Harmonic-drive reducers (also called strain-wave gearheads) cover single-stage ratios from 50:1 up to 100:1 and beyond in one mesh, with transmission errors of 60 arc-seconds (1 arc-minute) on standard cup/housing units and around 90 arc-seconds on short-cylinder (hat) units [S1][S4]. That one-mesh ratio is the fundamental sizing lever — it eliminates the second stage a planetary or cycloidal unit would need, which is why engineers reach for a harmonic drive on the last joint of a 6-axis robot, an AGV steering axis or a satellite tracker.
Selection is driven by four hard numbers: rated torque (N·m), peak/emergency torque, maximum input speed (RPM), and the acceptable transmission error in arc-seconds. Model code families such as DHS-25-100-U (67 N·m, ratio 100, ≤60″ error) and DHDG-14-50-U (3.7 N·m, ratio 50, ≤90″ error) show how tightly size, ratio and accuracy move together [S1][S4]. More on the underlying strain-wave principle is documented in MATLAB Simscape's harmonic drive block reference, which models the strain-wave generator, flexspline and circular spline as separate inertias.
Operating envelope: ratio, torque and speed
Standard off-the-shelf ratios cluster at 30:1, 50:1, 80:1, 100:1 and 120:1, with 50:1 and 100:1 being the two highest-volume SKUs across the DHS, DHDG and CSF series [S1][S3][S4]. Rated torque scales with the cup/hat model number: model 14 = 3.7 N·m at ratio 50, model 25 = 67 N·m at ratio 100, and model 32 sits in the next band up at the same 100:1 ratio — the model digit is effectively a frame-size code, not a ratio code [S1][S4].
Maximum input speed for current cup-series units typically tops out in the 3,000–4,500 RPM range, with the strain-wave generator acting as the input element; the flexspline then runs at (input speed − output speed). Higher input speeds shorten grease life, so duty-cycle derating applies even when average torque is well below the nameplate figure. The servo drive feeding the reducer usually has a current/torque limit lower than the reducer's mechanical peak, which means the upstream electronics — not the gear — usually trip first in a properly sized system.
Transmission error and backlash — the spec that actually matters
Backlash on a harmonic drive is on the order of a few arc-minutes by construction, often advertised as "near-zero" or "backlash-free" because the two tooth flanks are kept in continuous contact by the elliptical wave generator [S2]. What you actually see on the data sheet is the no-load transmission error (lost motion), expressed in arc-seconds: ≤60″ for cup/housing units like DHS-25-100-U and ≤90″ for short-cylinder (hat-type) units like DHDG-14-50-U [S1][S4]. That gap between 60″ and 90″ is the price you pay for the shorter axial package of a hat-type reducer.
Choose ≤60″ (1 arc-minute) class when the application is a robot last joint, a CNC rotary axis or a surgical/semi-con handler where pointing accuracy dominates. Choose ≤90″ (1.5 arc-minute) class for AGV steering, light-payload pick-and-place Z-axes, or any joint where stiffness and accuracy matter less than a 20–30 % shorter axial length. The double-arc tooth profile used in current-generation DHSG/DHDG units claims 20 %–30 % more teeth in simultaneous contact versus a single-arc involute profile, which is what brings the error class down at a given frame size [S4].
Sizing procedure — five numbers, one safety factor
Step 1: define the application torque profile — average, RMS, and peak/emergency torque at the joint. Step 2: read the rated torque for the candidate model from the maker's curve (e.g. 67 N·m for model 25 at ratio 100, 3.7 N·m for model 14 at ratio 50) [S1][S4]. Step 3: apply a service factor of 1.0 for uniform duty, 1.25–1.5 for reversing or light-impact duty, and ≥2.0 for high-shock press or stamping manipulator duty. Step 4: check peak/emergency torque against the catalogue's allowable peak — exceeding it will shear the flexspline teeth. Step 5: verify input speed is within the catalogue maximum and that the average input speed keeps the calculated L10 grease life above the target service interval (commonly 10,000–20,000 hours for industrial robots).
For a light-payload 6-axis robot last joint, the typical landed pick is a model 14 unit at 3.7 N·m rated torque and ≤90″ error; for a mid-payload robot, you step up to the model 25 / 32 frame at 67 N·m and ≤60″ error [S1][S4]. Compare this against a cycloidal reducer selection guide and you will see harmonic drives win on accuracy and ratio-density per stage, while cycloidal units win on shock-load tolerance and cost — the trade-off is real, not marketing.
Hat-type vs cup-type vs short-cylinder — which frame for which job
Three mechanical formats dominate the market. Cup/housing type (DHS, CSF, SHF series) is the standard length, highest-accuracy format and the volume leader — see SHG-25-50-2SH, CSF-17-50-2UH and SHF-17-50-2UH in the 14–25 model range [S3]. Short-cylinder / hat type (DHDG series) trims axial length and weight by dropping the input housing, accepting a slightly wider transmission error of ≤90″ and lower rated torque at a given model digit [S4]. Pancake / flat type puts the wave generator on the output face for hollow-shaft applications, used where cable or shaft pass-through matters more than peak torque.
Selection rule of thumb: pick cup-type unless the joint envelope forces a shorter axial length, in which case step down to a hat-type and accept the wider error band; pick pancake only when you need a through-bore. Model-code patterns worth memorising — the format "DHS-25-100-U-OC11" breaks down as series (DHS) + model (25) + ratio (100) + input type (U = European coupling) + output (OC11) [S1].
Integration with motor, lubrication and thermal limits
Match the reducer's input coupling (European, Japanese, rigid, or servo-clamp) to the servo motor's shaft and the drive's torque-ripple spectrum. "U" suffix = European input coupling; bare (no U) = rigid input for direct shaft-to-shaft mounting [S1][S4]. Greasing is sealed-for-life on most industrial units, so operating temperature and duty cycle determine service life more than ambient humidity. Continuous input speeds above 50 % of catalogue maximum materially shorten grease life — a common root cause of premature failures in 24/7 cells.
Harmonic drives are not the right call for heavily shock-loaded, high-inertia start/stop applications like press flywheels, large conveyor drives, or any duty that demands the reducer absorb a torque spike well above its rated peak. For those, a cycloidal or planetary unit is the correct spec. For a more general cost-and-spec frame on the broader gear-reducer market, see the industrial gear price & cost guide 2026 for material and tolerance levers that apply across gear types. When the harmonic drive is feeding a linear guide or a crossed-roller guide on a Cartesian or SCARA axis, the same 60″ / 90″ error budget flows straight through into the system's positioning repeatability.
Quick checklist before you commit to a part number
Confirm: (1) rated torque ≥ RMS application torque × service factor; (2) peak torque below catalogue allowable peak; (3) input speed ≤ catalogue maximum at the worst case; (4) transmission error ≤ joint pointing/positioning requirement (≤60″ for high-accuracy, ≤90″ acceptable for AGV/light-pick); (5) input coupling type and output flange match the motor and downstream load; (6) grease life estimate covers the planned service interval. If all six pass, the model code (e.g. DHS-25-100-U-OC11 or DHDG-14-50-U-R11) is locked in and the BOM line is defensible [S1][S4].
Trackable signals for the next 6 months: AGV and humanoid-robot volume continuing to push model 14 / 17 short-cylinder demand, and the gradual migration of double-arc tooth profiles into more model sizes — both are observable in distributor stock lists and OEM catalogue revisions.