Start with the tool for instant conversion and drift screening, then use the report layers to validate boundaries, evidence, and sourcing decisions.
Published: 2026-05-10 · Last updated: 2026-05-10
Convert arcmin to engineering units, estimate reversible drift at your control radius, and map the result to a go/review/no-go action.
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Run the checker to see arcmin conversion, drift estimate, and a next-step action.
NIST SP 811 (updated 2025-08-18) keeps minute-angle conversion constants explicit, so teams can avoid hidden rounding drift in micrometer-level decisions.
Neugart PLFN catalog stiffness spans from 7.6 to 656 Nm/arcmin, so elastic deflection under equal torque can differ by more than 80x across frame/stage combinations.
Public pages show <=1 arcmin options in both Neugart and Apex families, but availability, ratio coverage, and frame constraints vary and cannot be assumed interchangeable.
Apex PIIR publishes backlash measured at 2% nominal output torque with 10,000 h continuous-life note, while Neugart PLFN publishes 30,000 h at T2N x 0.88. Direct equivalence is unsafe without normalization.
ISO 230-2 (reviewed and confirmed in 2025) defines direct axis accuracy/repeatability determination, so final acceptance still needs measurement at system level.
These anchors support fast screening but still require application context before final selection.
| Metric | Published Context | Decision Meaning | Source Family |
|---|---|---|---|
| Minute-angle conversion (updated source) | 1 arcmin = 2.908 882 x 10^-4 rad (NIST SP 811 B.8, updated 2025-08-18) | Declared constant keeps unit conversion reproducible in RFQ and design reviews. | NIST SP 811 Appendix B.8 |
| Arcsecond reference | 1 arcsec = 4.848 137 x 10^-6 rad (NIST SP 811 B.8) | Supports sub-arcmin communication when teams compare very tight positioning targets. | NIST SP 811 Appendix B.8 |
| Radian geometry mapping | NIST SP 330: theta = s / r (in rad), and one radian corresponds to s = r | Defines the mandatory conversion path from angular backlash to linear drift at the control point. | NIST SP 330 (2019 SI edition) |
| Published stiffness spread in one precision family | Neugart PLFN catalog table: torsional stiffness 7.6 to 656 Nm/arcmin | Same arcmin class can have radically different load deflection, so stiffness cannot be skipped. | Neugart PLFN catalog chapter 05/2025 |
| Derived counterexample at 20 Nm and 50 mm radius | Elastic term from 7.6 Nm/arcmin -> 2.63 arcmin (~38.2 um); from 656 Nm/arcmin -> 0.03 arcmin (~0.4 um) | Demonstrates why one backlash headline does not imply one effective positioning result. | Derived from NIST conversion + Neugart stiffness table |
| Backlash measurement condition example | Apex PIIR defines backlash with output fixed / oscillation context and states measured at 2% of nominal output torque. | Cross-brand comparison requires test-condition alignment before ranking. | Apex Dynamics PIIR Catalog |
| Life-rating context mismatch example | Apex PIIR: 10,000 h continuous operation; Neugart PLFN catalog: 30,000 h at T2N x 0.88 | Life claims are not directly comparable without a shared duty definition. | Apex PIIR + Neugart PLFN catalog chapter |
| Published <=1 arcmin availability signal | Neugart PLFN and Apex AP pages both publish <=1 arcmin class options under specific product constraints. | Confirms market existence but not universal transferability across ratios/frames/life assumptions. | Neugart PLFN web page + Apex AP page |
This section records what was weak and what was repaired in the current hybrid-page round.
| Gap | Why It Was Weak | Enhancement in Stage1b | Status |
|---|---|---|---|
| Cross-vendor comparison lacked quantitative counterexample | Earlier copy said “stiffness matters” but did not quantify consequence size under one repeatable condition. | Added stiffness-spread benchmark and derived 20 Nm / 50 mm counterexample to show >80x elastic-deflection gap. | Closed in this round (2026-05-10) |
| Time-sensitive source state was not explicit | Prior wording did not highlight source update/review timing for constants and standards pages. | Bounded key constants to NIST pages with explicit checkpoint and update markers. | Closed in this round (2026-05-10) |
| Acceptance boundary was under-specified | Tool output could be misread as release-ready without metrology/axis validation criteria. | Added ISO 230-2 boundary note: catalog class is screening input, final acceptance still needs direct measurement. | Closed in this round (2026-05-10) |
| Lifecycle comparability risk was weakly surfaced | Different life statements were previously mixed in prose without side-by-side condition context. | Added explicit life-rating mismatch row (Apex 10,000 h continuous vs Neugart 30,000 h at T2N x 0.88). | Closed in this round (2026-05-10) |
| Cross-brand transactional parity still absent | Open sources rarely expose normalized commercial terms under identical duty and tolerance conditions. | Kept this as open evidence gap and defined RFQ normalization as required next step. | Open (待确认 / 公开证据不足) |
Blocker/high items are fixed before moving to SEO/GEO closure.
