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Sizing an Industrial Robot: Payload, Reach, Wrist Moment, and Inertia

An industrial robot is sized by where the combined load of part and gripper sits relative to the wrist, not by the rated payload alone, and a load that is well under the payload figure can still exceed the robot's load diagram or wrist inertia limit. UTEC Industrial designs, engineers, machines, fabricates, and installs custom material handling systems for aerospace and heavy industry from its Spokane Valley, WA facility, integrating Allen-Bradley PLC and motion control with in-house CNC machining, heat treating, and stress relief. This article works through the sizing checks in order, from what counts toward the payload to the load diagram, the wrist moment, and the wrist inertia, then runs one heavy load through a published robot specification as a worked example whose arithmetic is UTEC's own illustration, not a manufacturer statement. Sizing happens at the engineering link of the chain, design → engineering → parts machining → fabrication → assembly → weld fatigue → stress relief → drives → controls → tuning → monitoring, and the load case it fixes is the same one the robot controller, the cell PLC, and the monitoring later have to hold to.

What does sizing an industrial robot involve beyond the rated payload?​

The rated payload is the first filter, not the answer. A robot's specification sheet gives several limits that all have to be met at once, and a load under the payload figure can still fall outside the load diagram once a real gripper's CG is taken into account. The checks, in the order this article works through them, are:

  • Payload. The total mass hung from the wrist flange: part, gripper, adapter plates, and anything else mounted beyond the flange.
  • Load position. Where the combined center of gravity (CG) sits relative to the flange, checked against the manufacturer's load diagram.
  • Wrist moment. The moment the load's weight and offset put on the wrist axes.
  • Wrist inertia. The load's mass moment of inertia about the wrist axes, which sets how hard the wrist motors work to accelerate and stop it.
  • Reach. Whether the arm reaches every pick and drop pose with the load it carries there.
  • Arm-mounted loads. Valve banks, cable dress, and sensors mounted on the arm rather than beyond the flange.

The published figures show why payload alone misleads. ABB offers its IRB 8700 in two floor-mount variants: the -550/4.20 carries 550 kg at 4.20 m reach, and the -800/3.50 carries 800 kg at 3.50 m. FANUC's R-2000iD comes in three models with the same 2,605 mm reach and the same 1,150 kg mass, rated 210 kg, 165 kg, and 100 kg at the wrist, each with its own moment and inertia limits. Robotics terms are defined in the ISO robotics vocabulary, and ISO 9946 is the standard for how a manufacturer presents a robot's characteristics. Figures from two manufacturers are read with each sheet's own labels and conditions, as the repeatability section below explains (ABB 3HAC087213-001 Rev. H 2026, §1.1.2 p. 12 and §1.1.3 p. 13; FANUC RR-2000iD catalog 2022, p. 2; ISO 8373:2021; ISO 9946:1999).

What counts toward the payload a robot must carry?​

Everything the wrist flange carries counts, gripper included. For heavy handling, the payload list should include:

  • The heaviest part in the part family, at its heaviest tolerance, not the nominal.
  • The gripper or end-of-arm tool, including fingers, jaws, pads, cylinders, and any tool changer.
  • Adapter and riser plates between the flange and the gripper.
  • Hoses, cables, and fittings that hang from the gripper rather than the arm.
  • Sensors on the gripper, such as part-presence switches, a force sensor, or a camera.

Loads mounted on the arm itself are counted separately against their own allowances. FANUC's heavy-payload catalogs give a maximum load of 550 kg on the J2 base and 50 kg on the J3 arm or casing for the M-1000iA, M-950iA/500, and M-2000 families. ABB's IRB 8700 load diagrams assume 50 kg of extra load mounted on the upper arm housing, so a valve bank or dress pack heavier than that is a different load case from the one the diagram shows. A failure mode the article on choosing between a robot and a custom mechanism describes is a gripper designed after the robot was chosen, whose added tooling mass and offset push the arm past its moment rating, so that the cell is re-scoped late in the project; counting every item on this list at the start avoids it (FANUC RM-1000iA catalog 2022, p. 2; FANUC RM-950iA catalog 2023, p. 2; FANUC RM-2000 catalog 2024, p. 2; ABB 3HAC087213-001 Rev. H 2026, §1.6.1 p. 38).

