Gearboxes and harmonic drives

What a precision gearbox does

A gearbox between a servo or stepper motor and its load does three jobs. It multiplies torque, so a smaller motor can drive the load. It reduces speed to what the load needs. And it divides the load inertia seen by the motor by the square of the ratio, which makes the axis easier to control.

The cost is backlash, compliance, friction losses and extra inertia. Choosing a gearbox for a motion axis is mostly about how much of each you can accept for the torque, ratio and space you have.

Gearbox types compared

Type	Typical ratio per stage	Backlash	Efficiency	Best for
Planetary (inline)	3:1 to 10:1	Standard grades several arcmin; precision grades down to about 1 arcmin	About 97% one stage, 95% two stage	General servo axes, high stiffness per size
Strain-wave (harmonic)	About 30:1 to 160:1	Zero at the mesh; lost motion under 1 arcmin	Varies widely with speed, torque and temperature	Robot joints, compact high-ratio, hollow shaft
Cycloidal	Up to about 185:1	About 1 arcmin or less	Up to about 85% (RV-N)	Heavy, shock-loaded joints and positioners
Spiral bevel (right-angle)	Low single stage; combined with planetary up to about 200:1	Typically 10–30 arcmin in plain bevel sets	Up to about 98% per mesh	Right-angle layouts, short envelope
Worm	High single stage	Varies widely	Low, falling with ratio	Low-duty right-angle drives, holding

Figures are drawn from the Design World gearbox guide, Beckhoff AG3210 data, Harmonic Drive CSG-2A data and Nabtesco RV-N data listed in the sources. Individual series vary.

Planetary gearboxes

Planetary gearheads are the default for servo motors. Load is shared between several planets, giving high torque and stiffness in a short, coaxial package. Beckhoff’s AG3210 data, for example, quotes 97% efficiency for one stage and 95% for two, with standard backlash of up to 8 and 10 arcmin respectively (Beckhoff). Precision ranges go much lower: Apex AD/ADR and Wanshsin WSH offer backlash classes around 1 to 1.5 arcmin in single stage. Apex AB/ABR is a lower-backlash general-purpose range, and Harmonic Drive HPG uses a flexible internal gear to hold backlash low over life. For AGV wheels, rotating-housing designs such as Apex GL let the wheel mount directly on the gearbox.

Strain-wave (harmonic) gearing

An elliptical wave generator flexes a thin toothed cup (the flexspline) inside a rigid ring (the circular spline) that has two more teeth. Each turn of the wave generator moves the flexspline by two teeth, which is why single-stage ratios are so high. Harmonic Drive states that up to 30% of teeth are engaged at once (Harmonic Drive). Harmonic Drive is a trademark of Harmonic Drive LLC; strain-wave gearing is the generic term.

Component sets such as Harmonic Drive CSG, Harmonic Drive SHG and LeaderDrive LCS/LCSG are built into your own housing. Hollow-shaft units such as LeaderDrive LHS/LHSG pass cables through the centre. For CSG-2A, Harmonic Drive quotes lost motion and hysteresis loss under 1 arcmin, transmission accuracy under 1–1.5 arcmin depending on size, and repeatability under ±0.1 arcmin (CSG-2A data).

Cycloidal reducers

Cycloidal reducers drive lobed discs around pins. Many contact points share the load, giving high shock capacity and stiffness. Nabtesco’s RV-N range allows acceleration torque of 2.5 times rated and emergency-stop torque of five times rated, with lost motion under 1 arcmin on most sizes and efficiency up to 85% (Nabtesco). They tend to be the heaviest option for a given rated torque but cope best with collisions and heavy payloads.

Spiral bevel and right-angle planetary

Right-angle units fold the motor alongside the machine. Most precision servo versions add a spiral bevel stage to a planetary, for example Wanshsin WSHR and Apex AER/ADR. Spiral bevel meshes run at up to about 98% efficiency (Design World). For rotary tables, hollow-platform reducers such as Wanshsin WTN combine gearing with a crossed roller output bearing.

Worm gearboxes

Worms give a high ratio in one right-angle stage and can resist back-driving, but sliding contact means more heat and lower efficiency. Boston Gear’s engineering data estimates efficiency from lead angle and friction, and notes that self-locking may be expected below about 5° lead angle and back-driving above about 11°, without guarantee (Boston Gear). They are rarely the first choice on dynamic servo axes.

How to select and size a gearbox

1. Choose the ratio

Ratio = motor speed at full load speed ÷ required output speed, then check torque: output torque ≈ motor torque × ratio × efficiency. Also check the inertia ratio. Reflected load inertia = J_load / i². Most servo sizing aims for a load-to-motor inertia ratio of 10:1 or less (Motion Control Tips).

