Payload, Inertia, Speed and Cycle Time
Load charts, moment and inertia limits, joint torque and gearbox sizing, acceleration limits and how to shorten the cycle.
Payload is a chart
The payload on the datasheet is the mass the robot can carry at a stated distance from the wrist flange. Move the center of gravity (CG) of the load further out and the allowed mass falls, because the wrist motors must resist a larger moment and a larger inertia. Manufacturers publish a load chart (payload against CG offset in two directions); the single headline number is the best case.
Worked example: is the tool inside the chart?
A robot is rated 6 kg at 150 mm. Its wrist torque limit corresponds to Mmax = 6 × 9.81 × 0.15 = 8.83 N·m, and its wrist inertia limit is 0.25 kg·m².
- Tool A: 3.9 kg with its CG 260 mm from the flange. Moment = 3.9 × 9.81 × 0.26 = 9.95 N·m, over the limit of 8.83. Inertia = m d² = 3.9 × 0.26² = 0.264 kg·m², within 0.25. The allowed mass at 260 mm is 8.83 ÷ (9.81 × 0.26) = 3.46 kg: the tool is too heavy at that offset.
- Fix: shorten the tool so the CG is at 150 mm: the moment becomes 5.74 N·m, inside the limit, and 3.9 kg is allowed (rated 6 kg). Or take a lighter gripper, or a larger robot.
- Both the mass and where it sits matter. A 4 kg tool on a 250 mm stalk loads the wrist more than a 6 kg tool close to the flange.
- Include everything on the wrist: the gripper, the tool changer, valves, sensors, cables, hoses and the part, and the dress pack if it hangs from the arm.
- Enter the payload data in the controller (mass, CG, inertia). A wrong value makes the controller mis-estimate gravity, causes overload and collision faults, and reduces accuracy.
- Some robots have extra payload on the upper arm (for a valve block, a camera): it counts against the arm’s limits.
Moment and inertia limits
M = m g d J = Jcg + m d² parallel-axis rule
Worked example: inertia of an asymmetric tool
- A 1.8 kg bar-shaped gripper body, 0.30 m long, has its own inertia about its center Jcg = m L² ÷ 12 = 1.8 × 0.30² ÷ 12 = 0.014 kg·m².
- Its center is 0.20 m from the wrist axis, so about that axis J = 0.014 + 1.8 × 0.20² = 0.086 kg·m²: the offset adds more than the shape.
- A 0.5 kg part held 0.30 m away adds 0.5 × 0.30² = 0.045 kg·m², for a total of about 0.131 kg·m², to compare with the wrist limit on the datasheet.
- Inertia limits come first on the wrist axes: a tool can be within the mass rating and still overload axis 6 when it is wide.
Sizing an axis
The same arithmetic sizes a joint. The motor and gearbox must supply the torque to hold the load against gravity, to accelerate the inertia, and to overcome friction. For axis 1 (the vertical waist axis, no gravity torque) the acceleration torque is J α. The motor sees the torque divided by the gear ratio N and the efficiency η.
Worked example: the waist axis
- The arm has an inertia of 1.2 kg·m² about the waist. A 4.4 kg payload at 0.65 m adds 4.4 × 0.65² = 1.86 kg·m²: total 3.06 kg·m².
- Accelerating to 120°/s (2.09 rad/s) in 0.25 s needs α = 8.38 rad/s², so the joint torque is J α = 25.6 N·m.
- Through a 120:1 gearbox of 80 % efficiency the motor torque is 25.6 ÷ (120 × 0.8) = 0.27 N·m, at a motor speed of 2 400 rpm. A small servo motor can do this, which is why robot joints use high-ratio gearing.
- Gravity on the shoulder: a 9.0 kg forearm (CG at 0.20 m) plus the 4.4 kg payload at 0.65 m, held horizontal, needs 45.7 N·m even when standing still: 0.48 N·m at the motor, continuously. Brakes hold it when the power is off.
- The Motor Torque and Inertia Matching Calculator does these sums for a motor, gearbox and load. See Motion Control and Actuators for sizing in general.
Payload and acceleration
The more inertia, the less acceleration a given torque limit allows, and short moves are limited by acceleration (see Motion, Paths and Programming). So every kilogram on the wrist costs cycle time, not just capacity.
Worked example: a 400 mm move with different payloads
The waist axis can deliver a torque of 90 N·m at most. With the arm inertia 1.2 kg·m² and the payload at 0.65 m, the largest acceleration and the resulting time for a 400 mm tool move (speed limit 1 500 mm/s) are:
| Payload | Total inertia | Angular acceleration | Tool acceleration | Move time |
|---|---|---|---|---|
| 1.0 kg | 1.62 kg m² | 3 178 °/s² | 36 055 mm/s² | 0.31 s |
| 3.0 kg | 2.47 kg m² | 2 090 °/s² | 23 708 mm/s² | 0.33 s |
| 4.4 kg | 3.06 kg m² | 1 686 °/s² | 19 124 mm/s² | 0.35 s |
| 6.0 kg | 3.74 kg m² | 1 381 °/s² | 15 663 mm/s² | 0.36 s |
Going from 6.0 kg down to 1.0 kg changes the move time from 0.36 s to 0.31 s. Lighter tooling and a closer CG shorten the cycle for free; so does setting the robot’s payload data accurately, which lets the controller use the true acceleration limit.
