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End-of-Arm Tooling Design and Holding-Force Calculations

End-of-arm tooling has to hold the part through every move the robot makes, including acceleration and an emergency stop, and its holding force is calculated from the part's weight, the friction or form fit at the contact, the acceleration, and a safety factor. 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 holding-force methods that gripper and vacuum-component suppliers publish for friction grippers, vacuum cups, and magnetic grippers, with each supplier's convention kept as its own, and then covers loss of air or power, the interface standards, and the gripper's controls. The tooling spans the whole chain, design → engineering → parts machining → fabrication → assembly → weld fatigue → stress relief → drives → controls → tuning → monitoring, from a machined and stress-relieved frame to the sensors that confirm the grip every cycle.

What does end-of-arm tooling have to do in a heavy-handling cell?​

End-of-arm tooling is the gripper or other end effector mounted on the robot's wrist flange. As engineering reasoning, it carries three loads at once: the part's weight, the inertial force of every acceleration, and its own mass, which counts against the robot's payload. The robot-side checks, payload, load diagram, wrist moment, and wrist inertia, are worked through in Sizing an Industrial Robot: Payload, Reach, Wrist Moment, and Inertia, so this article stays on the grip itself.

The mounting face is standardized, but its load is not. ISO 9409-1:2004 "defines the main dimensions, designation and marking for a circular plate as mechanical interface" and "is intended to ensure the exchangeability and to keep the orientation of hand-mounted end effectors." It "does not define other requirements of the end effector coupling device," and it "does not contain any correlation of load-carrying ranges, as it is expected that the appropriate interface is selected depending on the application and the load-carrying capacity of the robot." The iso.org page lists the 2004 text as the third edition, last reviewed and confirmed in 2023.

A failure mode, stated as engineering reasoning, is a tool designed to the flange bolt pattern and nothing else, with no holding-force calculation behind its jaws or cups (ISO 9409-1:2004).

How do friction grip and capture grip differ?​

SCHUNK's how-to guide on gripper selection, published in ASSEMBLY magazine in April 2021, separates two ways of holding a part. A friction grip "is when the workpiece is gripped and held with friction alone," and SCHUNK says a coefficient of friction "between µ = 0.1 and 0.4 is typical for most automation applications." A capture grip "is when a workpiece has a groove, ridge, or hole that form-fit fingers can positively engage," and with a capture grip "the force required to safely hold the workpiece is less than if held by friction alone so a smaller gripper can be selected." SCHUNK's catalog note makes the same distinction for its ratings: "In the case of form-fit gripping, significatnly [sic] higher permissible workpiece weights are possible."

The friction a grip can develop has a ceiling. A statics text states the maximum static friction force as Ff max = µs N, the static coefficient of friction times the normal force. As engineering reasoning, for a gripper the normal force is the clamping force at the jaws.

The next two sentences are engineering reasoning. For heavy parts, a friction grip needs clamping force several times the part's weight at the coefficients above, while a capture grip carries the weight on a shoulder, pin, or hook and uses clamping force mainly to keep the part seated. Castings, weldments, and forgings that can be given a lifting lug, bore, or flange are candidates for capture features designed in with the part (SCHUNK How-To Guide 2021; SCHUNK, Centric Grippers catalog note, accessed 2026; Baker and Haynes 2026, §9.2 p. 316).

How is the grip force for a friction gripper calculated?​

SCHUNK states the convention behind its catalog ratings. Its recommended workpiece weight "is calculated for force-fit clamping with a coefficient of static friction of 0.1 and a safety factor of 2 against workpiece slippage at acceleration due to gravity g." Its printed example takes a gripping force of 1,000 N, µ 0.1, safety factor 2, and g 9.81 to a catalog workpiece weight of 5 kg.

The expression SCHUNK prints with that example does not evaluate to 5 kg as written. Rearranged, which is UTEC's own arithmetic and not SCHUNK's notation, the 5 kg follows from:

  • m = F × µ ÷ (g × S) = 1,000 N × 0.1 ÷ (9.81 m/s² × 2) ≈ 5.1 kg
  • or, solved for force, F = m × g × S ÷ µ

SCHUNK's how-to guide adds two points. It says the coefficient of friction "has the largest impact on the amount of grip force required," with a worked ratio: if the grip force required at µ = 0.1 is 2,000 N, raising µ to 0.2 halves it to 1,000 N. It names rubber pads, fiberglass inserts, or carbide material between fingers and part as ways to raise µ.