How does a load diagram limit payload by center-of-gravity position?​

A load diagram is the manufacturer's chart of how much mass the wrist may carry at each CG position. It plots the allowable load against two distances from the tool flange: Z, the CG distance along the flange axis, and L, the radial distance from that axis, where L = √(X² + Y²). The farther out the CG sits, the less mass the diagram allows.

ABB's IRB 8700 specification states the conditions behind its diagrams, and they are the conditions a sizing has to respect:

  • Assumed load inertia. The diagrams assume a nominal payload inertia J0 of 100 kg·m² about the load's own CG, plus 50 kg of extra load on the upper arm housing. A different inertia changes the diagram.
  • Consequence of exceeding it. ABB warns that incorrect load data, or loads outside the diagram, can damage the motors, gearboxes, and mechanical structure through overload, and that a robot run that way is not covered by the robot warranty.
  • Verification. ABB provides a load identification routine in the controller to determine the load parameters, and a separate load-check software tool to verify a specific load case.
  • Wrist-down case. For a wrist pointing down within ±10° of vertical, a separate "vertical wrist" diagram applies. For the wrist pointing straight down, at 0° from vertical, ABB lists a maximum load of 1,000 kg on the -800/3.50, with Zmax 0.662 m and Lmax 0.297 m, and 700 kg on the -550/4.20, with Zmax 0.602 m and Lmax 0.196 m.

The practical reading is that the usable payload for a real gripper is whatever the diagram allows at that gripper's CG, which can be well below the rated figure. The FANUC heavy-payload catalogs cited here give wrist moment and inertia ratings but no load diagram, so a FANUC load case is confirmed with FANUC's own data, as described below (ABB 3HAC087213-001 Rev. H 2026, §1.6.1 p. 38 and §1.6.2 pp. 40 and 43).

Why is a wrist moment rating not enough to set the allowable CG offset?​

A static wrist moment is the load's weight multiplied by its offset from the wrist axis, M = m × g × d. The robot-versus-mechanism article already works the basic case, a 1,000 kg part at 0.5 m giving 4,905 N·m, so it is not repeated here. What matters for sizing is that a moment rating divided by the load's weight looks like an allowable offset but should not be read as one.

ABB's IRB 8700 specification says so for its own figures. It lists maximum wrist torque of 6,043 N·m on axes 4 and 5 and 2,747 N·m on axis 6 for the -800/3.50, valid at 800 kg, and 5,279 N·m and 2,517 N·m, valid at 475 kg, for the -550/4.20. Dividing 6,043 N·m by the weight of 800 kg, 7,848 N, gives about 0.77 m; this is UTEC's own arithmetic, not an ABB figure. ABB states that its wrist torque values are for reference only and should not be used to calculate the permitted CG offset, because the main-axis torques and the dynamic loads also limit it and the arm loads influence the load diagram. ABB directs the user to its load-check tool for the absolute limits of the load diagram.

The failure mode is a sizing that treats the 0.77 m figure as an allowable offset and places the CG well outside the load diagram. Static moment is still a useful first screen, for example to reject a gripper concept early, but the load case is verified against the manufacturer's load diagram or with its load-check tool (ABB 3HAC087213-001 Rev. H 2026, §1.6.4 p. 47; Hibbeler 2021, Ch. 4).

How is load inertia at the robot wrist calculated?​

Mass moment of inertia measures how mass is distributed about an axis. For a set of point masses it is I = Σ m × r², and for a solid body it is the integral of the same quantity. The parallel-axis theorem moves an inertia from an axis through the CG to any parallel axis: I = I_cm + m × d², where d is the distance between the two axes. The consequence for a robot is that a load's inertia about a wrist axis grows with the square of its distance from that axis, so a CG moved twice as far out adds four times the transfer term.

