STATIC FIXTURE DESIGN WORKSHEET
Estimate lever, alignment and reference-force contributions at one static load point. Use the illustrative worksheet to prepare your engineering review.
Survey each force application point relative to the sensor origin. Use M = r × F with signed coordinates; three arm lengths alone do not establish a six-component wrench.
Source basis: JCGM 100:2008 — Guide to the expression of uncertainty in measurement. Engineering recommendations are the site’s interpretation; no source endorses this worksheet.
Correct known gravity, buoyancy and geometry biases first. If a correction is unknown, mark the budget incomplete rather than hiding it inside a generic random allowance.
Source basis: JCGM 100:2008 — Guide to the expression of uncertainty in measurement. Engineering recommendations are the site’s interpretation; no source endorses this worksheet.
Enter standard u = U/k on the same percent-of-reading basis as the force at the test point. An OIML weight class or ISO 376 class does not specify a universal uncertainty.
Source basis: OIML R 111:2004 — Weights: metrological and technical requirements. Engineering recommendations are the site’s interpretation; no source endorses this worksheet.
The worksheet uses 4:1 and 2:1 as planning bands only. Agree a decision rule using the full system uncertainty and measured error before deciding whether a sensor meets a specification.
Source basis: ILAC-G8:09/2019 — Decision rules and statements of conformity. Engineering recommendations are the site’s interpretation; no source endorses this worksheet.
Check mounting, cables, load reversal and combined loads. A static reference budget excludes sensor response and cannot validate dynamic bandwidth.
Source basis: EMPIR 18SIB08 ComTraForce — Final publishable report (VTT, 2025). Engineering recommendations are the site’s interpretation; no source endorses this worksheet.
Use a right-handed sensor frame and define r from the sensor origin to the load point. The following equations are rigid-body statics. The worksheet is a component sensitivity screen; it does not solve a load-frame Jacobian or reconstruct load-point coordinates.
| Quantity | Relation | Required record | Boundary |
|---|---|---|---|
| Force at sensor | F_s = R F_fixture | Frame rotation R and axis signs | R must be measured or defined |
| Moment at sensor | M_s = R M_fixture + r × F_s | Offset r in metres | Include applied free moment separately |
| Cross product | Mx=ryFz−rzFy; My=rzFx−rxFz; Mz=rxFy−ryFx | Signed positions and forces | A single force cannot generate an arbitrary wrench |
| Covariance | u²(y)=Σci²ui² + 2Σcicj uij | Correlated geometry and reference terms | Independent RSS is an assumption here |
Source basis: JCGM 100:2008 — Guide to the expression of uncertainty in measurement. Engineering recommendations are the site’s interpretation; no source endorses this worksheet.
Illustrative example: F=100 N, L=0.250 m, rectangular arm-location half-range ±0.020 mm and rectangular temperature half-range ±2 K. With assumed aluminum CTE 23.4 ppm/K and standard u(F)=0.010 N, the geometry contribution and reference force contribution can be recomputed below. Coefficients are design assumptions, not material certificates.
| Step | Calculation | Result | Interpretation |
|---|---|---|---|
| Thermal half-range | 0.250 × 23.4×10⁻⁶ × 2 | 11.7 µm | A bounded residual, not a measured drift |
| Standard arm uncertainty | sqrt((20/√3)² + (11.7/√3)²) | 13.38 µm | Independent rectangular components |
| Moment components | u_geom=100×13.38×10⁻⁶; u_ref=0.250×0.010 | 0.001338 N·m; 0.002500 N·m | Same units before combining |
| Subtotal expanded estimate | 2×sqrt(0.001338² + 0.002500²) | 0.00567 N·m (k=2) | Excludes alignment, friction, repeatability and covariance |
Source basis: JCGM 100:2008 — Guide to the expression of uncertainty in measurement. Engineering recommendations are the site’s interpretation; no source endorses this worksheet.
A tilted force produces transverse F sinθ and primary-axis F cosθ. The transverse error is first order in small angle; axial loss is second order. The calculator uses transverse component magnitude times standard angular uncertainty, assuming unknown rotation components are independent.
| Tilt (illustrative) | Transverse at 1,000 N | Primary-axis loss | Action |
|---|---|---|---|
| 0.2 mrad | 0.200 N | 0.000020 N | Compare with receiving-axis allowance |
| 1.0 mrad | 1.000 N | 0.000500 N | Measure alignment under load |
| 5.0 mrad | 5.000 N | 0.012500 N | Correct rotation and recheck residuals |
| Worksheet θ input | Half-range / √3 | Not a deterministic tilt correction | Document the assumed distribution |
Source basis: JCGM 100:2008 — Guide to the expression of uncertainty in measurement. Engineering recommendations are the site’s interpretation; no source endorses this worksheet.