The catalog rating is at g only. The note does not say how robot acceleration, finger length, or the number of contact faces change it, so any such extension is engineering reasoning, labelled where it appears below. As engineering reasoning, a failure mode is reading a catalog workpiece weight as the load the gripper can carry on a fast robot (SCHUNK, Centric Grippers catalog note, accessed 2026; SCHUNK How-To Guide 2021).

How does robot acceleration change the grip force required?​

SCHUNK's guide separates speed from acceleration: speed "is a constant and does not affect the required grip force," while acceleration "imparts a force on all masses that are slowing down or speeding up." Its example: a part held still has 1G acting on it, and "If the robot moves the part upward at 1G, there is now 2G of acceleration acting on the part." SCHUNK states that "Typically, robot acceleration values tend to be between 0.25G and 3G for automation applications"; that range is SCHUNK's statement, not a measured figure for heavy robots.

The following worked figures are UTEC's own illustration, extending SCHUNK's catalog convention by replacing g with g + a. They are not a SCHUNK rating. Take a 200 kg steel part held by friction, µ = 0.1, S = 2:

CaseAcceleration termRequired clamping force, F = m × (g + a) × S ÷ µ
Held still9.81 m/s²200 × 9.81 × 2 ÷ 0.1 = 39,240 N
Lifted at 1G19.62 m/s²200 × 19.62 × 2 ÷ 0.1 = 78,480 N
Held still, pads raising µ to 0.29.81 m/s²200 × 9.81 × 2 ÷ 0.2 = 19,620 N

In the table, the 1G lift doubles the force, and doubling µ halves it. For suction cups, Schmalz marks the acceleration term in its load cases II and III with "keep in mind Emergency Stop situations!" As engineering reasoning, a failure mode is a gripper sized at g that holds the part in normal moves and lets it slide on the first emergency stop (SCHUNK How-To Guide 2021; SCHUNK, Centric Grippers catalog note, accessed 2026; Schmalz, Theoretical Holding Force of a Suction Cup, accessed 2026).

How is a vacuum cup's holding force calculated?​

Schmalz's glossary defines holding force as "the force that can be exerted by a suction cup to grip a workpiece," calculated "by multiplying the pressure difference by the effective suction area of the suction cup (F = Δp x A)." Schmalz adds that it "is a theoretical value, specified without safety factors," and that "It is usual to state the holding force of a suction cup with a relative vacuum of 60%." The 60% figure is Schmalz's convention for quoting a cup's rating, not a recommended operating vacuum.

Schmalz's system-design page gives the required theoretical holding force, F_TH, for what it calls "the three most important and most frequently occurring load cases," and says the calculation "must be based on the worst load case with the highest, theoretical holding force":

  • Load case I, cup horizontal, force vertical: F_TH = m × (g + a) × S
  • Load case II, cup horizontal, force horizontal: F_TH = m × (g + a/µ) × S
  • Load case III, cup vertical, force vertical: F_TH = (m/µ) × (g + a) × S

The safety factor S "must be adjusted in accordance with the condition of workpiece surface": a minimum of 1.5 "for smooth and dense workpieces," and "2.0 or greater must be used for critical, heterogeneous, porous, rough or oiled workpieces." For µ, Schmalz says it "cannot issue generally valid specifications" and that µ "has to be determined correctly through tests"; its reference values are 0.2 to 0.3 for wet surfaces, 0.5 for wood, metal, glass, stone, and similar, and 0.6 for rough surfaces, and for oiled surfaces with standard cups without a specified lateral force it recommends a reference value of µ = 0.1 to 0.3, with tests on the original workpiece for a more precise value (Schmalz, Holding force glossary, accessed 2026; Schmalz, Theoretical Holding Force of a Suction Cup, accessed 2026).

