The Robot That Faulted Every Time It Picked Heavy
We mounted a gripper on a 6 kg payload robot. The gripper weighed 3 kg. The part weighed 2 kg. Total payload: 5 kg — under the 6 kg rating. On the floor, the robot faulted with “overload” every time it picked the part and rotated. The problem wasn’t the total weight — it was the moment. The gripper extended 200 mm from the wrist. The moment at the wrist was (3 kg + 2 kg) × 0.2 m = 10 N·m. The robot’s wrist moment rating was 8 N·m. The payload was within spec, but the wrist moment was over. We switched to a 12 kg robot (with a 25 N·m wrist moment rating). The overload fault stopped. The mistake was checking the payload (weight) but not the wrist moment.
Robot payload and moment load calculation isn’t just adding up the weight. The wrist sees moments (from the gripper extending away from the faceplate) that the payload rating doesn’t capture. This article runs the numbers.
Two Limits: Payload and Wrist Moment
A robot’s datasheet gives two limits. Check both.
- Payload (kg): The total weight the wrist can carry. Weight of gripper + part + tooling.
- Wrist moment (N·m): The bending moment at the wrist faceplate. This depends on how far the mass is from the wrist center.
A robot can be within payload but over moment. The weight is fine, but the offset creates a bending load that the wrist bearings can’t handle.
Step 1: Calculate the Payload (Weight)
Sum everything attached to the wrist:
- Gripper (EOAT): frame, fingers, actuators, valves.
- The part being picked (maximum weight).
- Cables, fittings, sensors on the gripper.
Example: gripper = 3 kg, part = 2 kg, cables/sensors = 0.5 kg. Total payload = 5.5 kg. The robot is rated for 6 kg — within payload.
Step 2: Calculate the Wrist Moments
The moment is the weight × distance from the wrist center. The robot datasheet gives three moment limits (Mx, My, Mz — rotation around the three axes).
M = m_total × g × d
Where m_total is the total mass (kg), g is 9.81, and d is the distance from the wrist faceplate to the center of gravity (m).
For our example: m_total = 5.5 kg, d = 0.2 m (the gripper extends 200 mm from the wrist). M = 5.5 × 9.81 × 0.2 = 10.8 N·m. The robot’s wrist moment rating was 8 N·m. Over by 35%.
But there are three moments (not just one):
- My (pitch moment): The mass extends forward. The wrist bends up/down. This is the big one.
- Mx (roll moment): If the mass is offset to one side, it twists the wrist.
- Mz (yaw moment): The mass offset sideways, rotating around the vertical axis.
The datasheet gives separate ratings for each. Check all three.
| Robot Size | Payload | Wrist Moment (typical) | Wrist Inertia |
|---|---|---|---|
| 3 kg (small delta/scara) | 3 kg | 3–5 N·m | 0.05 kg·m² |
| 6 kg (mid 6-axis) | 6 kg | 8–15 N·m | 0.15 kg·m² |
| 12 kg (mid-large) | 12 kg | 25–40 N·m | 0.5 kg·m² |
| 20 kg (large) | 20 kg | 50–80 N·m | 1.5 kg·m² |
| 50 kg (heavy) | 50 kg | 150–250 N·m | 8 kg·m² |
Step 3: Wrist Inertia (For Acceleration)
The wrist also has an inertia rating. The gripper + part has a moment of inertia around the wrist axes. When the robot accelerates (rotates), the wrist must overcome this inertia.
For a point mass at distance d: J = m × d². For our example: J = 5.5 × 0.2² = 0.22 kg·m². The robot’s wrist inertia rating was 0.15 kg·m². Over again. The heavier robot (12 kg) had a 0.5 kg·m² rating — fine.
The inertia matters at high acceleration. A slow robot (10°/s²) doesn’t stress the wrist inertia. A fast pick-and-place (100°/s²) does. Check the inertia against the robot’s wrist rating, especially for fast cycles.
Step 4: The CG Location Is Everything
The moment depends on where the center of gravity (CG) is. A gripper that extends 100 mm from the wrist has half the moment of one that extends 200 mm.
