | Input pulley speed. |
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: Driver pitch diameter
- What it is
- The diameter of the driving pulley measured at the belt’s pitch (or datum) line, usually on the motor shaft.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger driver raises output speed, belt speed and belt length.
- Get it right
- Use the pitch or datum diameter from the catalogue, not the pulley outside diameter.
What this means: Driven pitch diameter
- What it is
- The diameter of the driven pulley on the output shaft, measured at the belt’s pitch (or datum) line.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Output speed is inversely proportional to the driven diameter.
- Get it right
- Match the belt maker’s pitch or datum convention for both pulleys.
What this means: Centre distance
- What it is
- The distance between the centres of the two parallel pulley shafts.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 500 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A longer centre distance increases belt length and the wrap on the small pulley.
- Get it right
- Allow adjustment range for tensioning and fitting; it must exceed the sum of the two pitch radii.
What this means: Driver speed
- What it is
- The rotational speed of the driving pulley, usually the motor full-load speed.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0 rpm to 1000000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1500 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Output speed and belt speed are directly proportional to driver speed; length does not change.
- Get it right
- Use the motor’s loaded speed rather than its synchronous speed.
Method and formulas
- Let r and R be smaller and larger pitch radii, C the centres and a = asin((R−r)/C).
- Exact ideal pitch length = 2 × sqrt(C²−(R−r)²) + π × (R+r) + 2 × a × (R−r).
- Small-pulley wrap = 180° − 2a in degrees. Output RPM = input RPM × driver diameter / driven diameter.
- Belt speed (m/s) = π × driver diameter × RPM / 60000. Example 100/200 mm at 500 mm centres gives about 1476.243 mm pitch length and 750 rpm output from 1500 rpm.
Limitations
- Open, coplanar, no-slip drive only; no idlers, belt stretch or crossed drive.
- Pitch length is not necessarily the manufacturer’s outside or datum length. No power rating is calculated.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- pulley ratio
- belt length
- belt speed
Who it is for
- Designers
- Maintenance technicians
What you get
- Geometric pitch length
- Small-pulley wrap
- Ideal output speed
- Belt speed
Interpreting the result
- Select a catalogue belt and recheck centres, tension, wrap and supplier service factors.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2484–2487. Topic reference; no source tables or recommended settings are reproduced.
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