Gears transmit torque and angular velocity between shafts (or convert rotation to translation) by meshing teeth. They are the usual way to get a fixed ratio, direction change, and mechanical advantage without relying on friction the way a belt does.
This folder is the gear home for the notes. Torque and DoF live in eragon/structure.md; materials and 3D-print constraints live in eragon/material.md. Tooth geometry that every type shares lives in fundamentals.md.
| Note | Variant | Shafts / motion |
|---|---|---|
| fundamentals.md | Shared vocabulary (involute, module, backlash) | — |
| spur.md | Spur | Parallel |
| helical.md | Helical | Parallel (or crossed) |
| herringbone.md | Herringbone / double helical | Parallel |
| internal.md | Internal (ring) | Parallel, coplanar |
| bevel.md | Straight bevel (incl. miter) | Intersecting |
| spiral-bevel.md | Spiral bevel | Intersecting |
| hypoid.md | Hypoid | Skew (offset, ~90°) |
| worm.md | Worm + worm wheel | Skew (90°) |
| rack-and-pinion.md | Rack and pinion | Rotary ↔ linear |
| planetary.md | Planetary / epicyclic | Coaxial, compact |
| harmonic.md | Harmonic (strain wave) | Coaxial, high reduction |
| cycloidal.md | Cycloidal drive | Coaxial, high reduction |
Start from the shaft geometry, then the ratio and envelope, then noise / backlash / printability.
shafts parallel?
yes → need compact coaxial stack? → planetary / internal
need quiet / high speed? → helical (or herringbone if axial thrust is a problem)
otherwise → spur
shafts intersect (usually 90°)?
quiet / high load? → spiral bevel
otherwise → straight bevel (miter if 1:1)
shafts skew (non-intersecting, non-parallel)?
huge ratio / self-locking? → worm
offset like a differential? → hypoid
rotation must become a straight line? → rack and pinion
huge ratio in a tiny robot joint?
harmonic (arms, almost-zero backlash) or cycloidal (shock, industrial)
Qualitative, not a catalog. Exact numbers depend on module, materials, lubrication, and quality.
| Type | Efficiency (approx.) | Ratio in one stage | Noise | Axial thrust | Backlash (typical) | 3D-print friendly |
|---|---|---|---|---|---|---|
| Spur | 98–99% | 1:1 to ~8:1 | High at speed | None | Moderate | Excellent |
| Helical | 96–98% | 1:1 to ~8:1 | Low | Yes | Moderate | Fair (overhangs) |
| Herringbone | 97–99% | 1:1 to ~8:1 | Low | Cancels | Moderate | Poor (V-groove) |
| Internal | ~98% | 1:1 to ~8:1 | Similar to mate | As mate | Moderate | Fair |
| Straight bevel | 97–98% | 1:1 to ~6:1 | High at speed | Some | Moderate | Fair |
| Spiral bevel | 96–98% | 1:1 to ~8:1 | Low | Yes | Moderate | Poor |
| Hypoid | 90–96% | ~2:1 to 10:1 | Low | Yes | Moderate | Poor |
| Worm | 40–90% | ~5:1 to 100:1 | Low | High on worm | Can be low | Fair |
| Rack and pinion | ~98% (spur rack) | n/a (linear) | As pinion type | As pinion | Moderate | Excellent |
| Planetary | 90–97% | ~3:1 to 10:1 | Moderate | Low | Low–moderate | Fair (small teeth) |
| Harmonic | 60–85% | ~30:1 to 320:1 | Low | Low | Very low | Poor (flexspline) |
| Cycloidal | 50–85% | ~10:1 to 200:1 | Low | Low | Very low | Poor (lobes + pins) |
| Type | Wins when… | Loses when… |
|---|---|---|
| Spur | Cheap, efficient, easy to print and inspect | Noise, shock at tooth entry, parallel shafts only |
| Helical | Quiet, stronger (more teeth in mesh) | Axial thrust, extra bearing load, harder to print |
| Herringbone | Helical smoothness without net thrust | Hard to make; alignment of the V is unforgiving |
| Internal | Compact, same-direction rotation, high contact | Harder to machine/print; assembly access |
| Bevel | Simple 90° turn | Noisy; alignment of intersecting axes |
| Spiral bevel | Quiet right-angle power | Cost, thrust, specialized cutting |
| Hypoid | Offset packaging, high pinion strength | Sliding wear, special oil, not printable |
| Worm | Huge ratio, can self-lock, 90° in one stage | Heat, wear, low efficiency |
| Rack and pinion | Direct linear travel, easy to reason about | Finite rack length; backlash as positioning error |
| Planetary | Density, coaxial I/O, servo gearboxes | Many parts; load sharing if planets are unequal |
| Harmonic | Tiny backlash, huge ratio, robot arms | Flexspline fatigue, torque limits, cost |
| Cycloidal | Shock, stiffness, industrial reducers | Eccentric bearings, machining of the disc |
For a 3D-printed biped, the practical stack is usually:
- Spur (or printed planetary) in a joint gearbox when you control the ratio yourself
- Planetary already inside most hobby servos
- Harmonic or cycloidal if a joint needs near-zero backlash and a large reduction in a short stack
- Worm only if you want self-locking (and can live with heat and poor efficiency)
- Bevel / helical when a shaft must turn a corner and you cannot reroute with a belt or a printed 90° spur pair
Printable involute spurs are the right first experiment. See fundamentals.md before changing tooth type.