Brushed DC Motors for Robotics: The Ultimate Guide

A brushed DC motor is the oldest electric actuator still worth putting in a robot. Put a voltage across two terminals and it spins; reverse the leads and it spins the other way. Inside, a mechanical commutator does the one hard job that a brushless motor hands off to a silicon controller: it keeps switching which coil is energized as the rotor turns, so the torque always points the same way. That single mechanical trick is why a brushed motor needs nothing more than a battery and a switch to run, and it is also the part that wears out.

For half a century brushed motors ran everything from cordless drills to the Apollo lunar rover wheels. In 2026 they have lost the high end of robotics to brushless, but they hold a large and stubborn middle: cheap gearmotors on hobby rovers, window-lift and wiper motors repurposed for combat robots, the tiny vibration and pager motors in haptics, and countless low-duty mechanisms where a $4 motor and a $1 H-bridge beat a $40 brushless motor and its FOC drive on every axis that matters. Knowing when a brushed motor is the right answer, and how to size and drive one so it lasts, is still a core skill.

The take: A brushed DC motor is defined by three numbers you can measure with a multimeter and a bench supply: winding resistance R, the torque/back-EMF constant Kt = Ke, and the no-load speed. From those you get the entire torque-speed line, the stall current V/R (which is brutal and will cook the motor and the driver if you let it sit there), and the thermal limit that sets real continuous torque. Drive it with an H-bridge and PWM, respect the brushes as a wear item, and reach for brushed DC whenever cost, simplicity, and low duty cycle outrank efficiency and lifetime.

Companion reading: brushless DC motors (BLDC), motor controllers & FOC, robot actuators, stepper motors, and power electronics & motor drives.

Table of contents

1. Key takeaways
2. What a brushed DC motor is
3. Construction: armature, commutator, brushes, field
4. The governing equations
5. The torque-speed curve and operating point
6. PWM speed control and the H-bridge
7. Motor types: PMDC, wound-field, coreless, gearmotors
8. Brushed vs brushless: the honest tradeoff
9. Brush wear, arcing and motor life
10. Thermal limits and stall
11. Sizing a brushed motor: a worked example
12. How to choose
13. Frequently asked questions

What a brushed DC motor is

A brushed DC motor turns direct current into continuous rotation using the Lorentz force: current-carrying conductors sitting in a magnetic field feel a force. Put a loop of wire in a magnet's field, push current through it, and it twists. The problem is that once the loop rotates 180°, the same current would push it back the other way. You would get a quarter turn and then a stall.

The commutator solves that. It is a segmented copper ring on the shaft, wired to the armature coils, wiped by two (or more) spring-loaded carbon brushes fixed to the housing. As the rotor turns, the brushes slide from one commutator segment to the next, reversing the current in each coil at exactly the moment it would otherwise start fighting the field. The torque stays pointed the same way through the whole revolution. The commutator is a mechanical rotary switch synchronized to the rotor by the simple fact that it is bolted to the rotor.

That is the entire idea, and it is why a brushed motor is so easy to drive. The motor commutates itself. All the outside world has to supply is a DC voltage of the right polarity. There is no need to know the rotor angle, no need for three phases, no need for a controller that understands the motor. A battery and a switch make it spin. A battery, a switch, and a way to reverse polarity make it a reversible actuator. This is the lowest possible barrier to controllable motion, and it is the reason brushed motors refuse to disappear.

The price of that simplicity is the brushes. They are a sliding electrical contact under spring pressure, carrying the full armature current, sparking a little every time they cross a commutator gap. They wear. They erode the commutator. They throw electrical noise. Everything a brushed motor does badly traces back to that sliding contact, and everything it does cheaply traces back to it too.

Rule of thumb: if the drive electronics budget matters more than motor lifetime, and the duty cycle is intermittent rather than continuous, a brushed motor is probably the right call. If the motor must run for thousands of hours or live somewhere you cannot easily replace it, look at brushless first.

Construction: armature, commutator, brushes, field

Four parts do the work. Understanding each one tells you where the losses, the wear, and the failure modes live.