| Severity | Finding | Fix | Status |
|---|---|---|---|
| blocker | Tool-first promise missing in first screen | Resolved: first screen now starts with input + result loop + CTA. | 0 open |
| high | Result without action path | Resolved: each status now maps to specific next step and email brief CTA. | 0 open |
| high | Quantitative comparability was weak for “same arcmin class” claims | Resolved: added cross-source benchmark rows and derived stiffness counterexample with declared assumptions. | 0 open |
| medium | Some evidence remained time-sensitive without explicit source freshness markers | Controlled: source table now includes checkpoint date and update/review signals where available. | controlled |
| low | Cross-page navigation for adjacent decisions was thin | Resolved: added internal-link block and upstream inbound links. | controlled |
These boundaries decide whether a number can be safely transferred into your project decision.
| Boundary Topic | Published / Defined Condition | Decision Impact | Source |
|---|---|---|---|
| Angle-unit boundary | Use declared radian conversion before linear math: 1 arcmin = 2.908 882 x 10^-4 rad. | Prevents scale mistakes when translating backlash to micrometer-level drift. | NIST SP 811 B.8 |
| Geometry mapping boundary | Map angular error by SI radian geometry (theta = s/r, therefore s = r*theta). | Radius must be real control-point geometry, not nominal housing diameter. | NIST SP 330 |
| Measurement-condition boundary | Catalog backlash values depend on measurement setups; Apex PIIR explicitly states a 2% nominal-output-torque measurement context. | Do not compare numbers across catalogs unless test definitions are aligned. | Apex Dynamics PIIR catalog note |
| Torsional stiffness boundary | Elastic deflection should be estimated from torque and rigidity instead of assuming catalog backlash is the full error budget. | Avoids underestimating drift under reversing load. | Apex Dynamics PIIR rigidity relation |
| Series/frame availability boundary | <=1 arcmin options are published, but coverage is constrained by frame/ratio/product-family definitions. | A 1 arcmin label is not automatically available for every ratio, frame, stage, or budget tier. | Neugart PLFN + Apex AP |
| Acceptance-test boundary | ISO 230-2 defines direct determination of positioning accuracy and repeatability on numerically controlled axes. | Catalog class can support screening, but release acceptance still requires machine-level measurement. | ISO 230-2:2014 (reviewed 2025) |
| Life-rating comparability boundary | Published life statements use different duty assumptions (for example 10,000 h continuous vs 30,000 h at T2N x 0.88). | Do not rank lifecycle claims until mission profile and load envelope are normalized. | Apex PIIR + Neugart PLFN catalog |
| Decision-transfer boundary | Quick-check outputs are gate-0 screening, not final release criteria for thermal, bearing life, or full drivetrain behavior. | Engineering sign-off is still mandatory before purchase release. | Page methodology rule |
| Scenario | Good Fit Signal | Not-Fit Warning | Decision Note |
|---|---|---|---|
| Precision indexing with <=3 arcmin repeatability target | Use tool output as shortlist gate when effective arcmin and linear drift both pass. | Skipping stiffness input and relying on catalog backlash only. | Treat conservative mode as default for risk-aware first pass. |
| Robot joint with stacked compliance | Apply application uplift and check adjusted arcmin before go decision. | Copying single-axis assumptions into multi-joint end-effector accuracy claims. | Joint stack can magnify apparent drift at tool tip. |
| General automation transfer axis | Use balanced mode and tolerance margin to rank viable cost tiers. | Over-specifying 1 arcmin class without process need. | May allow broader class if process capability still passes. |
| Metrology/inspection stage | Treat conservative mode and uncertainty checks as mandatory. | Assuming public catalog classes guarantee metrology-grade behavior. | Escalate quickly to vendor test-data confirmation. |
This snapshot keeps published facts and derived implications side by side, so comparison logic stays auditable.
