Combined Payload Mass
M_{total} = M_{part} + M_{tool}
Static Gravity Torque
\tau_{static} = M_{total} \cdot g \cdot \left(\frac{offset}{1000}\right)
Mass Moment of Inertia (Point Mass)
I = M_{total} \cdot r^2 = M_{total} \cdot \left(\frac{offset}{1000}\right)^2
Total Peak Wrist Torque
\tau_{total} = \tau_{static} + I \cdot \alpha
Static wrist torque is linear with offset. Dynamic inertial torque scales quadratically ($r^2$) with offset.
Acceleration torque occurs during joint acceleration and deceleration. Emergency stops can exceed these values.
Always maintain a minimum 20% safety margin under the manufacturer's rated static and dynamic torque limits.