A linear motion stage needs a harmonic drive (strain wave gear) specified on the RFQ with seven concrete fields: reduction ratio, rated and peak torque, lost motion in arc-min, torsional stiffness, hollow-shaft bore, tilting moment on the integrated output bearing, and the lubrication/grease grade. Single-stage ratios of 30:1 to 160:1 are common, and 100:1 is the workhorse choice when the motor is a 3000 rpm servo driving a ballscrew or rack [S1][S7].
The selection matters because the flexspline flexes elastically every input revolution at roughly 0.3% strain at the major axis, and that fatigue cycle caps gearbox life at 7,000 to 35,000 hours depending on load profile. Buyers who omit the duty cycle, the peak torque, and the radial/tilting load on the output bearing force vendors to requote with conservative derating, which adds 20-30% to lead time and pushes the unit cost up [S1][S3].
What a Harmonic Drive Actually Is and Why It Fits a Linear Stage
A harmonic drive uses three parts: a wave generator (elliptical plug with a thin ball bearing), a flexspline (thin-walled cup with external teeth), and a circular spline (rigid ring with internal teeth, two more than the flexspline). Spinning the wave generator one revolution makes the flexspline rotate backward by exactly two teeth relative to the fixed circular spline, giving reduction magnitude Nf/d, where Nf is the flexspline tooth count and d is the tooth-count difference [S1][S5]. A 200-tooth flexspline with d=2 gives 100:1 in a single stage, which is the ratio most quoted for linear-axis servo packages.
For linear stages this single-stage architecture is a real advantage: the gearbox envelope stays the same regardless of ratio, so a 50:1 and a 160:1 unit of the same frame size bolt to the same motor adapter plate. Form factor is the only physical variable, and harmonic drives ship in two variants: cup type (solid output shaft, higher stiffness) and hat/hollow-shaft type (through-bore for cables, pneumatics, or a through-shaft encoder) [S2][S7][S8]. Hollow-shaft bores of 14 mm to 70 mm are typical, frame sizes run 14 to 58, and maximum torque spans 9 Nm to 1840 Nm across the family [S8].
Ratio, Torque, Backlash, and the Numbers Behind Each Spec Line
Single-stage harmonic ratio range is 30:1 to 320:1, with 30:1 to 160:1 being the production-common window used on industrial stages; planetary gearboxes by comparison only reach 3:1 to 10:1 per stage, and cycloidal reducers 10:1 to 200:1 [S1]. Nominal torque on a mid-size harmonic stage (SMD series) covers 5.4 Nm to 402 Nm across the catalog, with ratios of 50:1 to 160:1 as standard builds and 1:1 specialty ratios also offered [S6].
Lost motion (the no-load rotational play at the output) is 0.5 to 2 arc-min on a harmonic drive, against 3 to 15 arc-min on a planetary and 0.5 to 3 arc-min on a cycloidal, and that is the figure the RFQ must call out by arc-min, not by a vague "precision" label. Torsional stiffness on a mid-size harmonic stage is around 1.5x10^4 Nm/rad against 5x10^4 on a planetary and 3x10^4 on a cycloidal; harmonic drives accept peak torque roughly 3x rated for brief overloads versus 2.5x for planetary, but they pay for it in efficiency: 70-85% versus 92-97% for planetary and 80-90% for cycloidal [S1]. SMD's high-end line pushes backlash down to as low as 12 arc-seconds, which is the figure to specify when the downstream linear element is a precision-ground ballscrew with lead accuracy under 5 micron/300 mm [S6].
Cup vs Hat (Hollow Shaft) Form Factor Decision
Choose cup type (CSG-2UK, PMCG, PMCD) when the design needs a solid output shaft, maximum torsional stiffness, and the shortest axial length on the stage, and choose hat/hollow-shaft type (SHG-2UJ, SHF-2UJ, PMHG, PMHD) when cables, pneumatic lines, a through-shaft encoder, or a slip ring must pass through the gearbox centerline [S2][S4][S8]. Hat type typically integrates a cross-roller bearing at the output for direct mounting to the linear stage's driven member, and the SHG-2UJ ships in ratios of 30:1 to 160:1 with high rigidity, while the SHF-2UJ spans 50:1 to 160:1 across 10 frame sizes [S4].