Armature (rotor)

In the common permanent-magnet DC motor, the armature is the spinning part and it carries the windings. It is a laminated silicon-steel core with slots, wound with enamelled copper, mounted on the shaft. The laminations exist for the same reason as in any AC machine: a solid iron core would let eddy currents circulate and waste power as heat. Because the windings spin, the armature also carries its own heat, and getting that heat out through the air gap and the shaft is harder than cooling a stationary stator. This is one reason brushed motors are thermally limited more tightly than their brushless cousins, which put the copper on the outside.

Commutator

The commutator is the segmented copper cylinder on the shaft, one segment per armature coil connection. Its surface must stay smooth and concentric; as it wears it develops grooves and a "patina" of transferred brush material. A healthy commutator has an even dark film. Ridging, burning, or a visible spark ring means trouble. The gaps between segments (the mica insulation) are where the brush momentarily shorts and sparks during the switch, and that spark is both the noise source and the erosion source.

Brushes

The brushes are the sliding contacts. Cheap motors use a folded copper or bronze leaf (a "metal brush", common in tiny toy and pager motors); serious motors use carbon-graphite blocks pushed by a spring. Graphite is chosen because it is a decent conductor, self-lubricating, and forms a protective film on the copper. Brush pressure is a compromise: too light and the contact arcs and bounces, too heavy and the brush and commutator wear fast from friction. The brushes are the designed wear item. In a rebuildable motor they are a replaceable part behind a cap; in a sealed motor they set the motor's life.

Field (stator)

The stationary field supplies the magnetic flux the armature current pushes against. In a permanent-magnet DC motor (PMDC), the field is a pair of curved ferrite or neodymium magnets bonded inside the steel housing, and that steel housing doubles as the magnetic return path (the "back iron"). In a wound-field motor, the field is an electromagnet, a second winding, which opens up series, shunt, and compound configurations with different torque-speed characters. Most robotics-scale brushed motors are PMDC because permanent magnets are simpler, more efficient, and cheaper at small sizes.

War story: A team built a small inspection rover on cheap 6 V gearmotors and could not work out why two of six motors kept dying after a few hours while the others were fine. The dead ones were the two driving the front wheels, which carried more load on inclines and ran hotter. Heat had softened the commutator's brush film and accelerated brush wear; by the time the brushes were half gone the sparking got worse, which eroded the commutator faster, a runaway. The fix was gearing the drive so no motor ran near stall on the worst grade, plus a current limit in firmware. Brush motors punish sustained high load far more than an occasional peak.

The governing equations

A brushed DC motor obeys two equations that between them explain everything it does. They are worth carrying in your head.

The voltage equation

The applied voltage splits between the resistive drop across the windings and the back-EMF the spinning motor generates:

V  =  I·R  +  Ke·ω

Here V is terminal voltage, I is armature current, R is winding resistance, ω is shaft speed in rad/s, and Ke is the back-EMF constant in V·s/rad. Back-EMF is the voltage a spinning motor makes on its own terminals; it opposes the applied voltage, and it is why current (and therefore torque) falls as the motor speeds up. At standstill ω = 0, back-EMF is zero, and the only thing limiting current is R.

The torque equation

Torque is proportional to armature current:

τ  =  Kt·I

Kt is the torque constant in N·m/A. And here is the identity every motor engineer should know: in SI units Kt = Ke. They are the same physical constant, one seen from the mechanical side and one from the electrical side. It falls out of energy conservation in one line. The electrical power delivered to the back-EMF must equal the mechanical power at the shaft:

P_elec  =  P_mech
(Ke·ω)·I  =  τ·ω  =  (Kt·I)·ω
⇒  Ke = Kt        (V·s/rad  ≡  N·m/A)

Cancel the common ω·I and the two constants must be numerically equal. If a datasheet lists them with different SI numbers, someone has a unit slip hiding in it (usually Ke quoted per 1000 RPM rather than per rad/s). Datasheets sometimes give the speed constant Kv in RPM/V instead, in which case:

