Force, Torque, Speed, and Power
Actuator sizing starts with force, torque, speed, and power. If these are wrong, no amount of firmware tuning can make the machine behave correctly.
Learning Objectives
By the end of this lesson, you should be able to:
- convert between force and torque using radius;
- calculate mechanical power;
- distinguish speed requirement from torque requirement;
- include efficiency and safety margin;
- identify common sizing errors.
Force and Torque
Torque is rotational force at a distance:
$$
\tau = F r
$$
where tau is torque in N m, F is force in N, and r is radius in m.
A belt pulley with radius 20 mm that must pull 50 N needs:
$$
\tau = 50\ N \times 0.020\ m = 1.0\ N m
$$
Speed and Power
Linear mechanical power:
$$
P = Fv
$$
Rotational mechanical power:
$$
P = \tau\omega
$$
Convert RPM to rad/s:
$$
\omega = \frac{2\pi \times RPM}{60}
$$
Worked Example
A wheel needs 1.2 N m at 300 RPM.
$$
\omega = \frac{2\pi\times300}{60}=31.4\ rad/s
$$
$$
P = 1.2\times31.4=37.7\ W
$$
If drivetrain efficiency is 70%:
$$
P_\text{motor} = \frac{37.7}{0.70}=53.9\ W
$$
Choose a motor and driver with margin above this value.
Torque-Speed Curves
Motors do not deliver maximum torque at every speed. DC motors have high stall torque and decreasing torque with speed. Steppers lose torque rapidly at high speed. Servos have rated speed-torque envelopes.
Common Mistakes
- Confusing torque with power.
- Selecting by stall torque without checking operating speed.
- Ignoring acceleration.
- Forgetting gearbox efficiency.
- Running a motor continuously at a short-time rating.
Summary
Force and torque create motion; speed determines how fast work happens; power combines effort and speed. Good sizing uses worst-case load, motion profile, efficiency, duty cycle, and thermal limits.
Further Reading
- Maxon and Portescap motor-selection guides.
- Oriental Motor motor sizing basics.
- Machine Design torque, speed, and power tutorials.