7. Harmonic and cycloidal drives
These two dominate robot joints, and both work on the same trick: mesh two toothed rings that differ by a tiny number of teeth, and the difference — not the tooth count — sets the ratio.
Strain wave (harmonic) drive
An elliptical wave generator deforms a thin flexible cup so its teeth engage the rigid circular spline at two opposite points. The cup has fewer teeth, so one turn of the generator walks it backwards by that difference.
i = − zfzc − zf
→ 200 and 202 teeth give −100 : 1strain wave gearing
- Why robots use it: 1:30 to 1:320 in one stage, essentially zero backlash, coaxial, light, and a large hollow bore for cables.
- What you pay: torsional compliance that is deliberately non-linear near zero, hysteresis of a few arc-minutes, efficiency that falls off at high ratio and low temperature, and a price.
Cycloidal drive
An eccentric drives a lobed disc that rolls inside a ring of pins. One lobe fewer than there are pins means one pin-pitch of output per input turn.
r = P − LL → reduction = LP − L
→ 40 pins and 39 lobes give 39 : 1cycloidal drive
- Why robots use it: very high shock capacity, high stiffness, long life — the usual choice for the big lower joints of a heavy arm.
- What you pay: more backlash than a harmonic drive, a rotating eccentric mass that has to be balanced, and more parts.
| Planetary | Harmonic | Cycloidal | |
|---|---|---|---|
| Ratio, one stage | 3 – 10 | 30 – 320 | 10 – 120 |
| Backlash | 3 – 15 arcmin | < 1 arcmin | 1 – 3 arcmin |
| Efficiency | 0.95 – 0.98 | 0.70 – 0.85 | 0.85 – 0.93 |
| Shock capacity | medium | low | high |
| Typical use | servo gearhead | arm wrist joints | arm base joints |
These figures are ranges, not a datasheet. They are here so the
comparison makes sense. Any real selection is made from the manufacturer's curves for the specific
size, ratio, duty cycle and temperature.