Kt [N·m/A]  =  9.549 / Kv [RPM/V]
Ke [V·s/rad]  =  Kt [N·m/A]

What the constants let you compute

With R, Kt (= Ke), and V, you have the whole machine. Substitute τ = Kt·I into the voltage equation and solve for speed:

ω  =  (V − I·R) / Ke
   =  V/Ke  −  (R / (Kt·Ke)) · τ

The first term V/Ke is the no-load speed (call it ω_0, the speed at which back-EMF equals the supply and current stops). The second term is the linear droop with torque. Everything follows from these three measurables.

The torque-speed curve and operating point

Plot speed against torque at a fixed voltage and you get a straight line. This is the single most useful picture of a brushed DC motor.

ω  =  ω_0  −  (R / (Kt·Ke)) · τ

At the top-left the motor spins at no-load speed ω_0 = V/Ke, drawing only the small no-load current I_0 needed to overcome bearing friction and windage. At the bottom-right it stalls: speed zero, torque at its maximum, current at V/R. Between those two corners the line is straight, and the motor can sit anywhere on it depending on the load.

Three quantities live on this line:

no-load speed:   ω_0     =  V / Ke
stall torque:    τ_stall =  Kt · (V/R)
stall current:   I_stall =  V / R

Mechanical output power is τ·ω, a downward parabola that is zero at both corners (no torque at no load, no speed at stall) and peaks in the middle, at roughly half the no-load speed and half the stall torque:

P_mech,max  ≈  (τ_stall · ω_0) / 4     (at ω_0/2, τ_stall/2)

Efficiency, though, peaks somewhere else entirely, up near no-load speed, at a small fraction of stall torque, typically 10 to 30% of stall. That is because copper loss is I²R and grows with the square of torque, so the most efficient operating point is at low current, well away from where the motor makes peak power. A well-matched brushed motor runs 70 to 85% efficient at its best point; the same motor near stall might be under 40%.

The trap for beginners: the torque-speed line is the motor's electromagnetic capability, not its safe operating envelope. The line says the motor can make τ_stall of torque at zero speed. The thermal reality says it can only do that for a second or two before the windings cook, because at stall the current is V/R and every watt of I²R goes straight into heat with no mechanical output to carry it away. Your usable continuous operating point sits far up and to the left of stall.

Rule of thumb: a brushed motor's happy place is near its maximum-efficiency point, roughly 10 to 30% of stall torque and 70 to 90% of no-load speed. Gear your mechanism so the motor lives there under normal load, and keep stall as a rare, brief, current-limited event.

PWM speed control and the H-bridge

You control a brushed motor's speed by controlling its average voltage, and the efficient way to do that is pulse-width modulation (PWM): switch the full supply voltage on and off fast, and vary the fraction of time it is on (the duty cycle). Because the motor's inductance and mechanical inertia both act as low-pass filters, the motor responds to the average, not the individual pulses.

V_avg  =  D · V_supply        (D = duty cycle, 0 to 1)

A 50% duty cycle on a 12 V supply behaves roughly like 6 V. PWM is efficient because the switch is either fully on (low voltage drop, low loss) or fully off (no current, no loss), so it wastes little compared to a series resistor dropping the same voltage as heat.

PWM frequency matters. Too low (say below a few hundred Hz) and you hear it as an audible whine and the current ripples badly. Too high and switching losses in the transistors climb. A common range for small robot motors is 16 to 25 kHz, above human hearing and gentle on the switches. The motor's electrical time constant L/R sets how much the current ripples at a given frequency; low-inductance motors (coreless especially) need higher PWM frequencies to keep ripple sane.

The H-bridge

To reverse a motor you must reverse the current, which means swapping which terminal is positive. The H-bridge does this with four switches (MOSFETs) arranged in an H around the motor:

        +V
        |
   [Q1]   [Q3]
     |      |
     A------B        (motor connects A to B)
     |      |
   [Q2]   [Q4]
        |
       GND

• Close Q1 and Q4: current flows A to B, motor turns one way.
• Close Q3 and Q2: current flows B to A, motor turns the other way.
• Never close Q1 and Q2 (or Q3 and Q4) at once: that is "shoot-through", a dead short across the supply that destroys the transistors. Real drivers insert a small "dead time" between switching to prevent it.

