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When selecting a precision planetary gearbox, you may encounter specifications such as “3 arcmin backlash” or “low lost motion.” These describe transmission clearance characteristics. They do not directly specify the positioning accuracy of the complete machine.
For equipment engineers and mechanical designers, the key is to understand the specification, convert angular clearance into displacement at the working point, and check it against application requirements. This article explains the terminology and provides rotary table and ball screw examples, together with an interactive displacement calculator.
What Is the Difference Between Tooth Clearance, Backlash, Lost Motion, and Arcminutes?
Tooth clearance describes the gap between mating gear tooth flanks. Gearbox catalogs may use backlash or lost motion to describe angular play at the output under specified test conditions. An arcminute is a unit of angle. Terminology and measurement methods vary between manufacturers, so definitions and test conditions must be checked before comparing products.
| Term | Meaning | What to Check |
|---|---|---|
| Tooth clearance | Clearance between mating tooth flanks, defined according to the measurement direction. | Clearance in one gear pair is not the same as angular clearance at the complete gearbox output. |
| Backlash | In gearbox specifications, it commonly describes angular play during a change in transmission direction. | Check the measurement location, applied torque, and manufacturer’s definition. |
| Lost motion | May describe the output angular displacement between specified positive and negative test torques with the input fixed. | Depending on the definition and test method, it may include clearance and elastic deformation. Do not assume it is interchangeable with backlash. |
| Arcminute (arcmin) | A unit of angle equal to 1/60 of a degree. | It is a unit, not a separate accuracy specification. |
How Much Is One Arcminute? What Does 3 arcmin Mean?
- 1 degree = 60 arcminutes.
- 1 arcminute = 60 arcseconds.
- 1 revolution = 360 degrees = 21,600 arcminutes.
Therefore, 3 arcmin = 3/60 degree = 0.05°. A gearbox specification of 3 arcmin backlash describes the angular backlash according to its catalog definition and test conditions.
It does not mean that 0.05° of error accumulates with every revolution, or that the machine’s positioning accuracy is necessarily ±0.05°.
Why Does Backlash Affect Positioning During Reversal?
When the transmission direction changes, the previously loaded tooth flanks unload. The opposite flanks must make contact before transmitting power. This transition can create lost travel: the motor may already be moving while the working point has not yet moved correspondingly.
This matters in rotary table positioning, reversing screw or rack drives, repeated robot acceleration and deceleration, and direction changes in machining or inspection equipment.
When motion stays in one direction and the load maintains tooth contact, the effect of reversal clearance is generally smaller. However, reversing loads, external disturbances, and deceleration can still change which flanks are in contact.
How Much Displacement Does 3 arcmin Produce at the Working Point?
Rotary Tables: Converting an Angle into Arc Length
For the same angular clearance, a larger working radius produces a larger corresponding displacement.
Arc length s = 2 × π × Radius r × Angle θ ÷ 21,600
s and r are in mm; θ is in arcmin.
For a 300 mm radius and 3 arcmin angular clearance: s = 2 × π × 300 × 3 ÷ 21,600 ≈ 0.262 mm.
| Radius | 1 arcmin | 3 arcmin | 5 arcmin |
|---|---|---|---|
| 100 mm | 0.029 mm | 0.087 mm | 0.145 mm |
| 300 mm | 0.087 mm | 0.262 mm | 0.436 mm |
| 500 mm | 0.145 mm | 0.436 mm | 0.727 mm |
Ball Screws: Converting an Angle into Linear Travel
When the gearbox output connects directly to the screw with no additional transmission ratio:
Linear travel Δx = Screw lead L × Angle θ ÷ 21,600
Δx is in mm; L is in mm/rev; θ is in arcmin.
For a screw lead of 20 mm/rev and 3 arcmin angular clearance: Δx = 20 × 3 ÷ 21,600 ≈ 0.00278 mm = 2.78 μm.
These values describe geometric displacement corresponding to angular clearance, not the actual positioning error of the complete machine. They exclude screw, bearing, coupling, structural, and control errors. Additional transmission stages require their ratios to be included.
