Application notes

How to size a harmonic drive: torque, ratio, and envelope

Sizing a strain wave gear is four questions asked in the right order. Here's the order, the traps, and a worked example that ends at a part number.

01Start from the load, not the motor

List what the output must actually do: the peak torque it must deliver (including acceleration of inertia, gravity terms, and friction), the average torque over the duty cycle, and the maximum output speed. Sizing from the motor backwards is the most common mistake we see in RFQs: it bakes the wrong gear into the design before the load is understood.

02Match torque ratings the way the datasheet means them

Harmonic drive datasheets quote several torque numbers, and they are not interchangeable:

Rule of thumb: pick the frame size so your worst regular acceleration peak stays under the repeated-peak rating with ~20–30% margin, then confirm the RMS torque clears the rated value. Margin is cheaper than a field failure.

03Choose the ratio from output speed and the input speed limit

With the frame size provisionally set, the ratio follows from speed: input speed = output speed × ratio, and it must stay below the gear's input speed limit (thousands of rpm for these sizes). Higher ratios buy you more torque multiplication and finer effective resolution; the cost is output speed. Standard ratios run 51, 81, 101, 121, and 161:1 depending on frame size and series.

04Check the envelope and the interfaces

Strain wave gears are short and coaxial, which is why they fit in joints, but confirm outside diameter, axial length, and the hollow-shaft bore if you're passing cables. Then check mounting: output flange bolt circle, housing lugs, and input coupling. Our catalogue pages list every series with mass and rated torque side by side.

The range at a glance

The torque-sensing harmonic servo joints (AS-SJ3) — the series we fit to robot joints — as a representative slice of the catalogue:

FrameRated torquePeak torqueRatiosMass
117.3 N·m18 N·m51 / 81 / 1010.51 kg
1421 N·m35 N·m51 / 81 / 1010.88 kg
1732 N·m54 N·m51 / 81 / 1011.1 kg
2063 N·m111 N·m51 / 81 / 101 / 1211.43 kg
25127 N·m235 N·m51 / 81 / 101 / 1212.43 kg
32300 N·m430 N·m51 / 101 / 1614.57 kg
40557 N·m800 N·m51 / 81 / 101 / 121 / 1617.49 kg

Worked example: a collaborative robot elbow

Say the elbow joint must deliver a 90 N·m acceleration peak, an RMS duty of 55 N·m, and an output speed of 25 rpm.

  1. Frame size: Frame 17 (32 N·m rated) fails the 55 N·m RMS check outright. Frame 20 (63 N·m rated, 111 N·m peak) technically clears both numbers, but 55 of 63 N·m leaves ~13% continuous margin, thinner than we'd sign off for a joint that accelerates all day. Frame 25 rates 127 N·m continuous and 235 N·m peak; both requirements clear with margin to spare. Provisional pick: Frame 25.
  2. Ratio: 25 rpm output × 101 = 2525 rpm input, right in the sweet spot for the motors typically paired here. Pick 101:1.
  3. Envelope: Frame 25 adds 2.4 kg to the moving arm. Check it against the payload budget; if the arm is mass-critical, revisit with the duty cycle in hand rather than dropping a size blind.
  4. Part number: AS-SJ3-25, ratio 101:1. Done.

That's the whole method. When a case doesn't fit it — heavy shock loads, thermal extremes, unusual duty cycles — send us the numbers and an application engineer will run it properly, usually the same working day.

Related: What is a strain wave gear? · Backlash, lost motion, and stiffness: reading the datasheet.

We'll size it for you.

Peak torque, output speed, envelope — send the three numbers and get a candidate part number back.

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