PWM is applied to the active switches to set speed while the bridge sets direction. When the switches open, the motor's inductance still wants to push current, and that current flows through freewheel diodes (the MOSFET body diodes or added Schottkys) back into the supply or around a low-side loop. This is also how you get braking: short both motor terminals together (both low-side switches on) and the motor's own back-EMF drives a current that opposes its motion, dumping the rotor's kinetic energy as heat in the windings. That is "dynamic braking", distinct from just letting it coast.

Ready-made driver chips and modules cover most robotics needs: the classic L298 (dual bridge, lossy bipolar, fine for hobby), the DRV8871 and TB6612 (efficient MOSFET drivers for small motors), the VNH5019 and BTS7960 (tens of amps for combat and drive robots), and Pololu and Cytron carrier boards that package them with protection. For anything past a few amps, pick a driver rated well above your motor's stall current, because a stalled motor pulls V/R and the bridge sees all of it.

Rule of thumb: size the H-bridge for the stall current V/R, not the running current. A motor that draws 2 A moving can pull 20 A stalled, and the moment it jams against a wall your undersized driver is the part that dies.

Motor types: PMDC, wound-field, coreless, gearmotors

"Brushed DC motor" covers a family with meaningfully different characters. Here are the ones that show up in robotics.

Permanent-magnet DC (PMDC)

The default. Field supplied by permanent magnets, windings on an iron-core armature. Simple, efficient at small sizes, linear torque-speed line, cheap. This is what almost every hobby gearmotor and small robot drive uses. Magnet choice (ferrite vs neodymium) trades cost against torque density; neodymium PMDC motors pack more torque into a smaller can but cost more and demagnetize if overheated.

Wound-field (series, shunt, compound)

The field is an electromagnet instead of a magnet. The winding connection sets the character:

• Series: field winding carries the armature current. Enormous starting torque, but speed runs away at no load (a fully unloaded series motor can overspeed and destroy itself). This is the classic starter-motor and traction-motor topology.
• Shunt: field across the supply, nearly constant flux, nearly constant speed under varying load. Well-behaved.
• Compound: both, blending series torque with shunt speed regulation.

Wound-field motors are rare below a few hundred watts because permanent magnets are simpler and more efficient at that scale. You mostly meet them in large traction and industrial legacy equipment.

Coreless (ironless) DC

The armature winding is a self-supporting basket of copper with no iron core; the magnet sits inside it. Consequences: zero cogging (nothing for the magnet to detent against), very low inductance and rotor inertia, and a very fast electrical and mechanical response. The efficiency is high and the low-speed smoothness excellent. The cost is money (Maxon, Faulhaber, Portescap territory) and fragility, the delicate winding is easy to overheat because it has little thermal mass, and stall can destroy it in a fraction of a second. Coreless motors run cameras, surgical tools, prosthetics, and precision haptics.

Gearmotors

Any of the above with an integrated gearbox (spur, planetary, or worm) on the output. This is how brushed motors actually appear in most robots, because a bare small DC motor spins too fast (thousands of RPM) and makes too little torque to be useful directly. The gearbox trades speed for torque by the ratio N and reflects load inertia back by N². A worm gearbox additionally offers self-locking (it holds position unpowered) at the cost of efficiency. Pololu's micro-metal and 37D gearmotors, and Pittman and Maxon geared units, are the workhorses here.

Type	Cogging	Cost	Efficiency	Robotics use
PMDC (iron core)	Moderate	$	70-85%	Drive wheels, hobby, general
Wound-field series	Moderate	$$	75-85%	Traction, big legacy drives
Coreless	None	$$$$	85-90%	Cameras, medical, haptics, prosthetics
Gearmotor (any)	Inherits motor	$ to $$$	Motor × gear (60-85%)	Most robot drives and joints

Brushed vs brushless: the honest tradeoff

The question is which one fits the job. Here is the fair comparison. For the full brushless treatment see the BLDC guide.

