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The End Effector

Map the Payload-Reach Envelope

Payload and reach define a performance envelope together. The applications a robot can serve are determined by where that envelope overlaps task demands.

Parameter ExplorerEarthwardAtomsApril 19, 2026
Payload-Reach Envelope
10 kg
1 kg50 kg
1300 mm
300 mm2500 mm
UR10e
UR20
FANUC M-20iD
Your spec

Match: Machine tending, Palletizing

2robots
Electronics assemblyMachine tendingBin pickingPalletizing40060080010001200140016001800200022002400Reach (mm)5101520253035404550Payload (kg)

Teardown: Envelope Equations

UR10e Payload Limit at Reach

payload_limit = 12.5 if reach 900, else 12.5 - (reach - 900) x (4.5 / 400)

At 1300 mm: max = 8.0 kg | you: 10 kgOUTSIDE envelope

UR20 Payload Limit at Reach

payload_limit = 20 if reach 1200, else 20 - (reach - 1200) x (5 / 550)

At 1300 mm: max = 19.1 kg | you: 10 kgINSIDE envelope

FANUC M-20iD Payload Limit at Reach

payload_limit = 20 if reach 1300, else 20 - (reach - 1300) x (8 / 510)

At 1300 mm: max = 20.0 kg | you: 10 kgINSIDE envelope

Envelope Check Result

matched_robots = UR20, FANUC M-20iD

Linear interpolation from flatReachEnd to maxReach for each robot. Inside if payload payload_limit AND reach maxReach.

Assumptions

medium impact

Payload-at-reach curves are linearized approximations. Actual envelopes are slightly curved due to nonlinear moment loading across joint configurations.

medium impact

The model assumes worst-case arm configuration (fully extended horizontally). Many tasks operate within a smaller effective workspace where higher payloads are achievable.

low impact

Application zones (electronics assembly, machine tending, bin picking, palletizing) are defined as rectangular regions. Real application requirements form irregular shapes.

Sources

Universal Robots UR10e Technical Specifications (2024) — 12.5 kg payload, 1,300mm reach, ±0.05mm repeatability

Universal Robots UR20 Technical Specifications (2023) — 20 kg payload, 1,750mm reach, ±0.1mm repeatability

FANUC M-20iD Datasheet (2024) — 20 kg payload, 1,810mm reach, ±0.02mm repeatability

Tip Deflection

0.034 mm

Near datasheet spec

Teardown: Deflection Estimate

Structural Deflection Estimate

deflection_mm = (payload_kg x reach_mm²) / 5e8

deflection(10, 1300) = 10 x 1300² / 5e8 = 0.0338 mm

Simplified cantilever beam approximation: deflection = (F x L²) / k, where F = payload force, L = reach, and k = 5e8 is a composite stiffness constant. The quadratic relationship with reach is the key insight: doubling reach quadruples deflection.

Classification Rules

IF deflection < 0.05 mm Near datasheet spec

IF 0.05 ≤ deflection ≤ 0.2 mm Moderate deflection; verify in deployment

IF deflection > 0.2 mm Significant deflection; field accuracy lags datasheet

Assumptions

high impact

Uses a single composite stiffness constant (5e8) for all three robot types. In practice, the FANUC M-20iD is significantly stiffer than the UR series due to its heavier, more rigid structure (~190 kg vs. ~33.5 kg).

medium impact

Deflection model ignores joint compliance (backlash and gear elasticity), which adds 0.01–0.05mm of positioning uncertainty independent of structural deflection.

medium impact

Thermal effects are not modeled. After 2+ hours of operation, thermal expansion of aluminum arm links can add 0.02–0.1mm of drift.

Sources

Universal Robots (2024). Application note: Accuracy vs. Repeatability in UR Cobots

Gere, J. M. & Goodno, B. J. (2018). Mechanics of Materials. 9th ed. — Beam deflection theory

THE DEBRIEF

At 10kg payload and 1300mm reach, 2 robots qualify: UR20, FANUC M-20iD. Machine tending requires this combination.

Int. 2.2

What to take away

  • 01UR10e carries 12.5 kg within 900mm of reach but drops to 8 kg at its 1,300mm full extension, which is why the UR20 opened a palletizing market that the UR10e could never serve.
  • 02FANUC's M-20iD hits 5x better repeatability than the UR series (±0.02mm vs ±0.1mm) because it weighs 190 kg versus 33.5 kg, which is stiffness not precision engineering per se.
  • 03Structural deflection scales with reach squared: doubling reach quadruples positional error under load.
  • 04Datasheet specs are measured at 20°C in rated configurations; field conditions typically degrade them 2 to 5 times, a gap every integrator should price in.

Robot arm datasheets print two headline numbers: payload capacity and repeatability. Both are real specifications, and both are misleading on their own. A robot that carries 20 kg at its base cannot carry 20 kg at full reach, because moment loading cuts capacity as the arm extends. A robot that repeats to 0.02mm in a warmed-up lab cannot repeat to 0.02mm under production load after two hours of duty cycling. The combination of payload and reach defines a performance envelope, and that envelope is what determines which applications the robot can actually serve.

Payload and reach together determine which arm can do the job. This interactive plots three reference arms on a payload-reach grid: the Universal Robots UR10e (12.5 kg, 1,300mm), the UR20 (20 kg, 1,750mm), and the Fanuc M-20iD (Fanuc; 20 kg, 1,810mm). Four application zones are overlaid: electronics assembly, bin picking, machine tending, and palletizing. Drag the payload and reach sliders and a marker moves across the chart, reporting whether your point falls inside any of the three arms' envelopes and inside any of the application zones.

Envelope curves are linearized from the published UR10e, UR20, and FANUC M-20iD datasheets. The deflection estimate uses a simplified cantilever-beam approximation calibrated to match published cobot-class deflection data. Stiffness is treated as a single composite constant across all three arms, which understates how much stiffer the FANUC M-20iD is thanks to its heavier structure. Joint backlash, thermal expansion, and the difference between rated and field performance are not modeled; consult Universal Robots' thermal compensation application notes before promising datasheet accuracy in deployment.

Start at the defaults (10 kg, 1,300mm) and notice that your point sits inside both the UR10e and UR20 envelopes, on the boundary between machine tending and bin picking. Then push payload to 20 kg at 1,700mm. The UR10e drops out entirely, but the UR20 envelope still covers you because Universal Robots redesigned the arm specifically to open this region. Drag further, to 40 kg at 2,000mm, and no standard cobot applies; the palletizing application zone extends there, but covering it requires a heavier industrial arm or a custom solution. That transition is where a mechanical redesign creates a market, not where marketing finds one.

Referenced in

Revision history · 2
  1. Apr 24, 2026tee-ix-int-02-02-20260424-ec055c

    Narrative lint — voice, specificity, structure.

  2. Apr 19, 2026tee-ix-int-02-02-20260419-067d18

    Initial editorial draft.

Originally published alongside Core Robotics

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