Worked example: what holding force does a vacuum gripper need for a steel sheet?​

Schmalz's own example is a steel sheet of 2.5 × 1.25 m and 61.33 kg, moved at a = 5 m/s² with µ = 0.5:

  • Load case I, S = 1.5: F_TH = 61.33 × (9.81 + 5) × 1.5 ≈ 1,362 N (Schmalz prints 1,363 N)
  • Load case II, S = 1.5: F_TH = 61.33 × (9.81 + 5/0.5) × 1.5 = 1,822 N
  • Load case III, with S = 2 in Schmalz's example: F_TH = (61.33/0.5) × (9.81 + 5) × 2 = 3,633 N

Schmalz's application lifts the sheet off a pallet, moves it to the side, and places it on a machining center; Schmalz states that the rotary motion of load case III is not needed there and takes load case II, 1,822 N, as the design value.

The extension below is UTEC's own illustration, not a Schmalz figure. The same sheet arrives oiled. Schmalz's oiled-surface reference range is µ = 0.1 to 0.3, and it calls for S of 2.0 or greater on oiled workpieces. At µ = 0.1 and S = 2.0, load case II gives F_TH = 61.33 × (9.81 + 5/0.1) × 2.0 = 61.33 × 59.81 × 2.0 = 7,336 N, about four times the dry-sheet value. Assuming, for this illustration only, that 60% relative vacuum corresponds to a pressure difference of 60% of a standard atmosphere, 0.6 × 101,325 Pa ≈ 60,800 Pa, the total effective suction area would be A = F ÷ Δp = 7,336 ÷ 60,800 ≈ 0.121 m², or about 1,210 cm², before any test on the real sheet.

The assumptions are: a rigid sheet, every cup sealed, the acceleration Schmalz gives, sea-level atmosphere, and cup ratings compared with F_TH, which already carries S, while each cup's quoted holding force carries no safety factor. As engineering reasoning, a failure mode is a gripper sized on the dry figure and then run on oiled stock (Schmalz, Theoretical Holding Force of a Suction Cup, accessed 2026; Schmalz, Holding force glossary, accessed 2026).

When does a magnetic gripper suit ferrous parts, and what limits its holding force?​

SCHUNK's product information for its EMH series describes an electro-permanent magnetic gripper that combines AlNiCo and neodymium magnets; an electric current pulse through a coil reverses the polarity of the AlNiCo magnets to switch the gripper on or off. SCHUNK says the gripper "remains in the selected status, even in case of a power failure or emergency stop," and that holding force can be set in four stages through digital inputs: 15, 25, 35, and 100 percent.

The holding force depends on the part. SCHUNK states that "The achievable holding force depends, among other things, on the respective workpiece material," and gives material efficiencies of 100 percent for conventional steel, labelled Fe 360, 90 percent for ferromagnetic crude steel, 70 to 80 percent for tool, case-hardened, and sectional steels, 65 percent for magnetic stainless steel, and 50 percent for cast iron. Workpiece thickness and air gap also change the holding force, but SCHUNK presents those effects as charts without printed values, and no derating figure is given here.

Other limits SCHUNK lists:

  • Heat. Each activation raises the internal temperature, and overheating "reduces the magnetic characteristics and can destroy the product," and the number of activations per minute "must be adjusted so that the maximum permissible product temperature is not reached."
  • Pole extensions. They "alter the magnetic flux and can affect the holding force if incorrectly designed."
  • Environment. The modules are "primarily designed for the use in clean to slightly contaminated environments."
  • Sizing. "Verifying the sizing of the selected unit is necessary, since otherwise overloading can result."

The EMH-RP 045 is listed at 1,360 N holding force, 10.75 cm² magnet area, and a payload of 22.5 kg with the magnet surface horizontal or 9 kg with it vertical. As UTEC's own arithmetic, 1,360 N is the weight of about 139 kg at g, and the document does not state the safety factor or friction value between that figure and the 22.5 kg payload. As engineering reasoning, the payload column, not the holding force, is then the figure to start from, with the sizing verification SCHUNK calls for (SCHUNK EMH RP 045 Product Information 2022, pp. 3, 4, 6, 7, and 10).

How must a gripper behave when air, vacuum, or power is lost?​

As engineering reasoning, a part held in the air is stored energy whatever holds it. OSHA's lockout/tagout rule covers "the servicing and maintenance of machines and equipment in which the unexpected energization or start up of the machines or equipment, or release of stored energy could cause injury to employees," and after lockout or tagout devices are applied, "all potentially hazardous stored or residual energy shall be relieved, disconnected, restrained, and otherwise rendered safe." The regulation does not name gravity. OSHA's enforcement directive, which states that it "is not a standard, regulation or any other type of substantive rule," defines hazardous energy as any energy, including mechanical energy such as gravity, and pneumatic and hydraulic energy, "that could cause injury to employees," and adds that "Danger is only present when energy may be released in quantities or at rates that could injure employees."