Property	Brushed DC	Brushless (BLDC/PMSM)
Commutation	Mechanical (brushes)	Electronic (ESC / FOC drive)
Controller to run	Battery + switch, or H-bridge	Three half-bridges + firmware
Drive cost	Very low	Higher (but falling every year)
Wear item	Brushes + commutator	Bearings only
Lifetime	Hundreds to few thousand hours	Tens of thousands of hours
Peak efficiency	70-85%	80-94%
Power density	Moderate	High
EMI / sparking	Sparks, noisy	Clean
Torque at zero speed	Yes (stalls hot)	Yes, if sensored (FOC)
Cost at the motor	Very low	Higher

Where brushed still wins:

• Total system cost. A brushed gearmotor plus a $2 H-bridge undercuts a brushless motor plus its FOC drive by a wide margin. On a bill of materials for a cost-sensitive product or a classroom robot, this is decisive.
• Drive simplicity. No rotor-angle sensing, no phase current sensing, no commutation firmware. You can drive a brushed motor with an Arduino pin and a transistor. Getting a brushless motor to hold torque at zero speed needs an encoder and FOC.
• Low duty cycle. If the motor runs a few minutes a day (a gate, a deployable arm, a dispenser), brush wear never becomes the limiting factor, and the lifetime advantage of brushless is wasted.
• Simple bidirectional torque at standstill. A brushed motor holds torque at zero speed with a plain H-bridge and no feedback at all. A brushless motor needs sensored FOC to do the same.

Where brushed loses: sustained high-duty operation, anything needing top efficiency and power density, clean-EMI or vacuum or flammable environments (the sparking is a hard no), and long unattended service life. That covers most serious drone, legged, and industrial-arm actuation, which is exactly where brushless has taken over.

Rule of thumb: below roughly 100 W, intermittent duty, cost-driven, brushed usually wins. Continuous duty, high efficiency, long life, or a joint that must be finely torque-controlled, brushless wins. The crossover has been sliding toward brushless for years as FOC drive chips get cheaper.

Brush wear, arcing and motor life

The brushes are the whole life story of a brushed motor. They wear from two mechanisms: mechanical abrasion (the brush sliding on the commutator) and electrical erosion (the spark that jumps the commutator gap during each switch). Both eat brush and commutator material, and they feed each other, worn geometry sparks more, and more sparking erodes faster.

Brush life ranges widely:

• Cheap metal-brush toy and pager motors: tens to a few hundred hours.
• Mid-grade graphite-brush gearmotors: several hundred to ~2000 hours of running time.
• Premium motors with good brush grades and clean commutation: a few thousand hours, occasionally more, with rebuildable brushes extending it.

Several things shorten brush life, most of them within your control:

• High current. Erosion scales with the current the brush switches and the energy in each spark. Running near stall or continuously at high load burns brushes fast.
• Sparking from inductive kick. Each coil the commutator switches off dumps its stored magnetic energy as a spark. This is why many motors have a small capacitor across the terminals (and sometimes ferrite beads or a cap from each terminal to the case): it absorbs the spike, cuts the arc, and reduces both wear and EMI. Add these caps if the motor did not ship with them.
• Overspeed and vibration. Brush bounce at high RPM breaks contact and arcs across the gap.
• Contamination and heat. Dust, oil mist, and high temperature degrade the protective brush film on the commutator, after which wear accelerates.

The arcing is also an EMI source. A brushed motor is a broadband noise generator that can upset nearby radio, sensors, and microcontrollers. Suppression capacitors, twisted and shielded motor leads, and keeping motor wiring away from signal wiring are the standard mitigations. See the robot wiring, cables and connectors guide for layout practice.

