A DC motor does not produce the same torque at every speed, so robot designers use a torque-speed curve to predict how the motor will behave under load. The curve shows the tradeoff between torque and rotational speed, from maximum torque at zero speed to maximum speed at nearly zero torque. This matters in robotics because wheels, arms, lifts, and grippers must accelerate loads without overheating or stalling.
Reading the curve helps you choose a motor and gear ratio that can do the job safely.
For an ideal DC motor at fixed voltage, torque decreases roughly linearly as speed increases. Mechanical power is P = τω, so power is zero at stall, zero at free speed, and highest near half the stall torque and half the free speed. A load line or required operating point can be placed on the graph to check whether the motor can supply enough torque at the needed speed.
Good motor sizing keeps the normal operating point below continuous torque limits, not at stall torque.
Understanding Robotics: Stall Torque and Torque-Speed Curve
Inside a brushed DC motor, the spinning rotor creates a voltage that opposes the battery voltage. This opposing voltage is called back electromotive force. At low speed, back electromotive force is small, so a large current can flow through the windings.
Current creates the magnetic force that turns the shaft. As the motor speeds up, the opposing voltage grows. Less current flows, so the available turning force falls.
This electrical process is the reason the performance curve has its familiar slope. It is not simply a graph to memorize. It describes the changing balance between battery voltage, motor current, magnetic force, and rotation.
A robot rarely runs at one steady speed from the moment it starts. When a wheel begins moving, the motor must accelerate the wheel, gearbox, robot mass, and anything the robot carries. A lift must first overcome gravity.
An arm must overcome gravity differently at each angle. Friction in bearings, belts, gears, and wheel contact adds more required torque. The motor settles at the speed where its available torque matches the load torque.
If the load needs more torque than the motor can provide at every speed, the shaft stops. This is a stall. A stalled robot may look harmless, but the motor can still pull very high current from the battery.
Gears change what the motor shaft experiences. A reduction lets the motor spin faster while the output turns more slowly. This is useful because a motor often works more efficiently away from very low speed.
For a drive train, extra reduction can improve pushing force and acceleration, but it reduces top speed. Too little reduction can make the robot feel fast with its wheels off the ground, yet weak when placed on the floor.
For a lifting mechanism, designers calculate the torque needed at the output shaft, then work backward through the gear ratio while allowing for friction and gearbox losses. Larger wheels need more wheel torque to produce the same ground force, so wheel size matters as much as motor choice.
The curve is usually measured at a stated voltage, so battery condition matters. A battery voltage can drop when several motors draw current together. Wiring, connectors, motor controllers, and batteries all have some resistance.
Their voltage losses reduce motor speed and available torque during hard acceleration. Heat is another limit. Motor winding resistance turns electrical energy into heat, especially when current is high.
Short bursts near the high torque end may be acceptable, while holding that load for a long time may damage the motor. When reading a graph, check the voltage, whether ratings are continuous or brief peaks, the gearbox efficiency, and the units used for torque and speed. Treat a calculated operating point as an estimate, then test the real robot under its heaviest expected load.
Key Facts
- Mechanical power is P = τω, where τ is torque in N·m and ω is angular speed in rad/s.
- For an ideal DC motor, τ = τ_stall(1 − ω/ω_free) at a fixed supply voltage.
- Stall torque τ_stall is the maximum torque at ω = 0, but the motor draws maximum current and can overheat quickly.
- Free speed ω_free is the no-load speed where torque is approximately zero.
- Peak mechanical power occurs near τ = τ_stall/2 and ω = ω_free/2 for an ideal linear torque-speed curve.
- Gear reduction increases output torque and decreases output speed: τ_out ≈ ηGτ_motor and ω_out ≈ ω_motor/G.
Vocabulary
- Stall torque
- The maximum torque a motor can produce when its shaft is not rotating.
- Free speed
- The speed of a motor when it spins with no external load and produces almost no torque.
- Torque-speed curve
- A graph showing how the available torque of a motor changes as its rotational speed changes.
- Peak power point
- The operating point where the product of torque and angular speed is greatest.
- Gear ratio
- The ratio that compares motor shaft speed to output shaft speed and determines how speed is traded for torque.
Common Mistakes to Avoid
- Using stall torque as the normal operating torque, which is wrong because stall conditions draw very high current and can overheat or damage the motor.
- Ignoring units for speed, which is wrong because RPM must be converted to rad/s before using P = τω in watts.
- Assuming maximum torque and maximum speed happen at the same time, which is wrong because a DC motor’s torque decreases as speed increases.
- Forgetting gearbox efficiency, which is wrong because real gears lose energy to friction, so output torque is less than the ideal gear ratio prediction.
Practice Questions
- 1 A motor has τ_stall = 2.4 N·m and ω_free = 6000 RPM. Assuming a linear torque-speed curve, what torque is available at 3000 RPM?
- 2 A motor operates at τ = 0.80 N·m and 150 rad/s. What mechanical power does it deliver in watts?
- 3 A robot arm needs high torque at low speed to lift a load. Explain whether a high gear reduction, a low gear reduction, or no gearbox is most appropriate, and describe the tradeoff.