Payload Holding Torque

This formula gives the turning effect a robot joint must resist when it holds a mass still at some distance from the joint. It comes from the basic moment rule torque = force × perpendicular distance, with the payload’s weight equal to mg, so the holding torque is mgL. The farther the load is from the joint, or the heavier it is, the more torque the motor or gearbox must supply to keep the arm from rotating.

Use this when checking whether a robotic arm, gripper, or hinge can support a payload at a fixed reach without moving. It is a quick first estimate for static loading in basic mechanism and robot design problems.

• Using the payload mass directly as torque instead of first converting it to weight with mg
• Forgetting that the reach L is measured from the joint axis to the load in meters
• Ignoring other effects such as the arm’s own weight, acceleration, or friction when the real system is not perfectly static