Bearing type alone cannot establish parasitic-force uncertainty. The calculator contains deliberately illustrative effective residual coefficients for sensitivity comparisons. Measure reaction loads, load reversal and elastic restoring moments before replacing assumptions with a validated rig model.
| Option | Potential benefit | Cost or limitation | Verification |
|---|---|---|---|
| Air bearing | Low contact friction | Air supply, cleanliness and alignment effort | Measure residuals with pressure variation |
| Crossed flexure | No sliding contact | Restoring torque, travel and fatigue limits | Characterize torque vs angle and hysteresis |
| Knife edge | Simple passive pivot | Wear and contact relocation | Repeat load placement and reversal |
| Spherical joint or rigid clamp | Compact, easy to assemble | Constraint reactions depend on geometry | Measure side loads; avoid assumed zero parasitics |
Source basis: EMPIR 18SIB08 ComTraForce — Final publishable report (VTT, 2025) · JCGM 100:2008 — Guide to the expression of uncertainty in measurement. Engineering recommendations are the site’s interpretation; no source endorses this worksheet.
For true mass m in air, F=m g_local(1−ρ_air/ρ_mass). A conventional-mass certificate needs the appropriate mass-convention conversion. The calculator only records whether corrections are confirmed; it does not calculate local gravity or buoyancy. Reference u must include their residual uncertainties.
| Evidence | Known or unknown | How to use it | Fallback |
|---|---|---|---|
| Mass certificate | Mass correction, U, k and density needed | Convert mass convention; derive standard force u | Request the certificate and density basis |
| Local gravity | Site value and uncertainty needed | Apply measured or justified site value | Unconfirmed → incomplete estimate |
| Buoyancy | At ρ_air=1.2 and ρ_mass=8000 kg/m³, ρ_air/ρ_mass=150 ppm | Illustrative buoyant reduction for true mass | Determine density and mass convention |
| Reference transducer | Certificate U, coverage and load range needed | u=U/k; convert absolute or FS basis to reading basis | Class label alone is insufficient |
Source basis: OIML R 111:2004 — Weights: metrological and technical requirements · JCGM 100:2008 — Guide to the expression of uncertainty in measurement. Engineering recommendations are the site’s interpretation; no source endorses this worksheet.
A rotational spring approximation gives θ=M/kθ. Translational stiffness must use matching force and length units. The calculator uses the entered moment resultant only; it excludes additional moments from force offsets, mounting deformation and nonuniform mode shapes.
| Model | Illustrative input | Computed displacement | Boundary |
|---|---|---|---|
| Rotational spring | M=50 N·m; kθ=250 kN·m/rad | 0.2 mrad | Must measure the relevant load path |
| Translational spring | F=500 N; k=500 kN/m | 1.0 mm | A 0.1 mm target would require 5000 kN/m |
| Load direction | F=1000 N; tilt=0.2 mrad | 0.2 N transverse projection | Direction depends on actual rotation axis |
| Mounting joint | Torque, flatness and preload unknown | Not calculated | Use supplier mounting procedure; record retorque drift |
Source basis: JCGM 100:2008 — Guide to the expression of uncertainty in measurement · EMPIR 18SIB08 ComTraForce — Final publishable report (VTT, 2025). Engineering recommendations are the site’s interpretation; no source endorses this worksheet.
Ready to compare your load point? Estimate and export your fixture budget
Record all six sensor channels at each input load. Normalize columns by appropriate force and moment scales before comparing condition numbers. Point count alone does not guarantee rank, conditioning or nonlinear model identifiability.
| Design choice | Reproducible property | What it supports | What it does not establish |
|---|---|---|---|
| Signed single-axis loads | At least ± each component plus zero/repeats | Can identify a full linear cross-sensitivity matrix if rank is six | Does not test all combined-load nonlinearities |
| Three independent factors at three levels | 3³ = 27 points | A three-factor design | Not a full six-component factorial |
| Six independent factors at three levels | 3⁶ = 729 points | A full six-factor design if mechanically feasible | No automatic safe load envelope |
| Complete quadratic in six inputs | 1+6+6+15=28 terms per output; 168 for six outputs | Fit only with adequate independent data and validation | No universal κ from 27 or 64 points |
Source basis: JCGM 100:2008 — Guide to the expression of uncertainty in measurement · EMPIR 18SIB08 ComTraForce — Final publishable report (VTT, 2025). Engineering recommendations are the site’s interpretation; no source endorses this worksheet.