The hat-type integrated cross-roller bearing is rated by tilting moment, and the catalog range across frame sizes is 74 Nm to 2180 Nm; that tilting-moment number is what the linear-stage RFQ must match to the stage's overturning load, or the bearing will brinell within the first duty cycle. For reference on how an output bearing interacts with downstream mechanics, see the linear bearing and linear actuator encyclopedia entries, and the harmonic reducer reference for ratio/backlash comparisons.
The Seven RFQ Lines That Must Be on the Spec
Line 1, reduction ratio: state the absolute number, not "high" or "low"; 50:1, 100:1, and 160:1 cover most stage applications and you should match the motor's max RPM to the linear element's max feed rate before picking the ratio. Line 2, rated torque (Nm) at the output, continuous duty; this is the RMS torque over the move profile, not the peak. Line 3, peak/emergency stop torque (Nm) and allowable duration, because harmonic drives accept roughly 3x rated briefly, but that envelope collapses fast above 1 second [S1].
Line 4, lost motion in arc-min, with a max value (e.g. "<1 arc-min"). Line 5, torsional stiffness in Nm/rad if the stage is a precision-ground ballscrew drive, since a 1.5x10^4 Nm/rad flexspline will be the weakest link in the drivetrain and the closed-loop controller must be tuned to it. Line 6, hollow-shaft bore in mm and required bearing type (cross-roller vs tapered roller) for hat-type units. Line 7, tilting moment on the output bearing in Nm, plus axial and radial load if the application pushes the stage through combined loading. Lines omitted from the RFQ are where the requote cost hides: vendors derate by 30-50% on torque, 2x on price, and 4-6 weeks on lead time when any of lines 2, 3, or 7 are missing. For a worked example of how adjacent subsystems are specified on a positioning axis, see the servo drive RFQ spec map.
Who Should and Should Not Use a Harmonic Drive on a Linear Stage
Harmonic drives are the right call when the stage needs sub-arc-min pointing, a high ratio in a short axial package, a hollow-shaft cable pass-through, and a duty cycle that stays inside 7,000-35,000 hours at rated load. They are wrong for high-continuous-duty conveyor or palletizing axes where efficiency below 85% wastes motor power and heat, and they are wrong for shock-loaded press feeds where cycloidal's 5x peak-torque tolerance handles the hammer pulse better [S1][S3].
For a closed-loop positioning axis, the feedback device also matters: a harmonic drive on a ballscrew stage almost always pairs with a linear encoder on the stage carriage and a motion controller tuned for the 1.5x10^4 Nm/rad torsional compliance, because the closed-loop bandwidth will be limited by the resonance of the flexspline and the integrated bearing if the controller is set to ignore that mechanical filter.
Lubrication, Environment, and the Failure Modes to Block on the RFQ
The proprietary grease (SK-1A or vendor equivalent) carries the entire tooth-mesh load, and once it shears down, tooth wear accelerates exponentially; specify the grease grade on the RFQ (SK-1A, Krytox GPL 205, or food-grade per FDA 21 CFR 178.3570 if the stage is in pharma/food), and require the vendor to state the relubrication interval in hours, not "lifetime" [S1].
IP rating matters for washdown or cleanroom stages: a sealed CSG-2UK or SHG-2UJ is the default for factory automation, but if the stage lives near coolant splash or outdoors, ask for IP65 and confirm the wave-generator bearing seal material (NBR vs FKM). A common failure pattern is wave-generator bearing wear that lets the ellipse lose shape, after which the unit develops audible ratcheting under torque, followed by flexspline tooth-tip fatigue cracks at the major axis after a few hundred hours of over-strain; the RFQ should ask the vendor to publish the rated peak-torque cycles to fatigue, not just the static peak number. For selection context on adjacent motion-control components, see the harmonic filter encyclopedia entry (note: that entry covers electrical harmonics, not the strain-wave mechanism, but the naming overlap causes spec confusion on RFQs that should be disambiguated up front).