Guide
Gearbox backlash explained: arcmin, lost motion, hysteresis and how much you need
What backlash means on a datasheet, how it is measured, how it differs from lost motion and hysteresis, and a table converting arcmin to millimetres at the load.
Key takeaways
- Backlash is free play at near-zero torque, in arcmin (1/60 of a degree).
- Error at the load = radius × angle in radians. 1 arcmin at 500 mm ≈ 0.15 mm.
- Only load reversals expose backlash; one-directional loads hide it.
What backlash is
Backlash is the angle the output can turn when the input is locked, caused by clearance between mating teeth. It is quoted in arc-minutes (1° = 60 arcmin = 3,600 arcsec). A common way to measure it: lock the input, apply a small torque — often about 2% of rated — to the output in each direction, and measure the rotation with a dial indicator on an arm of known length.
Arcmin to millimetres
The error at the load is r × θ, with θ in radians (1 arcmin = 2.909 × 10⁻⁴ rad).
| Radius | 20 arcsec | 1 arcmin | 3 arcmin | 5 arcmin | 8 arcmin |
|---|---|---|---|---|---|
| 100 mm | 0.010 | 0.029 | 0.087 | 0.145 | 0.233 |
| 250 mm | 0.024 | 0.073 | 0.218 | 0.364 | 0.582 |
| 500 mm | 0.048 | 0.145 | 0.436 | 0.727 | 1.164 |
| 1,000 mm | 0.097 | 0.291 | 0.873 | 1.454 | 2.327 |
On a robot arm, the base joint's backlash is multiplied by the full reach, which is why robot joints use reducers of 1 arcmin or less.
Lost motion and hysteresis
Lost motion is measured at a higher torque, commonly ±3% of rated, and includes backlash plus the elastic twist of the parts near zero load. RV and cycloidal makers usually quote lost motion because it better predicts servo positioning. Hysteresis loss is the harmonic drive equivalent: there is no tooth clearance, but when the torque reverses the output traces a small loop, typically under 1 arcmin.
Torsional stiffness: the other half
Under load, every reducer twists. A gearbox with 10 N·m/arcmin stiffness deflects 3 arcmin at 30 N·m — more than its backlash. For machining or heavy robot arms, compare stiffness as carefully as backlash.
How much backlash can you accept?
| Application | Typical backlash |
|---|---|
| Conveyors, AGV wheels, feeders | 8–15 arcmin |
| Servo gantries, packaging, rack and pinion | 3–5 arcmin |
| Robot joints, index tables, machine-tool axes | ≤ 1 arcmin |
| Robot wrists, optics, metrology | Arc-second class (harmonic drives) |
References
- ISO 230-2, Determination of accuracy and repeatability of positioning of numerically controlled axes (reversal error).
- ISO 9283, Manipulating industrial robots — Performance criteria and related test methods.
Frequently asked questions
How do I convert arcmin to mm?
Multiply the radius in mm by the angle in radians. One arcmin is 0.000291 rad, so at a 500 mm radius 1 arcmin is 0.145 mm and 3 arcmin is 0.436 mm.
What is the difference between backlash and lost motion?
Backlash is the free play measured at a very small torque. Lost motion is measured at a higher torque (often ±3% of rated) and includes the elastic twist of the parts near zero load, so it is the more realistic figure for servo positioning.
Does backlash matter on a vertical axis?
Much less. Gravity keeps the gear teeth loaded in one direction, so the axis never crosses the backlash zone unless the load reverses.
