Gearboxes for joints

Why a gearbox

An electric motor is fast but weak. With ratio N: speed ÷ N, torque × N. Power (P = torque · speed) isn’t created; some of it is lost to friction.

Example: a motor at 3000 rpm with 10:1 → joint at 300 rpm with about 10 times the torque, minus losses.

Analogy: the gears on a bike. A low gear for climbing a hill: lots of torque, little speed.

Families

• Spur gears: simple and cheap (inside every SO-101 servo).
• Planetary: compact and robust. Sun, planets, ring and carrier. With the ring fixed, the sun as input and the carrier as output: ratio = 1 + Nring / Nsun. Example: 9-tooth sun, 47-tooth ring → ≈ 6.2:1.
• Harmonic drive (strain wave): a flexible gear deformed by an elliptical wave generator turns inside a rigid ring with 2 more teeth. ratio = Nflex / 2 (100 teeth → 50:1). High ratio in a single stage and almost no backlash, but very hard to move from outside. Typical of industrial arms.
• Cycloidal: handles shocks well.

Quasi-direct drive and back-drive

• High ratio: lots of torque but stiff; hard to move from outside (not back-drivable) and an impact can break teeth.
• Low ratio (quasi-direct drive): less torque, the leg gives way on impact and the motor current can be used to measure force.

Humanoids and quadrupeds hit the ground with every step: they need to feel and absorb impacts. That’s why they use brushless motors with low-ratio planetary gearboxes, and make up for it with bigger motors.

Common questions

Why don’t legs use harmonic drives? Because they are stiff and hard to move from outside; a leg needs to give way when it strikes the ground. They are also more expensive.

What is a series elastic actuator? A spring between the motor and the load, used to measure force (from how much the spring deforms) and to absorb impacts.