The gripper types behave differently on a loss of supply. SCHUNK's electro-permanent magnet stays in its selected state through a power failure or emergency stop, by SCHUNK's description. For vacuum and pneumatic grippers, the state on loss of air is, as engineering reasoning, a design choice. ISO 4414:2010, Pneumatic fluid power — General rules and safety requirements for systems and their components, covers pneumatic systems by its title, and it is cited here at title level only.

The next two sentences are engineering reasoning. A gripper that holds on loss of supply still has to be released deliberately before anyone works under it, and a gripper that drops on loss of supply needs the part supported or lowered first. Blocking gravity loads and bleeding trapped air are covered in Stored Energy and LOTO: Accumulators, Trapped Pressure, and Gravity Loads (OSHA 29 CFR 1910.147-1989, (a)(1)(i) and (d)(5)(i); OSHA Instruction CPL 02-00-147, 2008, Ch. 1 p. 1-6; SCHUNK EMH RP 045 Product Information 2022, p. 4; ISO 4414:2010).

What do the flange and tool-changer standards specify, and what do they leave out?​

Two ISO documents cover the interface between the robot and the tool. ISO 9409-1:2004 fixes the circular mounting plate's main dimensions, designation, and marking for exchangeability and orientation, and expressly leaves out the coupling device's other requirements and any correlation of load-carrying ranges, as set out above.

ISO 11593:2022, Robots for industrial environments — Automatic end effector exchange systems — Vocabulary, "defines terms relevant to automatic end-effector exchange systems used as a part of robot systems in accordance with ISO 10218-2." It is a vocabulary: the iso.org page lists the 2022 text as the second edition, 19 pages, replacing the 1996 edition, which is withdrawn. It is cited here as the terminology source only, with no performance or safety requirement drawn from it.

As engineering reasoning, the load rating of a flange adapter or tool changer therefore comes from its maker's data and from the robot's own limits, not from either standard, and a failure mode is a tool changer chosen by interface size alone (ISO 9409-1:2004; ISO 11593:2022).

How do finger length and tooling mass affect the grip and the robot?​

SCHUNK's guide states that "Grip force diminishes as finger length increases," and its order of work is to "calculate the grip force required, then evaluate the finger length to make sure the gripper has enough grip force at the required finger length." The same guide says there are "generally two categories of grippers; long stroke/low force and short stroke/high force," and says extra stroke adds time, energy, size, weight, and cost.

As engineering reasoning, on the robot side the tool's mass and centre of gravity add to the load the wrist carries. The parallel-axis theorem gives the moment of inertia about a parallel axis as the inertia about the centre of mass plus m × d², the mass times the square of the distance between the axes, and the sizing article applies it to wrist inertia. In FANUC's R-2000iD catalog, three models with the same 2,605 mm reach carry 210, 165, and 100 kg at the wrist with J4 and J5 moment ratings of 1,380, 1,000, and 850 N·m.

As engineering reasoning, longer fingers move the part's centre of gravity away from the flange and raise the wrist moment and inertia at the same time as they lower the grip force, and a failure mode is a finger extension added after the robot was sized (SCHUNK How-To Guide 2021; Moebs, Ling, and Sanny 2016, §10.5, Eq. 10.20; FANUC RR-2000iD catalog 2022, p. 2).

What controls and sensing does end-of-arm tooling need?​

The tooling is part of the intelligence layer, and its sensors confirm the grip that the calculation assumed:

  • Part presence. SCHUNK's EMH carries a presence sensor: after magnetization, an internal sensor measures the change in the magnetic field and outputs part presence once a threshold is exceeded. SCHUNK warns that pole extensions also affect component detection and "Workpieces may no longer be detected."
  • Force selection. The EMH's four holding-force stages are set through digital inputs, and SCHUNK's drawing labels the connector for PLC communication via digital I/O.
  • Vacuum level. As engineering reasoning, a vacuum gripper confirms the vacuum level at the cups before the robot lifts and monitors it during the move, so that the cell stops a move on a leak rather than after a drop.
  • Vision. Where part position varies, vision locates the part before the gripper closes. As engineering reasoning, the gripper's tolerance for position error sets how accurate the vision result must be; calibration is covered in Vision-Guided Robotics and Hand-Eye Calibration Explained.
  • PLC and robot handshake. Gripper commands and sensor states pass between the robot controller and the cell PLC, whose controller tasks can be configured as continuous, periodic, or event.