Signs a motor is near end of life: rising no-load current (friction from worn brushes and a dirty commutator), visible sparking through the vents, a burnt smell, audible roughness, and eventually intermittent contact. On a rebuildable motor, replacing brushes and cleaning the commutator restores it. On a sealed motor, that is the end.

Rule of thumb: if your motor did not ship with terminal suppression capacitors, add one 0.1 uF ceramic across the terminals (rated well above supply voltage) and consider two more from each terminal to the case. It costs cents, cuts EMI, and measurably extends brush life.

Thermal limits and stall

Like every electric motor, a brushed motor's continuous rating is a heat limit, not a magnetic one. The windings dissipate I²R, that heat has to escape through the armature, across the air gap, and out the housing, and the winding insulation and the magnets set a temperature ceiling.

T_winding  ≈  T_ambient  +  P_loss · R_th
P_loss     ≈  I²·R   (+ brush friction, iron, and windage losses)

R_th is the thermal resistance from winding to ambient in K/W. The continuous current rating is simply the current at which the winding settles at its insulation limit (often 100 to 155 °C, IEC insulation classes) given R_th and ambient. Brushed motors tend to run hotter for a given output than brushless of the same size because the heat-making copper is on the spinning inside, harder to cool, and because brush friction adds its own heat.

The transient behaviour is a first-order lag with thermal time constant τ_th = R_th · C_th (thermal resistance times thermal mass):

ΔT(t)  =  P_loss · R_th · (1 − e^(−t/τ_th))

A tiny coreless motor has a τ_th of a second or two, so it reaches steady temperature almost instantly and has almost no thermal reserve. A big iron-core motor takes minutes, giving it a thermal buffer to swallow acceleration transients. Size to the RMS current over the duty cycle, not the peak, because ΔT responds to mean I²:

I_rms  =  sqrt( mean( I(t)² ) )   over the motion cycle
# keep I_rms <= I_continuous, even if brief peaks go higher

Stall is the killer

Stall deserves its own warning because it is the most common way people destroy brushed motors. At stall the back-EMF is zero, so nothing limits current except the winding resistance:

I_stall  =  V / R

For a 12 V motor with R = 0.5 Ω, that is 24 A, all of it turning into heat in the windings with zero mechanical output to carry any of it away. A small motor sized for 2 A continuous will overheat in seconds at 24 A. Worse, stall is where torque is maximum and speed is zero, so a robot that drives into a wall, or an arm that hits its end stop, sits at full stall current until something gives. The brushes carry that full current at one spot on the commutator (the rotor is not turning), which pits and burns that spot.

Mitigations: current-limit in the driver or firmware, detect stall (current spike with no motion) and back off, gear the mechanism so the worst normal load stays well below stall, and add a thermal fuse or PTC on motors that could stall unattended. A servo, which is a brushed (or brushless) motor plus a controller and feedback, includes stall protection as part of the package; a bare motor does not.

Rule of thumb: assume every brushed motor in your robot will get stalled at some point, by a jam, a wall, or a bug in your code. Design the driver and the firmware so a stall is a survivable event (current-limited, timed out) rather than a fatal one.

Sizing a brushed motor: a worked example

Take a small differential-drive rover. Target: 3 kg robot, two driven wheels of 60 mm radius, cruise at 0.5 m/s, and it must climb a 15° ramp. Do the sizing in order.

1. Load torque and speed at the wheel

Climbing the ramp, the driving force per wheel must overcome the gravity component. Total gravity force along the incline:

F_incline  =  m·g·sin(15°)  =  3 · 9.81 · 0.259  ≈  7.6 N

Split over two wheels, plus a rolling-resistance and margin allowance, call it ~5 N per wheel. Torque at each wheel:

τ_wheel  =  F_wheel · r  =  5 · 0.060  =  0.30 N·m

Wheel speed at 0.5 m/s:

ω_wheel  =  v / r  =  0.5 / 0.060  =  8.3 rad/s  ≈  80 RPM

2. Choose a gear ratio

A bare small DC motor spins ~6000 to 10000 RPM and makes only a few mN·m directly, so it needs reduction. To turn ~80 RPM at the wheel from a motor that likes to run near ~5000 RPM at its efficient point, pick a ratio around:

