Harmonic Drive Backlash in Arcmin: What the Specification Really Tells You

Every harmonic drive datasheet leads with a backlash figure in arcmin. It is usually the first number an engineer compares — and the most frequently misread one in joint module design. A "lost motion ≤ 1 arcmin" marking does not mean the joint is rigid, and it does not mean your positioning error equals 1 arcmin. This article explains what the harmonic drive backlash specification actually measures, why harmonic reducers reach sub-arcmin values at all, how to convert arcmin into real-world accuracy, and how to set a backlash target that matches your application.

What Backlash Actually Measures on a Harmonic Drive?

The figure quoted as "lost motion" or "backlash" on a harmonic drive datasheet is measured under a specific, narrow condition:

• The input shaft is locked (not driven).

• A load of ±2% of rated torque is applied at the output and then reversed.

• The output angle difference between the two zero-torque crossings is the lost motion.

That is a dead zone measured near zero torque — not a stiffness curve and not a positioning error budget. One arcminute equals 1/60 of a degree, or 0.291 mrad. Datasheet values are maximum values, not typical values, and a unit-type reducer (with output bearing and flange) usually measures slightly larger than a component set. When comparing suppliers, confirm the measuring condition first: ±2% or ±5% of rated torque, and which series grade.

The Three Numbers Engineers Mix Up

The key trap: lost motion is captured around zero torque, while the full hysteresis loop width — the quantity your joint experiences under real load reversals — is typically two to three times larger. Reading only the arcmin backlash figure and assuming rigidity is the most common misjudgement in joint selection.

Why Harmonic Drives Achieve Sub-Arcmin Backlash?

Two structural properties make the small arcmin figures possible:

• High tooth engagement. In a harmonic drive, roughly 30% of the flexspline and circular spline teeth are engaged simultaneously, compared with two or three teeth in a conventional planetary stage. Manufacturing errors average out over dozens of meshing teeth instead of concentrating on one pair.

• Preloaded flexible gearing. The wave generator elastically deforms the flexspline so it meshes under permanent preload — there is no designed-in clearance to remove with adjustments, as planetary designs must do with floating sun gears or split gears.

The price of this elastic preload is a soft low-stiffness region (the K1 segment) right after the dead zone closes. A harmonic reducer can therefore have excellent lost motion and still show a wide hysteresis loop under full load. Backlash and torsional stiffness must be evaluated as a pair — the arcmin number alone will understate real reverse-loading error.

Converting Arcmin Into Millimetres You Can Defend

Backlash matters only when it becomes a linear error at the tool centre point. With arm length L and backlash θ (in radians), the error is e = L × θ:

Two further conversions matter at system level:

• Referred to the motor side, 1 arcmin at the output becomes i × 1 arcmin at the input — with a 100:1 reducer that is 1.67° at the motor. A motor-side encoder cannot see the dead zone at all; only an output-side (dual) encoder can.

• Working backwards from a tolerance: to hold ±0.05 mm at a 0.5 m reach, the allowable backlash is about 0.34 arcmin — already at the edge of precision-grade harmonic drives. At that point, backlash compensation via the output encoder is mandatory; the reducer alone will not carry the tolerance.H2: Where the Dead Zone Actually Hurts: Control-Side Symptoms

Reversal creep and limit cycles

A position loop integrator inside the dead zone saturates, then overshoots when the zone closes — visible as hunting or limit cycling during low-speed reciprocating motion, exactly the profile of scanning, dispensing and inspection axes.

Force control blind spots

In the dead zone, motor torque does not reach the output. Force-controlled joints and collision detection therefore inherit a torque "blind zone" whose width is set by lost motion plus friction — force-control bandwidth is limited by it.

The dual-encoder compensation trap

An output encoder can measure and compensate lost motion, but the correction loop adds phase lag and harmonic error. It needs limited bandwidth and notch filtering; simply raising the outer-loop gain destabilises the joint.