Heating and duty cycle
Motors and drives heat in proportion to the square of the torque. The thermal limit is the root-mean-square (RMS) torque over the whole cycle, not the peak: a motor can exceed its continuous rating briefly if the average stays within it. A cycle with long stationary holds against gravity heats a motor even though nothing moves.
Worked example: RMS torque over a cycle
One cycle at the waist: 25.6 N·m for 0.25 s (accelerate), 0 for 0.40 s (cruise), −25.6 for 0.25 s (decelerate), and 6.0 for 1.00 s (friction and a wait):
τRMS = √[(25.6² × 0.25 + 0 + -25.6² × 0.25 + 6.0² × 1.00) ÷ 1.90] = 13.8 N·m, well below the 25.6 N·m peak. The RMS value, with margin, must be below the continuous torque rating.
- Long waits at speed limits heat nothing; long holds under load heat a lot. Hold a heavy part in a pose that puts the weight on the structure, not on the motors (the arm near vertical).
- Heat is why ambient temperature and enclosure cooling matter: check the robot and controller ratings in a hot cell.
- The controller may report motor temperature or load; log it as a health indicator (see Commissioning, Maintenance and Troubleshooting).
Shortening the cycle
Worked example: from 2.40 s to 1.76 s
- The baseline cycle is 0.50 + 0.30 + 0.60 + 0.30 + 0.50 + 0.20 = 2.40 s (1 500 parts an hour).
- Blending the corners saves about 0.08 s on each of three robot moves; a faster valve and a shorter hose cut each gripper action from 0.30 s to 0.20 s; presenting the next part early removes the 0.20 s wait: total 1.76 s, or 2 045 parts an hour, which is 36 % more with no change to the robot’s speed.
- Most of the gain came from the gripper and the waiting, not from the arm.
| Lever | How | Watch out for |
|---|---|---|
| Shorter path | Put pick and place close together; lift only as high as needed; joint moves in free air | Collisions with the fixture and the part |
| Blend corners | Zones or radii on non-critical points | Corner cutting; actions firing early |
| Faster gripper | Fast valves, short hoses, vacuum with high flow, electric grippers with tuned speed | Dropping parts; sensors that need time to confirm |
| Overlap actions | Start the gripper while the arm is finishing the move; trigger outputs by distance | Gripping before the arm is in place |
| Keep the robot busy | Buffer parts, two stations, feed while it works | Space and cost |
| Right payload data and light tooling | Enter the true mass and CG; use aluminum or carbon fiber | Weaker tools |
| Raise acceleration | Use the controller’s acceleration and jerk settings in steps | Overload warnings, vibration, wear |
Cycle time is also limited by the rest of the cell: feeder rate, conveyor speed, the PLC handshake and any vision (see Cell Design, PLC Integration and Feeding). Measure where the time goes (a log of each step) before optimizing.
Stopping
A moving robot cannot stop instantly: it needs time and distance, which depend on speed, payload, pose and the type of stop (a controlled stop on the motors, or the brakes on their own). The stopping distance feeds directly into the safety distances in Safety: Standards, Safeguarding and Cobots.
Worked example: stopping from 1 m/s
At a tool speed of 1.0 m/s and a deceleration of 5 m/s², the robot stops in t = v ÷ a = 0.20 s and travels s = v² ÷ (2 a) = 100.00 mm. At half the deceleration the distance doubles, and the brake-only stop of a loaded arm can be much longer. Use the manufacturer’s stopping-distance data (ISO 10218 requires it) rather than a calculation, measured at the worst speed, payload and pose.
Running cost is small next to the cell price, but not zero: a robot drawing an average of 650 W for 6 000 hours a year uses 3 900 kWh, about $585 at $0.15 per kWh.
Related
- Industrial Robotics: the overview of this guide.
- End-of-Arm Tooling and Grippers: keeping the tool light and short.
- Motion, Paths and Programming: speed profiles and blending.
- Motion Control and Actuators and the Motor Torque and Inertia Matching Calculator.
FAQ
Why does the robot refuse my payload when the mass is below the rating?
The payload rating is for a stated center of gravity. A load further from the flange loads the wrist with more moment and inertia, so the allowed mass is lower. Check the load chart for your tool’s CG.
What happens if I enter the wrong payload?
The controller mis-estimates the gravity torque, so the arm may sag, trip overload or collision faults, move less accurately and run at the wrong acceleration. Enter measured mass, CG and inertia.
Why is my cycle slower than the datasheet suggests?
Short moves never reach top speed; acceleration is limited by payload inertia; stopping at points costs time; and the cell (gripper, waits, PLC) adds to the arm’s time. Log where the time goes.
How do I know if the motors will overheat?
Compute or measure the RMS torque over the whole cycle, including holds against gravity, and keep it with margin below the continuous rating. The controller usually reports motor load and temperature.
References
- Craig, J. J., Introduction to Robotics: Mechanics and Control, Pearson (dynamics); Spong, M., Hutchinson, S. and Vidyasagar, M., Robot Modeling and Control, Wiley.
- Robot manufacturers’ payload charts and selection tools (ABB RobotStudio, FANUC ROBOGUIDE, KUKA.Sim, Universal Robots calculators).
- ISO 9283 and ISO 10218; Hughes, A. and Drury, B., Electric Motors and Drives, Newnes (RMS torque and duty).
Last reviewed: October 2026. Inertias, torques and limits are illustrative: use your robot’s load chart and the maker’s selection software.