ABB's IRB 8700 specification gives its wrist-inertia checks as two formulas:

  • Axis 5: Ja5 = Load × ((Z + 0.310)² + L²) + max(J0x, J0y) ≤ 1,100 kg·m²
  • Axis 6: Ja6 = Load × L² + J0z ≤ 725 kg·m²

ABB footnotes the 0.310 m term in the axis-5 formula: for option 780-4, the value is 0.505 m instead.

Here Load is in kg, Z and L are in m from the tool flange, and J0x, J0y, and J0z are the load's own inertias about axes through its CG. The following is UTEC's reading of the formulas' form, not an ABB statement. Read through the parallel-axis theorem, the first term in each formula is the transfer term m × d², and the J0 term is I_cm. The (Z + 0.310) term then shows that the distance used for axis 5 is longer than the CG's distance from the flange.

For FANUC robots, the catalogs cited here give allowable load inertia ratings at J4, J5, and J6 rather than a formula, for example 228, 228, and 196 kg·m² on the R-2000iD/210FH and 1,750, 1,750, and 840 kg·m² on the M-1000iA. In the worked example below, the J0 values are taken from the gripper and part design model (Moebs, Ling, and Sanny 2016, §10.5, Eq. 10.20; ABB 3HAC087213-001 Rev. H 2026, §1.6.3 pp. 45-46).

Worked example: can one heavy robot carry a 700 kg part and gripper?​

This example checks one load against the ABB IRB 8700 specification. The load, geometry, and inertias are illustrative assumptions for a mining-equipment shop moving a cast wear-liner segment, not data from any real part, and the arithmetic is UTEC's own illustration.

InputSymbolValue
Part massm_p520 kg
Part CG from tool flange, along flange axisZ_p0.45 m
Part CG radial offset from flange axisX_p0.20 m (Y_p = 0)
Gripper massm_g180 kg
Gripper CG from tool flangeZ_g, X_g0.20 m, 0
Load's own inertia about its CG, from CADJ0x = J0y, J0z55 kg·m², 35 kg·m²
Arm-mounted valve bank—40 kg on the upper arm housing
Gravityg9.81 m/s²

Step 1, combined payload and CG. A composite CG is the mass-weighted average of the part CGs:

  • Load = 520 + 180 = 700 kg
  • Z = (520 × 0.45 + 180 × 0.20) ÷ 700 = 270 ÷ 700 = 0.386 m
  • L = X = (520 × 0.20 + 180 × 0) ÷ 700 = 104 ÷ 700 = 0.149 m

Step 2, payload and diagram. 700 kg is under the -800/3.50's 800 kg rating, but over the -550/4.20's 550 kg rating. The CG point, Z = 0.386 m and L = 0.149 m, is then plotted on the -800/3.50 load diagram in the specification; this article does not reproduce the curve. The load's J0 of 55 kg·m² does not exceed the 100 kg·m² the diagrams assume, and the 40 kg valve bank is within the 50 kg arm load they assume.

Step 3, wrist inertia. The example assumes a robot without option 780-4, so the axis-5 formula uses the 0.310 m term.

  • Ja5 = 700 × ((0.386 + 0.310)² + 0.149²) + 55 = 700 × (0.4844 + 0.0222) + 55 = 700 × 0.5066 + 55 = 355 + 55 = 410 kg·m², against a limit of 1,100 kg·m², or 37 percent
  • Ja6 = 700 × 0.149² + 35 = 700 × 0.0222 + 35 = 15.5 + 35 = 50.5 kg·m², against a limit of 725 kg·m², or 7 percent

Step 4, static screen. The load's weight is 700 × 9.81 = 6,867 N. Its static moment from the radial offset alone is 6,867 × 0.149 = 1,023 N·m. This is a screening figure only, for the reason given above.

Result. On these assumptions the load passes the -800/3.50 payload and inertia checks, subject to its CG plotting inside the load diagram. The -550/4.20 fails on payload for general orientations. It could carry the load only with the wrist pointing straight down, at 0° from vertical, where 700 kg equals that variant's listed maximum exactly, which leaves no margin for a heavier casting or for any tilt of the wrist (ABB 3HAC087213-001 Rev. H 2026, §1.6.2 pp. 40 and 43 and §1.6.3 pp. 45-46; Hibbeler 2021, Ch. 9).