Are Backlash, Positioning Accuracy, and Repeatability the Same?
No. Backlash is one factor affecting positioning performance. Positioning accuracy and repeatability describe the results of machine motion.
| Specification | Question It Answers |
|---|---|
| Backlash | How much angular play occurs when transmission direction changes? |
| Positioning accuracy | How far is the actual position from the target position? |
| Repeatability | How consistent are repeated moves to the same target? |
| Torsional stiffness | How much angular deflection occurs under applied torque? |
Gearboxes with the same backlash can produce different working-point displacements under load if their torsional stiffness differs. Precision positioning requires consideration of backlash, stiffness, transmission error, load, and feedback configuration.
How Is Gearbox Backlash Measured?
A common method fixes the input and applies specified positive and negative test torques at the output, measuring the angular displacement between them. Test torque, measurement location, temperature, and product condition can affect the result. When comparing brands, check that the test conditions are comparable.
For a preliminary on-site check using a lever arm and dial indicator, a small measured displacement can be converted into an approximate angle:
Angle θ (arcmin) ≈ Displacement b × 21,600 ÷ (2 × π × Measurement radius r)
This approximation applies to small angles with suitable indicator alignment and measurement geometry. Exclude fixture movement, coupling clearance, and other component deformation. An on-site check does not replace the specified product inspection method.
Further Detail: Chord Length Versus Arc Length
For radius r and angle α in degrees: chord length = 2r sin(α/2); arc length = 2πrα/360. The following comparison uses a 300 mm radius and illustrates geometric differences only.
| Angle | Chord (mm) | Arc (mm) | Difference (mm) |
|---|---|---|---|
| 30° | 155.2914 | 157.0796 | 1.7882 |
| 20° | 104.1889 | 104.7198 | 0.5309 |
| 10° | 52.2934 | 52.3599 | 0.0664 |
| 5° | 26.1716 | 26.1799 | 0.0083 |
| 1° | 5.2359 | 5.2360 | 0.0001 |
How Do You Select a Suitable Backlash Specification?
- Define the accuracy requirement: Distinguish positioning accuracy, repeatability, and permissible reversal travel. A machine requirement of ±0.01 mm is not directly a gearbox backlash specification.
- Convert the effect at the working point: Use radius for rotary mechanisms and lead for screws. Rack and belt drives require pitch dimensions and transmission configuration.
- Allocate an error budget: Include screws, bearings, couplings, installation, structural deformation, and the control system.
- Check load and dynamic conditions: Review torsional stiffness, rated torque, acceleration torque, speed, start-stop frequency, and external loads.
- Verify actual performance: Test under working loads, temperatures, and motion directions. Unidirectional and bidirectional tests can produce different results.
Frequently Asked Questions
Is Lower Backlash Always Better?
Lower backlash helps reduce reversal travel, but load, stiffness, speed, service life, and cost also matter. The goal is to meet application requirements while operating reliably.
Can a 3 arcmin Gearbox Achieve ±0.01 mm Positioning?
Backlash alone cannot answer this. You need the working radius, screw lead, or other transmission relationship, together with the complete mechanism’s errors, loads, and control method.
Can Higher Motor Encoder Resolution Eliminate Backlash?
No. Higher resolution does not remove mechanical clearance. With motor-side feedback only, output lost travel may remain unmeasured. Assess working-point feedback and control strategies for the application.
Can Software Backlash Compensation Replace a Low-Backlash Gearbox?
Compensation can improve reversal positioning under certain conditions, but it does not increase mechanical stiffness or fully remove the effects of changing loads, wear, and temperature. Validate its suitability through testing.
Can Backlash Change After a Period of Use?
Yes. Wear, lubrication condition, overloads, impacts, and loose components can affect transmission clearance. If reversal positioning deteriorates, inspect the gearbox and the complete transmission mechanism.
GearKo Planetary Gearbox Selection Support
Convert backlash into its effect at the working point and assess it alongside load, stiffness, and control conditions. Provide your motor model, transmission arrangement, working radius or screw lead, positioning requirement, load torque, and operating cycle to discuss a suitable configuration with the GearKo team.