KEVOS® MAKEOS · Gears
Rack and Pinion Speed, Force and Travel
What linear speed, force and travel does this rack and pinion give?
Pitch diameter, travel per revolution, linear speed and thrust force of a rack and pinion from module (or diametral pitch), pinion teeth, speed and torque, with the motor speed for a required linear speed.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Module | mm | Module of the rack and pinion (25.4 ÷ diametral pitch for inch gears). |
| Pinion teeth | teeth | Teeth on the pinion. |
| Pinion speed | rpm | Pinion speed. |
| Pinion torque | N·m | Torque at the pinion. |
| Mesh efficiency | % | Mesh efficiency. |
| Required linear speed (0 = none) | m/min | Linear speed you need, to find the pinion speed. |
Method and formulas
- Pitch diameter d = m z; travel per revolution = π m z.
- Linear speed = travel per revolution × rpm.
- Thrust = 2T ÷ d × efficiency.
- Example: module 2, 20 teeth at 300 rpm moves 37.699 m/min with 970 N thrust.
Limitations
- Mesh efficiency and torque only; guide friction and acceleration forces add to the drive load.
- Check rack tooth strength with the gear tooth tools.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a rack drive for a gantry or slide
- Find motor speed for a traverse speed
- Find the pinion torque for a thrust
Who it is for
- Automation engineers
- Machine designers
What you get
- Pitch diameter and travel per revolution
- Linear speed
- Thrust force
- Pinion speed for the required linear speed
Interpreting the result
- A smaller pinion gives more thrust per unit torque but higher speed for the same travel speed.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2131–2160. Topic reference; no source tables or recommended settings are reproduced.
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