How do published wrist ratings show that payload alone does not size a robot?​

FANUC's R-2000iD catalog is a clear case because its three models share one 2,605 mm reach and one 1,150 kg mass but carry three wrist ratings. The catalog figures are:

ModelMax load at wristAllowable moment J4 / J5 / J6Allowable inertia J4 / J5 / J6
R-2000iD/210FH210 kg1,380 / 1,380 / 735 N·m228 / 228 / 196 kg·m²
R-2000iD/165FH165 kg1,000 / 1,000 / 620 N·m122 / 122 / 100 kg·m²
R-2000iD/100FH100 kg850 / 850 / 450 N·m90 / 90 / 50 kg·m²

Dividing each J4 and J5 moment rating by the rated load's weight shows where a static load would reach the moment rating. This is UTEC's own arithmetic, not a FANUC statement or a FANUC allowable offset:

  • 210FH: 1,380 ÷ (210 × 9.81) = 0.67 m
  • 165FH: 1,000 ÷ (165 × 9.81) = 0.62 m
  • 100FH: 850 ÷ (100 × 9.81) = 0.87 m

The lightest-rated wrist gives the longest of these offsets at its rated load. The corresponding failure mode is choosing by payload alone: a 150 kg part and gripper with its CG 0.70 m out puts 150 × 9.81 × 0.70 = 1,030 N·m on the wrist, more than the 165FH's 1,000 N·m rating, although 150 kg is under its 165 kg payload. The 210FH carries the same load within its 1,380 N·m rating. For a FANUC robot, the load case is confirmed from FANUC's own data through a FANUC design and engineering partner, not from this arithmetic (FANUC RR-2000iD catalog 2022, p. 2; Hibbeler 2021, Ch. 4).

How does reach trade against payload in a heavy robot family?​

In both heavy families below, the longer-reach version carries less. The published pairs show the size of the trade:

  • ABB IRB 8700: the -550/4.20 reaches 0.70 m farther than the -800/3.50 and carries 250 kg less. ABB states both reaches at the wrist centre.
  • FANUC M-2000: the 1200F-37A and 2300F-37A models reach 3,734 mm and carry 1,200 kg and 2,300 kg; the 900F-47A and 1700F-47A models reach 4,683 mm and carry 900 kg and 1,700 kg.

Two sizing points follow. First, a reach stated at the wrist centre does not include the gripper, so the pose check adds the flange-to-grip distance and the approach clearance to the required reach. Second, where the reach needed at the far pose forces the longer-reach variant, the lower payload comes with it, and on the IRB 8700 a lower listed wrist torque as well, although the M-2000/900F-47A keeps the wrist moment and inertia ratings of the shorter 1200F-37A; moving the robot closer to the pick on a riser or a track can keep the shorter, stronger arm.

A failure mode is a layout checked with the arm's maximum reach envelope but not with the gripper and part at each pose, which can leave the far pose unreachable or reached only at a wrist angle the load diagram does not allow (ABB 3HAC087213-001 Rev. H 2026, §1.1.2 p. 12 and §1.1.3 p. 13; FANUC RM-2000 catalog 2024, p. 2).

How much margin should a robot sizing leave?​

No manufacturer source in this article sets a universal margin, and none is invented here. What the sources do set is the set of conditions under which the published limits hold, and each condition a real load breaks uses up margin:

  • Inertia assumption. ABB's diagrams assume J0 = 100 kg·m²; a load with a larger J0 is a different load case and needs re-evaluation.
  • Arm load assumption. The same diagrams assume 50 kg on the upper arm housing; FANUC lists 50 kg on the J3 arm or casing and 550 kg on the J2 base for the M-2000, M-1000iA, and M-950iA/500.
  • CG uncertainty. A casting or weldment may not have its CG exactly where the model puts it. Running the checks at the worst corner of the CG range, as the positioner sizing example does for a positioner, is the same discipline.
  • Part family growth. A part family that grows by one heavier size after startup changes the load case the sizing was built on.