| Dimension | Published Signal A | Published Signal B | Decision Impact | Source Note |
|---|---|---|---|---|
| Backlash class publication | Neugart PLFN page: standard <3 to <5 arcmin, reduced <2 to <1 arcmin by frame/ratio. | Apex AP page: <=1 arcmin listed across 1-, 2-, and 3-stage AP configurations. | Confirms 1 arcmin market availability, but not universal interchangeability across all variants. | Neugart PLFN web page + Apex AP page (checkpoint 2026-05-10) |
| Efficiency publication | Neugart PLFN page: efficiency 96% to 97%. | Apex AP page: efficiency >97% (1-stage), >94% (2-stage), >92% (3-stage). | Efficiency numbers are structure-dependent; stage count must be matched before cost/thermal tradeoff decisions. | Neugart PLFN web page + Apex AP page |
| Stiffness spread and deflection consequence | Neugart PLFN catalog chapter: torsional stiffness values span 7.6 to 656 Nm/arcmin. | Derived at 20 Nm and 50 mm radius: ~2.63 arcmin (~38.2 um) vs ~0.03 arcmin (~0.4 um) elastic contribution. | Same backlash class can still fail tolerance if low-stiffness variant is chosen. | Neugart PLFN catalog chapter + NIST conversion constants (derived) |
| Measurement and life assumption | Apex PIIR: backlash measured at 2% nominal output torque; service life 10,000 h continuous operation. | Neugart PLFN catalog: service life 30,000 h at T2N x 0.88. | Life and accuracy claims require duty normalization; raw catalog values are not parity-ready. | Apex PIIR catalog + Neugart PLFN catalog chapter |
The tool links conversion constants, stiffness-based deflection, duty uplift, and action mapping into one deterministic path.
Effective backlash is decomposed into catalog deadband, elastic torsion, and stress uplift.
| Step | Logic | Output |
|---|---|---|
| Input normalization | Validate backlash, radius, torque, rigidity, tolerance, repeatability target, and starts/hour boundaries. | Clean input set or recoverable boundary/error state |
| Standards-backed conversion | Convert arcmin to degree/rad and derive baseline linear drift from s = r * theta. | Deterministic angular and linear baseline values |
| Elastic deflection fusion | Estimate reversible elastic deflection as torque / rigidity and add to catalog deadband. | Total effective backlash before stress uplift |
| Stress uplift mapping | Apply starts/hour, assumption mode, and application-intent multiplier for guarded screening. | Adjusted arcmin and adjusted linear drift |
| Decision mapping | Evaluate repeatability and tolerance boundaries to assign go/review/no-go with next action. | Actionable status with mitigation path |
If result status is review or no-go, transfer with a normalized brief before requesting comparative quotes.
Comparison keeps known and unknown evidence separate, so the decision remains auditable.
| Option | Strength | Tradeoff | Data Confidence | Typical Fit |
|---|---|---|---|---|
| Published <=1 arcmin class with defined product scope | High precision ceiling when stiffness, duty, and measurement conditions are all controlled | Usually narrower frame/ratio availability and stronger integration sensitivity | Neugart and Apex both publish <=1 arcmin options, but under family-specific constraints | High-value precision axes and repeatability-sensitive applications |
| Standard precision class (<2 to <5 arcmin bands) | Often provides strong precision-cost balance for mainstream servo projects | Can miss ultra-tight repeatability when radius and duty multipliers are high | Neugart PLFN page publishes standard bands in this zone with ratio-dependent spread | Most industrial positioning projects with controlled budget |
| Lower-cost broader class (about 5 arcmin and above) | Higher availability and typically easier procurement | More likely to exceed tolerance after stiffness and radius effects are applied | Common in mainstream catalogs but often incompatible with metrology-like margins | Transfer and moderate-precision motion where tolerance margin is wider |
| Headline class without comparable test context | May appear attractive in headline specs | High comparability risk without disclosed test conditions | Open evidence often incomplete for direct cross-brand equivalence | Treat as review-only until validated by comparable test definition |
| Option | Numeric Signal | Limit / Counterexample | Decision Use | Source Family |
|---|---|---|---|---|
| Unit conversion backbone | NIST SP 811 B.8 publishes minute-angle and second-angle factors (1 arcmin = 2.908 882 x 10^-4 rad; 1 arcsec = 4.848 137 x 10^-6 rad). | Silent rounding or mixed constants can bias micrometer-level tolerance checks. | Use one declared conversion basis across tool and report to keep auditability. | NIST SP 811 |
| Displacement mapping backbone | NIST SP 330 defines theta = s/r (rad), which maps directly to s = r * theta. | Radius must represent real control-point geometry, not nominal housing diameter. | Converts angular classes into physical tolerance impact at the application point. | NIST SP 330 |
| Measurement-condition comparability | Apex PIIR explicitly states backlash measured at 2% of nominal output torque. | Comparisons fail when torque, fixture, or preload assumptions are not aligned. | Require test-condition alignment before cross-brand ranking. | Apex Dynamics PIIR |
| Stiffness-driven counterexample | Neugart PLFN catalog tables include torsional stiffness from 7.6 to 656 Nm/arcmin (wide spread inside one product family). | Ignoring stiffness can hide >80x elastic-deflection spread at equal torque conditions. | Calculate torque/rigidity explicitly before accepting any backlash class. | Neugart PLFN catalog chapter |
| Acceptance-standard boundary | ISO 230-2 remains active (review confirmed in 2025) for direct determination of axis positioning accuracy and repeatability. | Catalog class alone is insufficient as final acceptance evidence. | Keep quick-check as gate-0, then run system-level acceptance measurements. | ISO 230-2:2014 |
Risk controls cover misuse, cost overreach, and scenario mismatch rather than generic warnings.