UTEC Industrial integrates FANUC robotic cells, including vision, with a FANUC design and engineering partner, and builds the Allen-Bradley ControlLogix or CompactLogix cell controls around them. Where the risk assessment makes part retention a safety function, ISO 13849-1:2023 specifies a methodology and provides related requirements, recommendations and guidance for the design and integration of safety-related parts of control systems (SRP/CS) that perform safety functions; it applies to SRP/CS for high demand and continuous modes of operation and does not apply to low demand mode of operation (SCHUNK EMH RP 045 Product Information 2022, pp. 3, 4, and 7; Rockwell Automation 1756-RM094N-EN-P-2025, Ch. 5 p. 39; ISO 13849-1:2023).

Where does end-of-arm tooling sit in the build chain?​

The rest of this paragraph is engineering reasoning. A heavy gripper is built along the same chain as the system it serves. The design fixes the mass and centre-of-gravity budget that the robot sizing uses, and the holding-force calculation above sets the jaw force, cup area, or magnet size. The frame that carries the jaws or cups is a weldment or machined plate whose locating faces set where the part sits relative to the flange, and flatness and position of those faces carry straight into the grip point and the CG. Downstream, the drives and controls select the force stage or vacuum level, and tuning sets the acceleration the grip calculation allowed for.

The reasons welded frames are stress-relieved before final machining are covered in Stress Relief for Machine Bases and Frames Before Final Machining. UTEC Industrial machines to tolerances of ±0.001 in and stress-relieves welded frames with automated vibratory stress relief (VSR). Monitoring then watches the quantities the calculation depends on: SCHUNK says each activation of its magnetic gripper raises internal temperature and that the number of activations per minute "must be adjusted so that the maximum permissible product temperature is not reached," and Schmalz says µ "has to be determined correctly through tests," which as engineering reasoning makes a test with original parts the check that closes the loop between the calculation and the cell (SCHUNK EMH RP 045 Product Information 2022, p. 7; Schmalz, Theoretical Holding Force of a Suction Cup, accessed 2026).

Related Articles

References​

  • ISO 9409-1:2004: Manipulating industrial robots — Mechanical interfaces — Part 1: Plates. ISO, 2004.
  • SCHUNK. How to select the right gripper for your application. ASSEMBLY How-To Guide, April 2021.
  • SCHUNK. Centric Grippers (web catalog, recommended-workpiece-weight note). SCHUNK SE & Co. KG (undated web documentation, accessed September 2026).
  • Baker, D.W. and Haynes, W. Engineering Statics: Open and Interactive. Colorado State University and Massachusetts Maritime Academy, 2026.
  • J. Schmalz GmbH. Theoretical Holding Force of a Suction Cup (Vacuum Knowledge). Schmalz (undated web documentation, accessed September 2026).
  • J. Schmalz GmbH. Holding force (Know-How glossary). Schmalz (undated web documentation, accessed September 2026).
  • SCHUNK. Product Information: Magnetic gripper EMH RP 045. SCHUNK SE & Co. KG, 2022.
  • OSHA 29 CFR 1910.147-1989: The Control of Hazardous Energy (Lockout/Tagout). Occupational Safety and Health Administration, 1989.
  • OSHA Instruction CPL 02-00-147: The Control of Hazardous Energy – Enforcement Policy and Inspection Procedures. Occupational Safety and Health Administration, 2008.
  • ISO 4414:2010: Pneumatic fluid power — General rules and safety requirements for systems and their components. International Organization for Standardization, 2010.
  • ISO 11593:2022: Robots for industrial environments — Automatic end effector exchange systems — Vocabulary. ISO, 2022.
  • Moebs, W., Ling, S. J., and Sanny, J. University Physics Volume 1. OpenStax, 2016.
  • FANUC RR-2000iD(E)-03a: FANUC Robot R-2000iD. FANUC Corporation, 2022.
  • Rockwell Automation 1756-RM094N-EN-P-2025: Logix 5000 Controllers Design Considerations. Rockwell Automation, 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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