N  =  ω_motor / ω_wheel  ≈  5000 / 80  ≈  60:1

A 50:1 or 63:1 metal-gearmotor is a standard off-the-shelf choice. The gearbox multiplies torque and (at, say, 70% gear efficiency) the motor must supply:

τ_motor  =  τ_wheel / (N · η_gear)  =  0.30 / (60 · 0.70)  ≈  0.0071 N·m  ≈  7.1 mN·m

3. Convert torque to current with Kt

Suppose the candidate motor (a 12 V PMDC) has Kt ≈ 9.549 / Kv with Kv ≈ 900 RPM/V, giving Kt ≈ 0.0106 N·m/A. Current to make 7.1 mN·m:

I  =  τ_motor / Kt  =  0.0071 / 0.0106  ≈  0.67 A

That is the current to climb the ramp at speed, the continuous worst case. Check it against the motor's continuous rating: a small 12 V metal-gearmotor rated ~1.5 to 2 A continuous handles 0.67 A with comfortable margin. Good.

4. Check no-load speed and cruise

No-load speed of the motor: ω_0 = Kv · V ≈ 900 · 12 = 10800 RPM. After the 60:1 gearbox that is 180 RPM at the wheel unloaded, dropping under load toward the 80 RPM cruise point. Because cruise sits well below no-load, the motor runs in the efficient upper-left region of its torque-speed line, exactly where you want it.

5. Check stall current for the driver

Suppose the motor's winding resistance is R ≈ 3 Ω. Stall current:

I_stall  =  V / R  =  12 / 3  =  4 A per motor

Two motors could momentarily pull 8 A total. Pick an H-bridge rated comfortably above 4 A per channel (a TB6612 at ~1.2 A continuous is too small; a DRV8871 at ~3.6 A peak or a BTS7960 module is safer), and current-limit in firmware so a wall-jam does not sit at 4 A indefinitely. Size the battery leads and fuse for the stall case, not the cruise case.

6. Thermal sanity check

At 0.67 A the copper loss is I²R ≈ 0.67² · 3 ≈ 1.3 W per motor, easily dissipated by a metal-gearmotor can. At the 4 A stall it is 4² · 3 ≈ 48 W into a small motor, which is why stall must be brief and current-limited. The RMS current over a mixed drive-and-turn cycle stays near or below the ~0.7 A climbing figure, so continuous thermal margin is fine.

That is the whole method: load torque and speed at the output, pick a ratio, reflect to the motor, convert torque to current with Kt, check current against the continuous (thermal) rating, then check stall current against the driver and wiring. Leave 20 to 30% margin everywhere.

Rule of thumb: the number that sizes the driver and the battery leads is stall current V/R, and the number that sizes the motor is the continuous (RMS) current your load demands. Confusing the two either burns the driver or oversizes the motor.

How to choose

A short decision path for reaching for brushed DC and picking the right one.

1. Should it be brushed at all? If duty is intermittent, cost is tight, and lifetime past a few thousand hours does not matter, yes. If it runs continuously, needs top efficiency, must be finely torque-controlled at zero speed, or lives somewhere sparks are unwelcome, look at brushless or a servo/stepper instead.
2. Bare motor or gearmotor? Almost always a gearmotor. Compute the ratio from your output speed and torque as in the worked example. Consider a worm gearbox if you need it to hold position unpowered.
3. Voltage. Match your battery bus (6 V, 12 V, 24 V common). Higher voltage means lower current for the same power, thinner wires, and less I²R loss, at the cost of pricier switches.
4. Kt / Kv. Pick so no-load speed after the gearbox is comfortably above your cruise speed, and the current to make your load torque (I = τ/Kt) stays well under the continuous rating.
5. Iron-core or coreless? Iron-core for drive wheels, general mechanisms, and anything cost-sensitive or stall-prone. Coreless only when you need zero cogging, fast response, and smooth low-speed motion (cameras, medical, haptics), and can protect it from stall.
6. Driver. H-bridge rated above stall current V/R, with current limiting, and dead-time protection against shoot-through. Add terminal suppression capacitors for EMI and brush life.
7. Protection. Assume stall will happen. Add current limiting, stall detection, and where a jam could go unattended, a thermal fuse or PTC.