Move the CG Closer
Design the gripper so its mass is as close to the wrist as possible. Mount the actuators (valves, cylinders) near the wrist faceplate, not at the end of the gripper. The fingers at the end are light. The heavy components (pneumatic cylinders, vacuum generators) go on the wrist side.
Balance the Gripper
If the gripper must extend, add a counterweight behind the wrist. The counterweight pulls the CG back toward the wrist center. This reduces the net moment. But it adds weight (payload increases). Trade-off.
Step 5: Speed and Acceleration De-rate
The datasheet ratings assume a certain acceleration. At high speed, the dynamic moments are higher (F = m × a adds to the static weight).
- At low speed (slow moves): the static moment (m × g × d) is the main load.
- At high acceleration (fast pick-and-place): the dynamic moment (m × a × d) adds. If the robot accelerates at 10 m/s², the effective load is m(g + a) = m × 2g. The moment doubles.
For high-speed applications, de-rate the robot. Use 50–70% of the rated moment. The datasheet assumes moderate acceleration. Fast cycles stress the wrist more.
The robot sizing workflow: 1) Sum the total payload (gripper + part + cables). 2) Find the CG distance from the wrist faceplate. 3) Calculate moments M = mgd around each axis (Mx, My, Mz). 4) Calculate wrist inertia J = md². 5) Compare all three (payload, moments, inertia) to the robot’s ratings. 6) For high speed, de-rate by 30–50%. If any rating is exceeded, go to a bigger robot or move the CG closer.
Mounting Orientation: Ceiling, Wall, Floor
Robot datasheets are rated for floor mounting. When mounted on the ceiling or wall, the wrist moments change.
- Floor mount (upright): The wrist moment is as calculated. Standard.
- Ceiling mount (inverted): The wrist sees the weight pulling in the opposite direction. The moment rating is the same (the wrist bearings don’t care about direction), but the payload CG calculation is the same.
- Wall mount (sideways): The wrist sees a gravity moment in a different axis. Check the datasheet’s wall-mount derating. Some robots lose 20–30% of payload when wall-mounted.
For a wall or ceiling mount, check the manufacturer’s derating. The payload might be reduced even if the numbers “fit.”
Reach: Don’t Forget the Arm Extension
Payload is one limit. Reach is another. The robot must reach the pick and place positions with the arm extended.
A 6 kg robot with a 1.4 m reach can pick parts 1.4 m away. If the work cell needs 1.6 m reach, the robot can’t do it — even if the payload fits. Check the reach (the datasheet lists the maximum reach from the wrist center to the robot base).
Mount the robot close to the work area. If the cell is 2 m wide, a 1.4 m reach robot can’t reach both sides. Use a longer-reach robot or mount it on a linear track.
Payload De-rating for End-of-Arm Tooling
Some robot datasheets specify a “maximum tool weight” separate from the part. The robot’s payload includes the tool. If the gripper is 4 kg and the part is 2 kg, total is 6 kg. But if the robot is rated “6 kg payload including tool,” the tool + part must total 6 kg.
Read the datasheet carefully. Some specify payload as “part only” (tool is separate), others as “total.” Don’t confuse them.
A Robot Sizing Checklist
- What is the total payload? (Gripper + part + cables.)
- Where is the CG? (Distance from wrist faceplate.)
- Calculate Mx, My, Mz moments (mgd).
- Calculate wrist inertia J (md²).
- Compare payload, moments, inertia to robot ratings.
- For high speed: de-rate 30–50%.
- Does the reach cover the work area?
- Is the mounting orientation (floor, wall, ceiling) derated?
- Can the CG be moved closer (gripper design)?
- Is the gripper weight minimal (aluminum, not steel)?
- Are cables routed away from the wrist (not adding moment)?
- Does the robot clear all obstacles at full extension?
The Bottom Line
Robot payload and moment calculation isn’t weighing the gripper. The wrist sees moments (mgd) and inertia (md²) that the payload rating doesn’t capture. The robot that faulted on overload wasn’t over its payload — it was over its wrist moment because the gripper extended 200 mm. Calculate the CG distance, compute all three moments, check the wrist inertia, and de-rate for speed. Move the CG closer to the wrist (mount heavy components near the faceplate). The robot that picks heavy parts at speed without faulting wasn’t the biggest robot — it was sized for the moments, not just the weight.
