Moment of Inertia
Moment of inertia measures how a tool's mass is distributed around the robot wrist. High inertia limits acceleration and effective payload, even within rating.
Moment of inertia (mass moment of inertia) quantifies how an end effector and part's mass is distributed about the robot's wrist axes. A heavy tool mounted far from the flange has high inertia even if its weight is within the payload rating.
Robot datasheets specify allowable inertia alongside payload because the wrist motors must accelerate and decelerate the load. Exceeding the inertia limit causes faults, vibration, faster wear, and lost accuracy, so payload alone is not enough to confirm a tool fits.
When matching a used robot to a heavy or offset tool, check both payload and the allowable moment of inertia. The combined-load check is what protects cycle time and wrist life.