Dynamics & Actuation
Motor & Gearbox Sizing Calculator
Determine required continuous torque, peak stall torque, wheel RPM, and motor power for mobile robots on slopes and flat terrain.
🛠️ Robot & Environment Parameters
Presets:
Total Robot Mass (m)
5.0 kg
Includes chassis, batteries, motors, and maximum payload.
Number of Drive Motors (N)
2 motors
E.g., 2 for 2WD differential drive, 4 for 4WD skid-steer/mecanum.
Wheel Diameter (D)
10.0 cm
Wheel radius r = D / 2.
Desired Top Speed (v_max)
1.2 m/s
Equivalent to 4.3 km/h.
Maximum Incline Grade (α)
15.0°
Slope angle in degrees (15° = 26.8% slope).
Desired Acceleration (a)
0.8 m/s²
Time to reach top speed: 1.50 s.
Rolling Resistance Coefficient (C_rr)
0.020 (Smooth concrete)
Drivetrain & Gearbox Efficiency (η)
80%
Typical: 75-85% for multi-stage spur/planetary gears; 60% for worm drives.
Safety Factor (SF)
1.8x
Accounts for static friction breakout, shock loads, and voltage sag.
⚡ Motor Sizing Output (Per Motor)
Continuous Wheel Torque
0.45 N·m
4.59 kg·cm
Required Stall Torque (With SF)
0.81 N·m
8.26 kg·cm
Wheel Output Speed
229 RPM
24.0 rad/s
Mechanical Power (Per Motor)
10.8 W
Total Drivetrain: 21.6 W
Recommended Motor Selection
12V Planetary DC Gearmotor (37mm, ~250 RPM, 1.2 N·m Stall)
Standard 12V 25-37mm brushed or brushless DC gearmotor with integrated quadrature encoder will easily handle this load with 80% safety margin.
📊 Resistance Forces Breakdown
Slope Incline Force (m·g·sin α):
12.69 N
Rolling Resistance Force (m·g·cos α · C_rr):
0.95 N
Acceleration Force (m·a):
4.00 N
Total Tractive Force (F_total):
17.64 N
Governing Formulas:
• F_total = m·g·sin(α) + m·g·cos(α)·C_rr + m·a
• τ_wheel = (F_total / N) · (D / 2)
• RPM = (v_max / (π · D)) · 60
• P_mech = (τ_wheel · ω) / η
• F_total = m·g·sin(α) + m·g·cos(α)·C_rr + m·a
• τ_wheel = (F_total / N) · (D / 2)
• RPM = (v_max / (π · D)) · 60
• P_mech = (τ_wheel · ω) / η