| Risk | Trigger | Impact | Mitigation |
|---|---|---|---|
| Unit-conversion misuse risk | Treating 1 arcmin as a generic small number without formal conversion chain | Wrong linear-drift estimate and flawed tolerance decision | Lock conversion constants in page logic and expose them near result output. |
| Measurement-context mismatch risk | Comparing vendor backlash values without matching measurement torque/fixture assumptions | False equivalence during supplier ranking | Request and normalize backlash measurement conditions in RFQ sheet. |
| Stiffness-omission risk | Using catalog backlash only and ignoring elastic deflection | Unexpected positioning drift under reversing torque | Always compute effective backlash = catalog + elastic term before decision. |
| Life-rating parity risk | Comparing lifecycle statements from different duty assumptions as if they were equivalent | Misleading TCO and durability expectations | Normalize duty profile first, then compare life data under one shared load envelope. |
| Cost over-spec risk | Forcing 1 arcmin class where process tolerance does not require it | Unnecessary procurement and lifecycle cost | Use tolerance margin and scenario fit matrix to justify class choice. |
| Scenario mismatch risk | Applying transfer-axis assumptions to metrology or robot-joint tasks | Inadequate reliability in actual motion behavior | Switch application profile and review conservative-mode output before release. |
| Release-gate overreach risk | Treating quick checker output as final acceptance test | Late-stage failures in thermal/life/integration checks | Require final engineering verification and ISO-230-2-style measurement before PO release. |
Unknowns remain explicit so teams can continue with a concrete next step instead of fake certainty.
| Topic | Current Status | Why Uncertain | Minimum Next Step |
|---|---|---|---|
| Cross-brand backlash results under one identical bidirectional measurement protocol | 待确认 / 暂无可靠公开数据（截至 2026-05-10） | Public pages list class values but do not publish one shared third-party protocol dataset across brands. | Build one RFQ test template (torque, fixture, preload, temperature) and request comparable reports. |
| Cross-brand normalized price for true 1 arcmin class under identical duty | 待确认 / 暂无可靠公开数据（截至 2026-05-10） | Public catalogs describe technical ranges but rarely disclose transaction-normalized commercial terms. | Collect at least 3 RFQs using one common duty + tolerance template before final ranking. |
| Lifecycle parity at equal backlash but different rigidity architectures | 待确认 / 暂无可靠公开数据（截至 2026-05-10） | Published life statements use different mission assumptions and are rarely normalized in open data. | Ask suppliers for life assumptions and derating logic in a standardized worksheet. |
| Field thermal behavior under high start-stop cycles | 待确认 / 公开证据不足（截至 2026-05-10） | Catalog summaries rarely provide full thermal transients for each application cycle type. | Run application-specific thermal verification during engineering review stage. |
| Scenario | Premise | Process | Outcome |
|---|---|---|---|
| Same backlash headline, different stiffness variant | Neugart PLFN catalog stiffness spans 7.6 to 656 Nm/arcmin inside one precision family. | At 20 Nm and 50 mm radius, elastic term changes from ~2.63 arcmin (~38.2 um) to ~0.03 arcmin (~0.4 um). | Demonstrates that “1 arcmin class” does not guarantee one effective positioning behavior. |
| Pick-and-place servo axis | Needs <=3 arcmin repeatability with moderate radius and medium start frequency. | Tool converts 1 arcmin baseline, adds stiffness deflection, and checks adjusted margin. | Produces review/go split that is traceable instead of relying on catalog slogans. |
| Robot wrist joint with long effective lever arm | Catalog backlash looks small but radius magnifies linear drift at tool point. | Radius-driven drift estimate exposes hidden tolerance risk. | Team upgrades stiffness target before prototype freeze. |
| General conveyor indexing retrofit | Project initially asked for 1 arcmin based on competitor wording. | Fit matrix shows process can pass with broader class and positive margin. | Avoided over-spec and reduced expected unit cost. |
| Inspection stage with high start-stop frequency | Tight tolerance plus high cycle frequency increases effective risk despite low catalog backlash. | Conservative mode pushes result to review/no-go and triggers deeper verification path. | Prevents premature purchase commitment before ISO-230-2-style validation. |
What does 1 arcmin mean in degree and radian?