Worked example: a rotary table needs 60 rpm and 40 Nm, with 0.5 kg·m² inertia. A 3,000 rpm servo gives a ratio of 50:1. Motor torque ≈ 40 / (50 × 0.9) ≈ 0.9 Nm before acceleration. Reflected inertia = 0.5 / 2,500 = 0.0002 kg·m² (2 kg·cm²), which suits a motor with rotor inertia around 0.2 kg·cm² or more. At 50:1 you could use a two-stage planetary or a single-stage strain-wave gear; the choice comes down to backlash, stiffness and envelope.

2. Check the torque definitions

Precision gearbox catalogues usually give several torque limits rather than one rating:

• Rated (nominal) torque: the continuous reference for life. Harmonic Drive notes it is used for life calculation, not for dimensioning the gear.
• Repeatable peak / acceleration torque: the limit during normal acceleration and braking, sometimes at a stated maximum cycles per hour.
• Momentary / emergency-stop torque: for collisions or E-stops only, often limited to a set number of events over the gearbox life.

Check every torque in your cycle against the right limit. Servo motors can produce several times their rated torque, so an E-stop or a tuning error can exceed the gearbox’s peak limit. Limit drive current if necessary.

3. Check life and average torque

For strain-wave gears, life is governed by the wave generator bearing. Harmonic Drive gives L50 = Ln × (rated input speed ÷ average input speed) × (rated torque ÷ average torque)³, with Ln = 50,000 h for CSG. Planetary catalogues quote a service life at rated torque and speed. Either way, life falls steeply as average torque rises.

4. Backlash, lost motion and stiffness

Backlash matters when the load reverses. Stiffness matters for positioning under load and for servo bandwidth. Torsional wind-up = torque ÷ stiffness: a gearbox at 20 Nm/arcmin carrying 100 Nm twists 5 arcmin, which can be more than its backlash. Strain-wave stiffness is non-linear, with lower stiffness at low torque (Harmonic Drive’s K1, K2 and K3 regions), so use the region that matches your working torque.

5. Service factors, shock and duty

General-purpose gear drives use service factors for shock, start frequency and running hours. Precision servo gearboxes usually deal with this through the acceleration and emergency torque limits above. Either way, describe the load honestly: start-stops per hour, reversals, shock and hours per day.

6. Input speed, temperature and mounting

Check maximum and average input speed, as these drive heat and life. Check the motor adaptor fits your motor’s shaft and pilot, and the output bearing’s tilting moment and radial capacity against the load. An integrated output bearing often removes a separate bearing from the design.

For a deeper comparison, read harmonic vs planetary vs cycloidal.

Common mistakes

• Sizing on rated torque alone. Acceleration and E-stop peaks are often the limiting case.
• Confusing zero backlash with zero error. Stiffness and transmission accuracy still matter.
• Too high a ratio. The motor runs out of speed and the gearbox’s own inertia dominates.
• Relying on worm self-locking. Fit a brake where holding is safety-related.
• Ignoring output bearing loads. Pulleys, pinions and overhung tables load the output bearing as well as the gears.
• Not limiting motor current. A servo can exceed the gearbox’s momentary limit in a crash.

What to send an engineer for a quote

• Motor make, model, flange and shaft (or the motor you plan to use)
• Required output speed and torque profile, including acceleration and E-stop torques
• Load inertia, start-stops per hour, hours per day and expected life
• Allowable backlash, lost motion and stiffness
• Inline or right-angle, hollow shaft, and envelope limits
• Output loads: radial, axial and tilting moment
• Environment: temperature, IP rating, washdown, mounting orientation

Add these to the spec builder below and our engineers will propose a matched gearbox, or a frameless motor and gear combination where integration makes more sense.

Guides

Where gearboxes and harmonic drives are used

What we need to know to specify gearboxes and harmonic drives

These are the questions an applications engineer works through first. Approximate answers are fine: ranges narrow the options quickly, and we confirm the details with you.

• Type: Harmonic / strain wave, Planetary, Spiral bevel, Not sure
• Ratio: Under 10:1, 10–50:1, 50–100:1, Over 100:1
• Backlash: Zero / under 1 arcmin, Under 3 arcmin, Standard
• Output torque: Under 20 Nm, 20–100 Nm, 100–500 Nm, Over 500 Nm

We also ask about the environment (washdown, outdoor, subsea, ATEX, vacuum, shock and EMC), annual quantities and timescale, because these decide whether a standard, modified or custom design is the best fit.

124 series compared

Series from 30 manufacturers, grouped by type. Figures are the highest published for each series. Open a series for the full specification and, for brands outside our supply network, the alternatives that meet or exceed it.

Planetary gearbox (42)

Integrated robot joint actuator (30)

Strain-wave (harmonic) gear (16)

Harmonic actuator (14)

Cycloidal gearbox (14)

Spiral bevel gearbox (6)

Stainless planetary gearbox (1)

Worm gearbox (1)

Summarised from manufacturers' published data. Always confirm against the current datasheet; an engineer will check the fit before recommending anything.

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