harmonic drive (strain-wave gear)
A harmonic drive is a clever, compact gearbox that achieves a huge speed reduction in a single thin ring — and does it with almost no slop or wobble. Instead of stacking many rigid gears, it uses a flexible steel cup, called the flexspline, whose toothed rim is gently squashed into an oval by an inner egg-shaped hub. The oval pushes the cup's teeth into a slightly larger fixed outer ring at just two spots, on opposite sides. As the hub spins, the squashed shape sweeps around like a ripple traveling through the flexible cup — that traveling wave is the 'strain wave' the gear is named for.
Here is the trick: the flexible cup has just a couple fewer teeth than the rigid outer ring. So after the egg-shaped hub makes one full turn, the flexible cup has only crept backward by those few teeth — meaning the output barely moves per input turn, giving ratios like 100:1 or even 300:1 from one small unit. Because many teeth stay meshed at once and they are preloaded against each other, there is almost no backlash, the tiny dead play that lets ordinary gears rattle back and forth. That combination of high ratio, light weight, and near-zero slop is exactly what robot arm joints crave, which is why harmonic drives sit in the elbows and shoulders of most precise industrial and humanoid robots.
In a robot arm's wrist, a single harmonic drive turns a fast 6,000-rpm motor into a 60-rpm output with a 100:1 ratio — and because there is virtually no backlash, the tool tip holds a steady, repeatable position even when the motor reverses direction.
One thin ring, a 100:1 reduction, and almost no play — ideal for a precise joint.
The design was invented in the 1950s by C. Walton Musser. Its near-zero backlash is its headline virtue, but the flexible cup must bend millions of times without cracking, so these reducers are precision-made and pricey — a big reason robot joints cost what they do.