The worked example above leaves 100 kg of payload margin, 63 percent of the axis-5 inertia limit, and 93 percent of the axis-6 limit. Whether that is enough depends on the CG tolerance and on how the part family may grow, which the specification for the cell should state (ABB 3HAC087213-001 Rev. H 2026, §1.6.1 p. 38; FANUC RM-2000 catalog 2024, p. 2; FANUC RM-1000iA catalog 2022, p. 2; FANUC RM-950iA catalog 2023, p. 2).

What controls and sensing confirm a robot's load case in service?​

Sizing sets the load case on paper; the controls confirm it every cycle. In a heavy-handling cell the layers are:

  • Load data in the robot controller. ABB provides a load identification routine in the controller to determine the load parameters, and a separate software tool to check it against the load diagram.
  • Load data selected by part. This is this article's own design recommendation, not a robot maker's statement: where one gripper handles several part sizes, the cell design keeps a load data set for each part and has the cell PLC tell the robot which part is in the gripper, so that the load case in use matches the load carried.
  • Weight and presence checks. Load cells in a pick station, or part-presence sensors on the gripper, confirm that the part actually picked matches the part the PLC expected. Machine vision can confirm the part number where parts vary.
  • PLC handshake. The PLC and robot exchange part identity, gripper state, and permissives over EtherNet/IP; the article on connecting a FANUC robot to an Allen-Bradley PLC covers the connection, buffering, and handshake. Rockwell Automation's controller design manual says the controller's tasks can be configured as continuous, periodic, or event tasks.
  • Safety. The robot's own safety requirements sit under ISO 10218-1:2025 and the cell's under ISO 10218-2:2025, adopted in the US as ANSI/A3 R15.06-2025. ISO 13849-1:2023 specifies a methodology for the design and integration of safety-related parts of control systems that perform safety functions, and applies to high-demand and continuous modes of operation.

UTEC Industrial integrates FANUC robotic cells, including vision, with a FANUC design and engineering partner. A failure mode to design out is a cell where the PLC changes the part but the robot keeps the previous part's load data, which can run a heavier part on a lighter part's load data (ABB 3HAC087213-001 Rev. H 2026, §1.6.1 p. 38; Rockwell Automation 1756-RM094N-EN-P-2025, Ch. 5 p. 39; ISO 10218-1:2025; ISO 10218-2:2025; ANSI/A3 R15.06-2025; ISO 13849-1:2023).

Where do fabrication and the robot base enter the sizing?​

The load case is decided upstream of the robot. Where the gripper frame is a machined weldment, its mass and CG come from the design model; if the frame is built heavier than modeled, or distorts during welding so that the grip point moves, the CG moves with it. Heavy grippers and adapter plates are therefore designed to a mass and CG budget, machined where they locate on the flange and on the part, and checked against that budget before the robot is programmed.

The robot's own mass sizes the base. The published masses are 4,750 kg for the IRB 8700, excluding its dress pack, and, without controller, 5,300 kg for the M-1000iA, 2,500 kg for the M-950iA/500, and 8,600 to 12,500 kg across the M-2000 models. A riser or pedestal that lifts the robot closer to the pick carries that mass plus the reaction of the load in motion, and its mounting face has to stay flat for the robot to sit true; the article on stress relief for machine frames and bases covers why welded bases are stress-relieved before final machining. UTEC Industrial stress-relieves welded frames with automated vibratory stress relief (VSR) and machines their mounting faces in-house before assembly (ABB 3HAC087213-001 Rev. H 2026, §1.4 p. 23; FANUC RM-1000iA catalog 2022, p. 2; FANUC RM-950iA catalog 2023, p. 2; FANUC RM-2000 catalog 2024, p. 2).

Why is repeatability a separate check from sizing?​

Payload, moment, and inertia decide whether the robot can carry the load; repeatability decides whether it can place it. The two are specified separately, and a heavy load can pass every sizing check and still need a closer-placing robot or a locating fixture.

