Every other spec on a reducer datasheet describes a limit you design under. Torsional stiffness is different: it describes a behaviour that becomes part of your machine’s dynamics. Get it wrong and the joint does not fail, it just never tunes properly, and the reason is never obvious from the number you were given.
The number is a slope, not a property
Wind a strain wave gear up against a locked output and plot torque against deflection, and you do not get a straight line. You get a curve that stiffens as load increases, because more teeth come into full engagement as the flexspline is pressed harder into the circular spline. Manufacturers who publish the whole picture give it as three separate stiffness values over three torque bands, each one the slope of a segment.
A single published figure is therefore a slope over a stated band, and the band matters. Using a stiffness measured near rated torque to predict deflection at ten percent of rated will overestimate the stiffness, because you are on a softer part of the curve than the one that was measured.
How much wind-up that actually is
The number sounds abstract until you convert it to an angle at the output. Across our strain wave gear series:
| Part number | Torsional stiffness | Rated torque | Wind-up at rated | Transmission accuracy |
|---|---|---|---|---|
| AS-GS-35 | 7.1 kN·m/rad | 10 N·m | 291″ | <90″ |
| AS-GS-43 | 16 kN·m/rad | 31 N·m | 400″ | <90″ |
| AS-GS-51 | 29 kN·m/rad | 52 N·m | 370″ | <60″ |
| AS-GS-63 | 57 kN·m/rad | 87 N·m | 315″ | <60″ |
| AS-GS-81 | 120 kN·m/rad | 178 N·m | 306″ | <60″ |
Two things fall out of that table. First, the wind-up stays inside a fairly narrow band — 291 to 400 arcseconds, call it five to seven arcminutes — across a range where rated torque varies by nearly eighteen times. Stiffness broadly tracks torque capacity, so the deflection does not run away as the frames get bigger. Second, and this is the point: the same part numbers publish a transmission accuracy of <90″ or <60″. The elastic deflection under rated load is three to six times the drive’s own accuracy specification.
This is not a defect and it is not hidden — both figures are on the same page of the same datasheet. It is simply that one of them is quoted far more often than the other.
Hysteresis: the part that does not spring back
Unload the drive and it does not retrace the same curve. There is a loop, and the width of it at zero torque is hysteresis loss, published across our gear series as <1′. Note the unit: that is arcminutes, while backlash and transmission accuracy on the same range are quoted in arcseconds. Sixty arcseconds to the arcminute, and comparing the two figures without catching the switch is an order-of-magnitude error in the drive’s favour.
Hysteresis is not backlash. Backlash is free play with no torque applied; hysteresis is lost motion after a torque reversal, and it comes from friction in the tooth mesh and the bearing rather than from clearance. A zero-backlash drive still has it. If you reverse direction under load and land short, this is usually why, and no amount of gain fixes it — it is dissipative, not elastic. We separated those three measurements here.
Read the units before you compare two suppliers
Our own catalogue carries stiffness in two conventions, because the underlying series are characterised differently: the strain wave gear series in kN·m/rad, the planetary rotary actuators in N·m/arcmin. One radian is 3,437.75 arcminutes, so AS-PA-S at 46 N·m/arcmin is about 158 kN·m/rad — stiffer than every gear in the table above. Compare the raw numbers without converting and you will reach the opposite conclusion by a factor of three thousand.
What it does to the loop
A joint with a compliant reducer is a two-mass system: motor inertia on one side, load inertia on the other, a spring between them. That arrangement has a resonance, and it sits at roughly f = (1/2π)√(K/J) for a load inertia J against reducer stiffness K.
Put numbers in it. An AS-GS-63 at 57 kN·m/rad driving a 0.5 kg·m² load resonates at about 54 Hz. That is not a comfortable distance from where you would like a position loop to run. Push the bandwidth up to where the tracking error looks good on paper and the joint rings; back it off until it stops ringing and you have given up the performance you bought the drive for.
Three consequences worth designing around:
- The motor encoder cannot see the wind-up. It is on the wrong side of the spring. A motor-side loop can be perfectly converged while the output sits 300 arcseconds away, which is the strongest argument for output-side feedback — the trade-offs are in one encoder or two.
- Stiffness belongs in the model. A rigid-joint model will not predict the resonance, so the first time you meet it will be on the machine.
- A stiffer drive moves the problem, it does not remove it. Doubling stiffness raises the resonance by about 1.4×. Useful, not decisive, and usually paid for in mass.
The practical position: treat the published stiffness as a design starting point, find out which torque band it was measured over, and if the axis is performance-critical, measure the curve at your own operating point. We publish stiffness on eighteen part numbers and hysteresis loss on fifteen, and we will tell you the measurement conditions for any of them if you ask.
Related: One encoder or two? · Harmonic, planetary, or cycloidal?.