Servo Load Torque

Formula

Description

The torque required to move a load through a rotary actuator (servo motor, RC servo, stepper) equals the force at the load multiplied by the moment arm (perpendicular distance from the rotation axis to the force application point). This is the fundamental relationship for sizing servo motors in robotic arms, CNC machines, pan-tilt mechanisms, and any rotary actuation system. The force includes the weight of the load (F = m × g for gravity) plus any process forces (cutting, pressing, accelerating). Dynamic loads require additional torque for acceleration: T_accel = J × α.

Variables

• T — Required torque (N·m)
• F — Applied force (N)
• d — Moment arm length (m)

Practical Notes

For gravity loads: F = mass × 9.81 m/s². A 1 kg load at 0.1 m arm length requires T = 1 × 9.81 × 0.1 = 0.981 N·m. RC servos are rated in kg·cm: 1 kg·cm = 0.098 N·m. Standard RC servos provide 1-3 kg·cm (0.1-0.3 N·m), high-torque servos 10-25 kg·cm (1.0-2.5 N·m). Always include a safety factor of 1.5-2× to account for friction, dynamic loads, and manufacturing tolerances.