In a single-stage strain wave gear the reduction ratio is set by the tooth-count difference between the flexspline and the circular spline, normally just two teeth, so the ratio falls out as the flexspline tooth count divided by that 2-tooth difference [S3]. A 50:1 unit therefore uses roughly 100 flexspline teeth against 102 on the circular spline, a 100:1 unit uses 200 vs 202, and a 160:1 unit uses roughly 320 vs 322, with the pitch diameter growing almost in step with the ratio at a given frame size [S2][S3].
The rated output torque of a cup-type strain wave gear rises sharply with ratio in the same housing, because the flexspline is the load-carrying member and more teeth in mesh at the major ellipse means a higher mean tooth load before the [S1]-style "S" tooth profile gives out. Laifual's FS series literature states directly that "higher ratios increase output torque" within a given cup frame, and Harmonic Drive's CSF-GH housed unit is offered across the full 50:1 to 160:1 range with zero backlash, so a single SKU line is in fact three distinct mechanical designs under the same housing drawing [S7][S8].
Why Ratio Changes Torque Capacity in a Fixed Frame
At a constant housing diameter, the flexspline pitch diameter is fixed, so going from a 50:1 to a 160:1 ratio is not done by enlarging the gears but by changing the tooth count at near-constant module. A larger flexspline tooth count at the same module means finer teeth, smaller individual tooth loads for a given transmitted torque, and a higher total sum of tooth-load capacity along the major-axis contact band [S2]. Harmonic Drive's cup-type CSF/CSG component sets show a 30% torque-capacity gain for the CSG high-torque version over the CSF in the same frame, and that headroom comes from the "S" tooth profile engaging up to 30% of the total tooth count at the major axis versus roughly 15% for older profiles, which the OEM describes as "a 100% increase in torsional stiffness in the low and mid torque ranges" [S1].
The same mechanism is what makes a 160:1 unit feel stiffer than a 50:1 in identical size: more teeth in simultaneous contact means more springs in parallel resisting the same twist angle. In a 200-vs-202 (100:1) cup set, the contact band at the major ellipse is a 2-tooth-wide band repeated over a 200-tooth pitch, and a typical FANUC-class robot joint running on this geometry hits around ±0.01° repeatability, with the flexspline wall typically 0.5-1.5 mm thick depending on size and radial deformation under the wave generator held to 0.1-0.3% of the pitch diameter [S2].
Torsional Stiffness: 50:1 vs 100:1 vs 160:1
Stiffness scales with the square of the number of teeth in contact, which is why doubling the in-mesh tooth count roughly doubles torsional stiffness in the low and mid torque band on the "S" profile, and why a 160:1 unit at the same frame diameter measures noticeably stiffer than a 50:1 unit of the same part number [S1]. At higher ratios, however, the no-load running torque of the wave generator bearing and the elastic wind-up of the flexspline cup add to the measured torsional compliance, so the gain in contact-driven stiffness is partially offset by the longer thin-walled cup in a 320-tooth flexspline versus a 100-tooth flexspline.
For the same housing, a typical three-band comparison reads roughly: 50:1 = highest input speed, lowest rated torque, lowest no-load running torque, lowest backdriving torque; 100:1 = the workhorse, balanced torque and stiffness, the choice for general 6-axis robot joints and CNC rotary axes; 160:1 = highest rated torque in the same frame, highest torsional stiffness, but lower mechanical efficiency and higher no-load torque, so it is the choice when positioning resolution and torque density matter more than backdrivability [S4][S7][S8].
No-Load Torque, Efficiency, and Backdrivability
Mechanical efficiency in a strain wave gear sits roughly in the 70-80% band at moderate ratios and drops as the ratio climbs, because the wave generator bearing has to deform a stiffer, finer-toothed flexspline cup through each revolution [S3]. For a 50:1 cup set the no-load running torque is low enough that the unit is commonly treated as backdrivable in collaborative-robot joints; a 160:1 unit in the same frame is generally not backdriven by gravity loads and is instead used where motion is commanded, not free-floating [S4].