ISO 9283 is the international standard for robot performance criteria and test methods, but a 1999 handbook chapter on industrial robotics standards by a NIST author states that the ISO subcommittee did not intend it for comparing robots of similar capacity and size. The printed repeatability and accuracy figures for the heavy-payload models, with the label and basis each sheet uses, are set out in Heavy-Payload Industrial Robots Compared: Payload, Reach, Wrist Ratings, and a figure printed as "positioning accuracy" on one sheet cannot be assumed to be the same quantity as "repeatability" on another (ISO 9283:1998; Dagalakis 1999, pp. 447-459, DOI 10.1002/9780470172506.ch24).

What assumptions does the worked example make, and where do they break?​

Every number in the worked example follows from its stated inputs. The assumptions, and what happens when each fails, are:

  • Rigid part and gripper. A part that flexes or shifts in the jaws can move its CG outward and raise both L and the transfer term.
  • J0 from CAD. The 55 and 35 kg·m² values are assumed; a CAD model that omits fingers, hoses, or a tool changer understates them.
  • CG at the stated point. A cast part's real CG can differ from the model. The checks are rerun at the worst corner of the CG tolerance.
  • One load case. The example checks the loaded gripper only. The empty gripper, the gripper with a part caught at one end, and the heaviest part in the family are separate cases.
  • Static screening only. The 1,023 N·m moment is a static figure; acceleration and stops add dynamic load, which ABB names, with the main-axis torques, as a reason not to calculate the permitted CG offset from its wrist torque figures; ABB directs the user to its load-check tool for the absolute limits of the load diagram.
  • No reach or pose check. The example does not confirm that the arm reaches each pose with the wrist at an angle the diagram allows.

A sizing that states these assumptions, and is rerun whenever one of them changes, keeps the robot's load case aligned with what the gripper actually carries (ABB 3HAC087213-001 Rev. H 2026, §1.6.1 p. 38 and §1.6.4 p. 47; Hibbeler 2021, Ch. 9).

Related Articles

References​

  • ABB 3HAC087213-001 Rev. H: Product specification - IRB 8700 (OmniCore). ABB Robotics, 2026.
  • FANUC RR-2000iD(E)-03a: FANUC Robot R-2000iD. FANUC Corporation, 2022.
  • FANUC RM-1000iA(E)-02: FANUC Robot M-1000iA. FANUC Corporation, 2022.
  • FANUC RM-950iA(E)-01: FANUC Robot M-950iA/500. FANUC Corporation, 2023.
  • FANUC RM-2000(E)-01: FANUC Robot M-2000. FANUC Corporation, 2024.
  • ISO 8373:2021: Robotics — Vocabulary. ISO, 2021.
  • ISO 9946:1999: Manipulating industrial robots — Presentation of characteristics. ISO, 1999.
  • ISO 9283:1998: Manipulating industrial robots — Performance criteria and related test methods. ISO, 1998.
  • Hibbeler, R.C. Engineering Mechanics: Statics, 15th ed. Pearson, 2021. ISBN 9780137514663.
  • Moebs, W., Ling, S. J., and Sanny, J. University Physics Volume 1. OpenStax, 2016.
  • Dagalakis, N. G. (1999). "Industrial Robotics Standards." In S. Y. Nof (ed.), Handbook of Industrial Robotics, 2nd ed. Wiley, pp. 447-459.
  • Rockwell Automation 1756-RM094N-EN-P-2025: Logix 5000 Controllers Design Considerations. Rockwell Automation, 2025.
  • ISO 10218-1:2025: Robotics — Safety requirements — Part 1: Industrial robots. ISO, 2025.
  • ISO 10218-2:2025: Robotics — Safety requirements — Part 2: Industrial robot applications and robot cells. ISO, 2025.
  • ANSI/A3 R15.06-2025: American National Standard for Industrial Robots and Robot Systems – Safety Requirements. A3/ANSI, 2025.
  • ISO 13849-1:2023: Safety of machinery — Safety-related parts of control systems — Part 1: General principles for design. International Organization for Standardization, 2023.

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