Stiction plus backlash

At each reversal, static friction and the dead zone combine into stick-slip behaviour that is harder to compensate than either alone — a frequent root cause when a joint "passes backlash spec" on the bench but oscillates in the cell.H2: Setting a Backlash Target by Application

The rule of thumb: specify backlash last, after the accuracy budget. Convert the end-effector tolerance into an arcmin budget at the joint, reserve margin for hysteresis (2–3×), temperature growth and wear, then choose the grade.

Three Ways Backlash Grows in Service

• Ratcheting (overload slip): exceeding the peak torque limit lets the flexspline ratchet past the spline — lost motion increases permanently and irreversibly. Size the reducer with margin above peak torque, not just rated torque.

• Temperature and wear: lost motion grows with operating hours and heat; at end of life it can reach 30–100% above the as-shipped value. Precision applications should budget on end-of-life figures.

• Assembly eccentricity: out-of-flatness of the mounting face or housing misalignment makes backlash uneven around the rotation — a single-point bench measurement of 1 arcmin can coexist with 3 arcmin locally. Verify at multiple output positions.H2: How HONPINE Specifies Backlash

HONPINE harmonic reducers are supplied in component-set and unit configurations across standard and mini series. In the current catalogue the mini harmonic series (cup-type CSF, top-hat type SHD) is specified at 20 arcsec backlash — about 0.33 arcmin — across all sizes and ratios, with rated torques from 0.06 N·m (CSF-2.5) to 5 N·m (CSF-11), which places the whole series comfortably inside the ≤ 0.5 arcmin band required by precision positioning joints. Standard-series values, grades and unit-versus-component measuring conditions should be confirmed against the current datasheet for the specific frame size — [To be confirmed with HONPINE].

When you send an enquiry, state three things: the measuring condition you require (±2% or ±5%), the grade you expect, and whether lost motion is specified at delivery or at end of life. A supplier who answers all three precisely is a supplier whose arcmin number you can design on.

Pre-Purchase Backlash Checklist

1. Confirm the measuring condition: input locked, ±2% or ±5% rated torque, zero-torque crossings.

2. Ask whether the figure is max or typical, and for unit vs component set.

3. Get the hysteresis loop (or K1/K2 stiffness data), not just the lost motion figure.

4. Convert your end-effector tolerance to an arcmin budget and check the margin after hysteresis.

5. Plan the output encoder — motor-side encoders cannot observe the dead zone.

6. Verify backlash at several output positions after installation.

7. Size against peak torque with margin to avoid ratcheting.

8. Agree the end-of-life backlash allowance in the specification.

FAQ

Is 1 arcmin backlash good for a harmonic drive?

Yes — 1 arcmin (0.291 mrad) lost motion is a normal catalogue-grade figure for a precision harmonic drive and equals 0.145 mm of dead zone at a 0.5 m reach. Precision-grade units reach 0.5 arcmin and below; the figure that matters is your own arcmin budget after converting the end-effector tolerance.

Is harmonic drive backlash the same as hysteresis?

No. Backlash (lost motion) is measured near zero torque with the input locked; hysteresis is the width of the full torque–angle loop under ±rated torque and is typically 2–3 times larger. Both belong in a joint specification, but they are different numbers.

How do I convert arcmin to millimetres?

Multiply the arm length by the backlash in radians: 1 arcmin = 0.0002909 rad, so at 0.5 m the dead zone is 0.5 × 0.0002909 ≈ 0.145 mm.

Why does my joint hunt even though backlash is within spec?

The usual suspects are hysteresis (larger than the lost motion figure), static friction interacting with the dead zone, and an over-aggressive dual-encoder compensation loop adding phase lag. Diagnose the torque–angle loop before retuning gains.

Conclusion: the arcmin backlash figure on a harmonic drive datasheet is a structural advantage — the result of 30% multi-tooth engagement under elastic preload — but it is one term in a three-term equation completed by torsional stiffness and encoder bandwidth. Read it as a dead-zone measurement near zero torque, convert it to millimetres at your own reach, and specify the loop around it accordingly.