The peak torque limit on any ratio in the range is set by the ratcheting threshold, which is the torque at which the flexspline teeth jump out of mesh at the major ellipse and the unit emits a hard knock. Once a unit has ratcheted even once, the tooth flanks are damaged and the original positioning accuracy is lost, which is why sizing practice is to stay at or below the rated torque, not the ratcheting limit [S2]. For designers using a torque sensor to validate joint loading, this means the sensor head should be placed on the input side of the wave generator where the torque is the lowest by the ratio, and the rated torque is checked on the output side after multiplying back by the ratio.
Selection: Which Ratio to Specify
For 6-axis robot arm joints, CNC rotary tables, and surgical-robot wrists, a 100:1 strain wave gear in a CSF-GH-class housing is the default: zero backlash, balanced rated torque, and torsional stiffness that delivers the ±0.01° repeatability industrial users expect, with the harmonic drive itself being the only single-stage reducer that hits 50:1 to 320:1 in a single stage without backlash [S2][S7].
For higher-payload arms, heavy-payload collaborative robots, and large rotary index tables where the joint spends most of its life near a fixed pose, a 160:1 unit in the same frame trades backdrivability for higher rated torque and higher torsional stiffness, at the cost of a stiffer flexspline cup and a higher no-load running torque [S4][S7][S8]. For high-speed pick-and-place joints, delta robot wrists, and any application that benefits from a backdrivable gearbox for gravity compensation, a 50:1 unit is the right call, with the caveat that rated torque is the lowest of the three and the unit will ratchet at a lower output load [S2][S3].
When validating a new joint design, a common practice is to bench-test the unit on a torque wrench tester stand at the rated and ratcheting torques before mounting it to the arm, because the in-the-field failure mode is ratcheting, not gear-tooth wear, and the test reveals the true margin between rated and peak torque. The Yu and Gong ASEE kinematic reference is a useful starting point for engineers who need to derive the ratio equation from tooth counts rather than read it off a catalogue, and it gives a worked 160/162 example that maps directly to a 80:1 cup set when applied to a 158/160 flexspline/circular pair [S5].
Limits, Failure Modes, and What the Datasheet Hides
The ratcheting failure mode is the dominant field failure for any ratio, but the ratio itself changes how the unit fails at end of life. A 50:1 unit in a continuously running pick-and-place joint tends to fail first at the wave generator bearing as grease breaks down under the cyclic radial loading of the elliptical cam, because the higher input speed magnifies the bearing's load cycles. A 160:1 unit in a heavy-payload joint tends to fail at the flexspline cup base through fatigue cracking, with backlash gradually rising over thousands of hours before the tooth flanks finally give out [S2].
Typical efficiency sits around 70-80% across the ratio range, and drops toward the low end of that band as ratio climbs, which is why energy calculations on a multi-axis robot need to use the per-ratio efficiency curve, not a single number, and why a 160:1 joint in a heavily cycled application can run noticeably warmer than a 100:1 joint in the same duty cycle [S3]. For factory-floor integration, the lesson is to size the gearbox to stay below the rated torque in the worst-case pose and to validate the joint through a torque sensor before signing off the design, especially when the ratio has been pushed from 100:1 up to 160:1 to chase torque headroom in the same envelope.
Track the next revision of the cup-type CSF/CSG component-set catalogue for an updated torsional-stiffness curve at the 160:1 end, since the "S" tooth profile change roughly doubled stiffness in the low and mid torque band but datasheets still quote a single value that flattens the real curve [S1]. Also watch for OEM data on flexspline wall thickness versus tooth count, because the 0.5-1.5 mm wall range quoted in the field guide is what determines the ratcheting threshold more than the rated torque printed on the nameplate [S2].
Background reading: Hybrid vs Permanent Magnet vs Variable Reluctance Stepper Motors: 2026 Selection Specs.