Frequently asked questions

Why does a brushed motor need brushes at all? To keep the torque pointing the same way as the rotor turns. Without commutation, current in the armature coil would reverse its torque every half turn and the motor would oscillate instead of spin. The brushes and segmented commutator mechanically reverse the coil current at the right instant so torque stays unidirectional. Brushless motors do the same job electronically in a controller, which is why they need no brushes.

What is the single most important number for sizing? Two, really. The continuous (thermal) current limit sizes the motor: convert your load torque to current with I = τ/Kt and keep it under that limit. The stall current V/R sizes the driver, the wiring, and the fuse, because a jammed motor pulls that full current with nothing to limit it but winding resistance.

Is Kt really equal to Ke? Yes, in SI units they are numerically identical, because both come from the same electromagnetic coupling. It falls out of energy conservation: the electrical power into the back-EMF equals the mechanical power at the shaft, (Ke·ω)·I = (Kt·I)·ω, and cancelling ω·I leaves Ke = Kt. If a datasheet shows different numbers, one of them is in mixed units (often Ke per 1000 RPM rather than per rad/s).

Why does the motor slow down when I load it? Because torque needs current, and current needs voltage headroom. From V = I·R + Ke·ω, more torque means more current means a bigger I·R drop, which leaves less voltage for back-EMF Ke·ω, so ω falls. The relationship is linear: speed droops in a straight line from no-load down to stall as torque rises.

Why is stalling so damaging? At stall the back-EMF is zero, so current is limited only by winding resistance: I = V/R, often ten times the running current. All that current becomes I²R heat in the windings with no mechanical output to carry energy away, and the brushes carry it at one fixed spot on the commutator, pitting and burning it. Small motors can overheat in seconds. Always current-limit and detect stall.

Can I control speed just by lowering the voltage? You can, but a series resistor wastes the dropped voltage as heat and gives poor speed regulation under changing load. PWM through an H-bridge is far better: it switches the full voltage on and off fast so the transistor is either fully on or fully off, wasting little, and the motor responds to the average. PWM also gives you direction and braking with the same four switches.

Why does my brushed motor make so much electrical noise? The brush-commutator contact sparks every time it switches a coil, and that spark is a broadband EMI source. It can disturb nearby radios, sensors, and microcontrollers. Fit suppression capacitors across the terminals (and from each terminal to the case), twist and shield the motor leads, and route motor wiring away from signal wiring. These same capacitors also extend brush life by softening the arc.

When is a coreless motor worth the money? When you need zero cogging, very fast response, and smooth motion at low speed, and you can protect the delicate winding from stall. Cameras, surgical and dental tools, prosthetics, and precision haptics use coreless motors for exactly these reasons. For a drive wheel or a cost-sensitive mechanism that might jam, an iron-core PMDC is cheaper and far more robust.

How long do brushed motors last? Brush wear sets the life, from tens of hours for cheap metal-brush toy motors to a few thousand hours for quality graphite-brush motors, occasionally more with rebuildable brushes. High current, sparking, heat, and overspeed all shorten it. Brushless motors, limited only by bearings, run tens of thousands of hours, which is why continuous high-duty applications have moved to brushless.

Do brushed motors still make sense in 2026? For the right jobs, absolutely. Cost-sensitive, intermittent-duty, simple-drive applications (hobby rovers, educational robots, actuated mechanisms, haptics, and combat robots repurposing cheap high-torque automotive motors) still default to brushed DC because a brushed gearmotor plus an H-bridge is the cheapest controllable, reversible rotary actuator you can buy. The high-performance end of robotics has moved to brushless, and the crossover keeps sliding as FOC drive chips get cheaper.