Servos: torque, speed and splines

Torque, and the centimetre in kg.cm

Servo torque is quoted in kilogram-centimetres. It means: the servo can hold that many kilograms at a radius of one centimetre from the output shaft. At two centimetres it holds half as much, at four centimetres a quarter.

force at radius = torque in kg.cm ÷ radius in cm

So a 20 kg.cm servo with a horn arm 2 cm long produces 10 kg of force at the linkage. This is the calculation people skip, and it is why a servo that looked enormous on paper stalls in use.

Ounce-inches appear on American products. One kg.cm is about 13.9 oz-in.

Working out what you need

For a control surface, the load is the aerodynamic hinge moment, which grows with airspeed squared and with surface area. Nobody calculates this from first principles for a model, and the practical approach is to copy a known-good setup and add margin.

For a robot joint, it is more tractable: mass times gravity times the distance from the joint to the centre of mass, plus whatever acceleration you want. Then double it, because a servo held near its stall torque gets hot, draws heavily and dies.

design torque ≈ 2 × worst-case static torque

Speed, and the voltage that changes both

Speed is quoted as seconds per 60 degrees of travel, unloaded. A 0.10 s/60 servo is quick; a 0.20 s/60 servo is ordinary. Under load, both are slower.

Torque and speed are both quoted at a stated voltage, and both increase with it. A servo rated 20 kg.cm at 6.0 V and 24 kg.cm at 7.4 V is the same servo, and the two figures are not comparable across products unless the voltages match. This is the single most common way servo specifications mislead.

Gears, bearings and what they cost

Plastic or nylon gears are light, quiet and cheap, and they strip. Fine for light control surfaces, not for anything that takes a knock.

Metal gears survive shock loads and cost weight and noise. Titanium and hardened steel are the same trade further along.

Bearings matter more than the price difference suggests. A bushed servo has more slop and wears faster; dual ball bearings hold the output shaft properly and keep the linkage where you put it.

Splines: the thing nobody warns you about

The output shaft is splined, and the spline count differs between manufacturers. 25T is the common Futaba and clone standard, 23T is Airtronics and Sanwa, 21T is JR and 15T is common on micro servos.

A horn is not universal. Changing brand usually means changing every horn, and a 25T horn forced onto a 23T shaft will feel like it fits and then round off under load.

Check the spline before you buy the horn. This catalogue links horns to the servos they fit for exactly this reason.

Analog, digital and smart serial

Analog servos update their control loop about 50 times a second. Cheap, adequate, slightly soft in the centre.

Digital servos update several hundred times a second. They hold position harder, respond faster, and draw noticeably more idle current.

Smart serial servos, on a bus rather than a PWM wire, report position, load and temperature back. For a robot arm this changes what is possible; for a control surface it is usually more than you need.