THE ENGINEERING BEHIND THE TOOL
How to calculate robot motor torque
A wheeled robot must overcome gravity on a slope, rolling resistance, and the force needed to accelerate. A smaller wheel reduces torque demand, while a larger gear reduction trades motor speed for wheel torque.
F = mg sin(θ) + Crr mg cos(θ) + ma
τmotor = SF · F · r / (n · G · η)
RPMmotor = 60 · v · G / (2πr)
Pshaft,total = SF · F · v / η
m: mass · g: 9.80665 m/s² · θ: slope · a: acceleration · r: wheel radius · n: motors · G: reduction ratio · η: gear efficiency · SF: design factor.A worked motor sizing example
For a 12 kg robot with 150 mm wheels, two motors, a 10° slope, 0.5 m/s² acceleration, and a rolling coefficient of 0.03, the required tractive force is about 29.91 N. With a 1.5 design factor, a 30:1 gearbox, and 80% efficiency, each motor needs about 0.070 N·m at 3,820 RPM to reach 1 m/s under that design load. Total design mechanical shaft power is about 56.08 W.
The example motor's continuous torque is 0.060 N·m. It can move the virtual robot, but does not meet the specified design margin. Motion alone does not establish a suitable motor choice.
What the ramp simulator models
The simulator starts from rest and runs for eight seconds or until the robot travels five metres. An ideal speed controller requests your acceleration until it reaches the target speed. Available drive force is limited by a linear brushed DC motor torque–speed curve, the continuous torque setting, gearbox efficiency, and tire grip.
The design factor affects sizing results; it is not an extra physical load in the simulation. If available force cannot overcome the slope and rolling resistance, the robot remains at rest. Rollback, wheel inertia, aerodynamics, turning, weight transfer, motor heating, and battery voltage sag are outside this simplified model.
Which motor specifications should I enter?
Use no-load RPM, stall torque, and the manufacturer's continuous torque rating for the same motor shaft and supply voltage. A gearmotor's output specifications already include its internal reduction: set the ratio here to 1 unless you add another reduction. The example values are illustrative and do not describe a particular motor.
Stall torque is not a continuous operating rating. Use the motor and gearbox datasheets to verify continuous loading, current, temperature, and shaft limits. See Pololu's explanation of stall and continuous loading, and MIT's electric motor and robot drivetrain notes.
Does a higher gear ratio always help?
More reduction increases wheel torque but requires a higher motor RPM for the same ground speed. As RPM approaches no-load speed, available torque falls. The feasible ratio range solves both the continuous torque requirement and the motor torque–speed curve at your target speed, including the design factor. It assumes unchanged gear efficiency across ratios. A suitable gearbox must still exist with the necessary ratings.
Continue your design with the battery runtime estimator or the servo PWM mapper. Learn about the engineer behind these tools on Umar Masood's profile.