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Actuators & Motors

Motors, gearing, drives — how robots move.

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Prerequisites

Classical Mechanics

Why it matters in robotics

Actuators are where a robot's control intent becomes physical motion, and they set the electromechanical limits that bound everything upstream. Torque-speed curves, the inverse relationship between torque and speed, and how a gearbox trades one for the other (introducing backlash, added rotational inertia, and efficiency loss) govern how a joint or drive behaves, while motor sizing and the choice among DC, BLDC, servo, and stepper motors follow from precision, power, and cost. Basic motor equations relating voltage, current, and torque connect to real concerns like thermal limits, holding torque, stall current, and how current gets switched into motion.

What to study

✓Motor types and tradeoffs: brushed DC, BLDC, servo, and stepper - commutation, holding torque, precision, cost, and where each fits in robotics
✓Torque-speed curves and the motor equations: stall vs no-load, the linear DC curve, $\tau = K_t I$ and back-EMF $K_e \omega$ , plus how gearing scales torque/speed and reflected inertia
✓Drivers and control: H-bridges, PWM duty cycle for voltage/speed, current (torque) control loops, field-oriented control for BLDC, and microstepping for steppers
✓Actuator selection and sizing: computing required torque and speed for a load, choosing a gear ratio, and accounting for backlash, efficiency, thermal/duty-cycle limits, and safety margin

Where to study

Cheatsheet

Symbols used below

\tau

motor torque

K_t

torque constant

I

motor current

K_e

back-EMF constant

\omega

motor angular velocity

V

applied voltage

R

winding resistance

N

gear ratio

Motor torque and back-EMF

$\tau = K_t I$

$V = IR + K_e\omega$

Torque scales directly with current; as the motor spins it generates a back-EMF proportional to speed, which subtracts from the applied voltage and limits the current (and hence torque) available at higher speed.

Torque-speed curve

At a fixed voltage, torque falls off roughly linearly as speed rises:

Stall ( $\omega=0$ ): maximum torque, maximum current ( $I = V/R$ ) — the regime that risks overheating.

No-load ( $\tau=0$ ): maximum speed, current only overcomes friction.

Everywhere between is a straight line connecting these two extremes — the fundamental tradeoff between torque and speed at a given voltage.

Gearing trade-off

A gear reduction of ratio $N$ divides output speed by $N$ and multiplies output torque by $N$ (ideal, lossless case).

Inertia and friction reflected back to the motor scale by $1/N^2$ — so a large reduction makes a heavy load feel light to the motor, at the cost of backlash and some efficiency loss in the gears.

Motor type tradeoffs

Brushed DC: simple, cheap, wears out (brush contact).

BLDC: no brushes, efficient, needs commutation electronics (often field-oriented control) but lasts longer and runs cooler.

Servo: a DC or BLDC motor plus gearing, sensor, and closed-loop control packaged together — precise position control out of the box.

Stepper: moves in discrete steps open-loop, good holding torque at rest, simple to command but can skip steps under excess load.

PWM and current control

An H-bridge switches the full supply voltage on and off rapidly; the fraction of time it's on (duty cycle) sets the average voltage delivered, which sets average speed.

A current (torque) control loop instead regulates $I$ directly — since $\tau = K_t I$ , this gives direct torque control regardless of speed, which is what field-oriented control does for BLDC motors and microstepping approximates for steppers.

Sizing an actuator

Required motor torque before gearing is the load torque divided by gear ratio and efficiency: $\tau_{motor} \approx \dfrac{\tau_{load}}{N\,\eta}$ .

Check three limits against the duty cycle of the motion: thermal (continuous current rating), stall current (peak, brief), and holding torque (stepper/servo at rest) — then add a safety margin, since real loads and friction are rarely known exactly.

A gear reduction of ratio N trades speed for torque — output speed drops by N, torque rises by N — and inertia (and friction) reflected back to the motor scales by 1/N², so a big reduction makes the load feel light.

Application focus

Select an application above.