Start with what you need the joint to do
You’re sizing a motor for a robot joint or rotary stage, so begin with the motion profile you actually want: how fast, how quickly it accelerates, how long it holds position. If you’re looking at a frameless torque motor, these numbers matter more than the marketing copy. I’ve seen engineers validate their numbers at Automatica in Munich and then walk back to the bench with practical questions — that’s what this guide answers for you.
The core formula: inertia times acceleration, plus load
Calculate the torque required for motion with one clear equation: T_required = I_equiv * alpha + T_external. I_equiv is the motor-reflected inertia (kg·m²), alpha is angular acceleration (rad/s²), and T_external covers gravity, friction, or payload torques. Convert RPM to angular velocity with ω = 2π·RPM/60 and remember alpha often comes from how quickly you need to reach a certain angle: for constant acceleration from rest to sweep θ in time t, alpha ≈ 2·θ / t².
Step-by-step sizing you can copy
Do this in order so you don’t miss anything:- Estimate inertia of each rotating element. For a point mass at radius r: I = m·r². For a thin rod about one end, use its standard inertia or approximate as distributed mass.- Sum inertias and reflect any gearbox ratio squared: I_reflected = I_total / (gear_ratio)² if you have gearing.- Decide the motion: angle or speed and the time to achieve it. Compute alpha.- Compute T_inertia = I_reflected · alpha.- Add T_external (gravity: m·g·r for a horizontal link; friction/torque from bearings).- Add a safety margin — typically 1.2–2× depending on how aggressive the duty cycle and unknowns are.Keep units consistent: mass in kg, radius in meters, torque in N·m.
Concrete example you can follow
Say you have a 3 kg link with its mass effectively at 0.2 m from the joint. I ≈ 3·0.2² = 0.12 kg·m². You need a 90° move (π/2 rad) in 0.2 s. Alpha ≈ 2·(π/2) / 0.2² ≈ 78.5 rad/s². T_inertia = 0.12·78.5 ≈ 9.4 N·m. If gravity adds m·g·r = 3·9.81·0.2 ≈ 5.9 N·m, total = 15.3 N·m. Apply a safety factor of 1.5 → spec ~23 N·m. If you use a 5:1 gearbox, the motor needs ~4.6 N·m continuous (but the gearbox must handle peak and shock loads).
Continuous vs peak torque and thermal limits
Don’t confuse peak torque with what the motor can sustain. Continuous (RMS) torque depends on heating and duty cycle. If your motion has long holds or repeated cycles, size for continuous torque first and check that the motor’s peak torque covers short bursts. Look at duty cycle: higher duty cycles mean you need a larger continuous rating. If you’re unsure, size up rather than rely on a margin that’s too tight.
Common mistakes people make
Watch out for these: ignoring reflected inertia from couplings, using the wrong inertia formula for your geometry, forgetting gearbox efficiency and backlash, mixing units (rpm vs rad/s), and skipping thermal/continuous checks. Also don’t assume zero friction — bearings and seals add torque, especially at low speeds.
Quick practical checklist before you buy
– Confirm I_total and reflect through any gear ratio. – Calculate alpha from your real motion timings. – Sum inertial torque and external torques. – Compare required peak and RMS torques to motor specs, including thermal time constants. – Apply a safety factor based on unknowns (1.2–2). – Verify encoder and mounting stiffness support the application. If you want supplier data sheets and spec comparisons, check a reliable frameless torque motor manufacturer for torque curves and thermal ratings.
Final note — practical sizing that gets you on the bench faster
Do the arithmetic, sanity-check with a simple bench test, and pick a motor whose continuous and peak numbers both clear your worst-case profile. If you keep the calculations transparent and double-check inertia and time constants, you’ll avoid surprises when the assembly goes live — that’s how I end up returning to manufacturers like Kinco for detailed curves and mounting specs without wasting hours guessing.