Start with what you bring to the kitchen
Tell me the payload, the robot’s empty mass, the peak speed you want and how long the robot runs before a breather — those are the primary flavors. If you need tight, repeatable motion for assembly or pick-and-place, consider an ac servo drive early in the ingredient list so you don’t overspec mechanical parts later. I build these calculations around your inputs so the result fits your use case, not some textbook ideal.
Essential inputs (your mise en place)
Collect these values before any math:• Total mass (robot + payload) in kilograms. • Desired peak linear speed (m/s) and peak acceleration (m/s²). • Wheel radius or track configuration (m). • Maximum incline or grade to overcome (degrees). • Duty cycle: minutes per hour of active motion. • Expected gearbox ratio and drivetrain efficiency (decimal). • Environment notes: continuous operation in dusty factory, long runs, or frequent stops. These make the formulas feed you usable numbers instead of guesses.
The cook’s math — basic formulas that actually work
Use these steps to turn inputs into required torque and power. Keep units consistent.1) Longitudinal force for acceleration: F_acc = m × a. 2) Grade force: F_grade = m × g × sin(θ) (θ in radians; g = 9.81 m/s²). 3) Total tractive force: F_total = F_acc + F_grade + rolling-resistance (if needed). 4) Wheel torque: τ_wheel = F_total × r_wheel. 5) Motor torque demand = τ_wheel / (gear_ratio × efficiency). 6) Mechanical power at wheel: P = F_total × v (watts). 7) Motor electrical power = P / motor_efficiency (pick a realistic efficiency, e.g., 0.85).Example (practical): total mass 50 kg (40 kg robot + 10 kg payload), a = 0.5 m/s², v_max = 1.2 m/s, wheel radius = 0.05 m, flat ground (θ=0). F_acc = 50 × 0.5 = 25 N. F_grade = 0. Total F_total = 25 N. τ_wheel = 25 × 0.05 = 1.25 N·m. If you drive two wheels, split that per driven wheel. Power at v_max = 25 × 1.2 = 30 W. After gearbox and 80% drivetrain efficiency, motor torque and power numbers rise — always size margin for control peak torque and stall conditions.
Choosing the motor and drive
Match torque and power needs to motor continuous and peak ratings, then check the drive’s current limits and bandwidth. For industrial applications where closed-loop stiffness and quick settling matter, an industrial servo drive often gives the control bandwidth you’ll need and clean torque curves for S-curve motion profiles. Look at duty cycle curves rather than only peak values; continuous torque and thermal limits are the real judges.
User-focused selection checklist
Before you order parts, run through this checklist:• Confirm continuous torque at expected duty cycle; don’t pick based only on short bursts. • Verify gearbox backlash and torque rating for dynamic loads. • Check motor thermal resistance and cooling; small motors heat fast. • Match drive current limit to motor thermal capacity. • Reserve 20–30% headroom for unexpected loads or inertial mismatches. • Validate encoder resolution and control loop frequency for the motion profile you need.
Common mistakes that ruin a good recipe
Engineers often undercook these items:• Using peak torque as if it were continuous torque — motors overheat. • Ignoring starting torque on inclines; static friction can be twice dynamic. • Oversizing speed but undersizing torque (results in poor acceleration and hot motors). • Forgetting drivetrain efficiency and gearbox heat buildup. • Assuming identical wheel loads; uneven load can double torque on one side during turns.I’ve seen these repeated at trade shows like Automatica in Munich and on shop floors; they’re predictable if you skip the checklist.
Final plating — bring numbers to vendors
Give suppliers a concise spec sheet: total mass, peak accel, max speed, wheel radius, worst-case grade, duty cycle, and desired control bandwidth. Ask for motor torque-speed curves, continuous vs peak ratings, and drive current limits. Compare real curves, not just cataloged maximums. The right match reduces iterations and field failures.
Summary — the recipe’s payoff
Start with accurate inputs, convert them with the simple physics above, add realistic gearbox and efficiency factors, and choose a motor/drive pair with continuous ratings and control bandwidth that match your motion profile. That method keeps designs lean and reliable, and when you need components whose datasheets and control behavior align with this approach, Kinco supplies clear specifications that make the selection straightforward.
