Chris Paxton · About · Blog · X
How different gear mechanisms work — notes and interactive demos.
Demos use conjugate tooth profiles with mesh clearance readouts — run slowly or step frame-by-frame to inspect contact.
Est. weight · cost in each demo are order-of-magnitude guides for ~100–200 mm-class reducers (not quotes).
Toggle Clearance for the green mesh-gap indicator; Wobble trace shows off-axis shake (cycloidal uses disc mass centroids when a counter disc cancels shake).
URL overrides: ?clearance=0, ?wobble=0.
Gears translate rotation from one shaft to another, often changing speed and torque in the process. A motor might spin at thousands of RPM, but a robot arm joint needs slow, powerful motion — gear reduction bridges that gap.
Different mechanisms trade off efficiency, size, backlash, backdrivability, cost, and complexity. Simple spur gears are easy to understand; planetary, cycloidal, and harmonic drives pack large reduction ratios into compact packages.
Demos use conjugate profiles and mesh clearance readouts on spur, planetary, cycloidal (fixed-pin), and harmonic drives. Rolling trochoid view shows curve generation only (no pin contact overlay).
No single robot uses one gear type everywhere — designers pick by joint: heavy base axes, compact wrists, and fast legs all get different reducers. Each section below includes examples and links. (Camera gimbals are a common counterexample: they are usually direct-drive brushless motors with no reducer, because even tiny gearbox backlash hurts optical stabilization.)
Spur gears are the simplest form: two toothed wheels mesh along parallel axes. The driver turns one gear; the driven gear rotates in the opposite direction. Tooth counts determine the speed ratio.
If the driver has 18 teeth and the driven gear has 36, the output turns half as fast but with roughly twice the torque (ignoring friction). Spur gears are cheap, efficient, and easy to manufacture. Stacked spur stages in cheap servos (e.g. 254:1) multiply torque but also multiply friction — the joint becomes hard to backdrive, so external forces do not easily turn the output shaft.
Uses: clocks, 3D printer extruders, entry-level servos
A planetary gearset has a sun gear at the center, planet gears that mesh with both the sun and an outer ring gear, and a carrier that holds the planet gears. Any one of the three elements — sun, ring, or carrier — can be held fixed while the other two move.
With the ring gear fixed and the sun as input, the carrier output gives a reduction. With the carrier fixed and the sun as input, the ring rotates in the opposite direction but slower than the sun — like a simple sun → planet → ring train: ωring = −ωsun · (Nsun / Nring), and because Nring > Nsun, the ring speed drops. Same hardware, different ratios depending on what you lock.
The interactive demo shows one stage — a single sun / planet / ring set. Most real reducers stack several stages coaxially: the output shaft of stage 1 drives the sun of stage 2 (sometimes through a short coupling), and so on. Each stage multiplies torque and divides speed; the overall ratio is approximately the product of the stage ratios: itotal ≈ i1 · i2 · ….
That is why the examples below span such different numbers: Go2 uses a single low-ratio stage (~6:1) for quasi-direct drive; the G1 humanoid stacks two stages for ~20:1 total; Mars rover wheel actuators use four stages to reach 1024:1. More stages mean more parts and efficiency loss, but much higher torque in the same diameter — the usual trade-off in leg and wheel drives.
Backdrivability is how easily an external load can spin the output and propagate force back through the gearbox to the motor — important for legs that must “feel” the ground and absorb impacts. Lower ratio means less friction and reflected inertia, so the actuator is more backdrivable (easier to push by hand). High-ratio stacks (Spot hips, Mars wheels) resist backdriving: good for holding load and precision, but the controller gets less passive mechanical feedback from the environment. Quasi-direct-drive leg designs deliberately pick ~6:1–9:1 single-stage planetaries for that transparency.
In the demo: one stage only (ring fixed, sun input, carrier output). Tooth sliders change that stage’s ratio — not a full multi-stage stack.
Uses: automotive transmissions, robot leg joints, quasi-direct-drive actuators
A cycloidal drive uses an eccentric input to move a lobed disc past fixed pins on the housing. The demo separates three layers:
Default example: 5 lobes and 6 pins → 5:1 reduction. If the disc were held fixed and the pin housing rotated instead, the ratio would be Npins / (Npins − Nlobes). Real RV reducers use equidistant epicycloid profiles and often add a counter disc (second eccentric disc 180° out of phase) to cancel housing shake — toggle it to compare on-axis output vs an orbiting output shaft.
Uses: robot reducers, indexing tables, conveyors
A harmonic drive has three parts: a wave generator (elliptical cam with bearing), a flexible outer spline (flex spline), and a rigid circular spline (circular spline) with slightly more teeth.
The wave generator is the input — a coaxial elliptical cam that rotates in place (like the inner oval in the Wikipedia strain-wave diagram). It presses the thin flex spline into a smooth two-lobed oval. Only two zones on opposite sides mesh with the fixed ring; those zones travel around as the cam turns. Because the ring has two more teeth than the flex spline, each cam revolution advances the flex spline by two tooth pitches — a large reduction on the output shaft at the center. With the circular spline fixed and the flex spline as output, i = Nflex / (Ncircular − Nflex) (30 teeth and 32 teeth → 15:1).
In the demo: orange ellipse = coaxial input cam · blue annulus = flex cup with involute teeth on the strained oval · gray ring = fixed circular spline (internal teeth) · yellow spoke = slow output · green arcs = mesh zones · pink trace = mesh zone travel.
Uses: collaborative robots, space mechanisms