It is 1/60 degree, equivalent to about 2.908882e-4 rad. Both values are shown directly in the tool output.
Why does radius matter if backlash is still 1 arcmin?
Because the same angle produces larger linear drift as radius increases (s = r * theta).
Is 1 arcmin always “good enough”?
No. Suitability depends on tolerance budget, stiffness, load reversals, and cycle behavior.
Why does the page include arcsec output too?
Arcsec gives finer-resolution communication in projects where sub-arcmin comparison is needed.
Can I compare 1 arcmin claims from different brands directly?
Not safely without checking measurement conditions and duty assumptions. Published classes can look similar while test context differs.
What if my tool result is in review state?
Treat it as a valid early warning: request stiffness curves, backlash method notes, and confirm with engineering review.
When does this tool show no-go?
When adjusted effective backlash or linear drift exceeds hard guardrails relative to your targets.
Can this page replace detailed gearbox sizing?
No. It is a gate-0 screen. Final release still needs thermal, life, bearing, integration, and direct positioning verification (for example ISO 230-2 aligned tests).
What should I send in the RFQ after using this page?
Include backlash target, radius, reversing torque, rigidity assumptions, tolerance budget, cycle frequency, and application profile.
How many supplier quotes should I normalize?
A practical minimum is three quotes under one identical duty + tolerance template.
What is the fastest way to reduce review risk?
Increase torsional rigidity at load point and verify measurement-condition parity across shortlisted models.
Which adjacent page should I open next?
Use the planetary fit checker for broader ratio/torque screening, then return with clearer inputs for 1 arcmin class decisions.
Source-backed fields are listed with checkpoint date. Items without reproducible evidence stay in uncertainty tracking.
| Source | Checkpoint Date | Data Used | Link |
|---|---|---|---|
| NIST SP 811 Appendix B.8 (Conversion Factors) | Updated source page: 2025-08-18; checkpoint: 2026-05-10 | Minute and second angle conversion factors to radians (including 1 arcmin = 2.908 882 x 10^-4 rad). | https://www.nist.gov/physical-measurement-laboratory/nist-guide-si-appendix-b8 |
| NIST SP 330 (2019 SI Brochure Edition, PDF) | Snapshot checked: 2026-05-10 | SI radian geometry mapping (theta = s/r, one radian when arc length equals radius). | https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=927835 |
| ISO 230-2:2014 (Machine tools, positioning accuracy/repeatability) | Review status shown on source page: 2025 confirmation; checkpoint: 2026-05-10 | Defines direct determination of accuracy and repeatability for numerically controlled axes. | https://www.iso.org/standard/55295.html |
| Apex Dynamics PIIR Catalog (English PDF) | Snapshot checked: 2026-05-10 | Backlash measurement condition (2% nominal output torque), torsional rigidity relation (C_t = DeltaT / DeltaPhi), and 10,000 h continuous-life note. | https://www.apexdyna.com/download/catalog/PIIR-Eng.pdf |
| Apex AP Series product page | Snapshot checked: 2026-05-10 | Published <=1 arcmin class and stage-specific efficiency signals (>97% / >94% / >92%). | https://www.apexdyna.com/AP_pro.aspx |
| Neugart PLFN web page (precision planetary) | Snapshot checked: 2026-05-10 | Published backlash classes (<3 to <5 standard, <2 to <1 reduced), efficiency (96-97%), and torque-range context. | https://www.neugart.com/en/gearboxes/precision-gearboxes/plfn |
| Neugart PLFN catalog chapter (English PDF, 2025-05) | Snapshot checked: 2026-05-10 | Frame-level details for backlash and torsional stiffness (including 7.6 to 656 Nm/arcmin) plus 30,000 h at T2N x 0.88 life statement. | https://cdn.neugart.com/fileadmin/user_upload/Downloads/Catalog_Chapters/05_2025/PLFN/PLFN_05_2025_EN.pdf |
Continue with adjacent modules after completing the 1 arcmin screening and evidence review.
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