Here TUR is defined as tolerance half-width divided by the expanded estimate U (k=2). The 4:1 and 2:1 bands prioritize engineering effort; they are not universal ISO/IEC 17025 mandates. Conformance also needs the measured deviation, complete uncertainty, applicable specification and an agreed decision rule.
| Illustrative case | Tolerance half-width T | Expanded U | Interpretation |
|---|---|---|---|
| Ratio 4:1 | 0.200% FS | 0.050% FS | Planning target only; no guaranteed false-pass probability |
| Ratio 2:1 | 0.200% FS | 0.100% FS | Review dominant contributors and decision risk |
| Example guard band w=U | 0.200% FS | 0.050% FS | If agreed: accept |error|≤T−U=0.150% FS |
| Missing measured error or full U | Unknown | Worksheet subtotal only | No sensor conformance decision available |
Source basis: ILAC-G8:09/2019 — Decision rules and statements of conformity · JCGM 106:2012 — Measurement uncertainty in conformity assessment. Engineering recommendations are the site’s interpretation; no source endorses this worksheet.
Multiple actuators can generate combined wrenches, but each load path needs coordinate and force evidence. No cycle times, machine accuracy or available HexaForce fixture products are verified on this page. For a hexapod, the worksheet explicitly returns an incomplete-model state.
| Architecture | Extra evidence | Cost driver | Alternative |
|---|---|---|---|
| Parallel six-strut loader | Strut lines, force calibration, Jacobian and covariance | Metrology, controls, safety and maintenance | Use a validated external calibration service |
| Orthogonal actuator frame | Load path alignment, reaction isolation and control settling | More reference channels and alignment checks | Stage sequential loads for static screening |
| Manual lever rig | Mass/gravity chain, geometry and placement repeatability | Operator time and handling limits | Use fewer justified points with repeats |
Source basis: EMPIR 18SIB08 ComTraForce — Final publishable report (VTT, 2025). Engineering recommendations are the site’s interpretation; no source endorses this worksheet.
A static budget cannot certify frequency response. Dynamic force involves mass and acceleration; moments include inertia and angular acceleration with additional coupling. Avoid comparing fixture mass in kg with force capacity in N as a percentage.
| Test | Model or observation | Evidence needed | Boundary |
|---|---|---|---|
| Static loading | Settled F and M | Repeatability, creep, drift and load reversal | No bandwidth measurement |
| Linear acceleration | F_inertia = m a | Moving mass, acceleration and phase reference | Fixtures contribute inertia |
| Rotational excitation | M includes Iα and rotational coupling | Inertia tensor, angular motion and frame definition | Scalar static stiffness is insufficient |
| Frequency sweep | Complex transfer response vs frequency | Validated reference, coherence and fixture modes | No universal frequency cutoff or attenuation rating |
Source basis: EMPIR 18SIB08 ComTraForce — Final publishable report (VTT, 2025). Engineering recommendations are the site’s interpretation; no source endorses this worksheet.
Illustrative stationary payload: m=5 kg, g=9.806 m/s², r=(0,0,0.100) m in the sensor frame. Specify the gravity vector directly instead of unverified robot Euler-angle conventions. Mx=−0.100Fy, My=0.100Fx and Mz=0 for this payload. More orientations cannot make six independent wrench inputs: M=[r]×F, so the wrench family has rank at most three.
| Gravity direction in sensor frame | Force (N) | Moment (N·m) | Diagnostic limit |
|---|---|---|---|
| −Z | (0,0,−49.03) | (0,0,0) | Settled force check; not all-axis calibration |
| −X | (−49.03,0,0) | (0,−4.903,0) | Fx and My change together |
| −Y | (0,−49.03,0) | (+4.903,0,0) | Fy and Mx change together |
| Any orientation, fixed r | F=m Rᵀg_world | M=r×F; Mz=0 here | Use independent offsets or applied torque for missing modes |
Source basis: JCGM 100:2008 — Guide to the expression of uncertainty in measurement · EMPIR 18SIB08 ComTraForce — Final publishable report (VTT, 2025). Engineering recommendations are the site’s interpretation; no source endorses this worksheet.
Validate each design assumption before applying a calibration decision. Temperature uniformity and equilibrium depend on the assembly, sensor and load path. No fixed soak time, blanket material approval or accredited service capability is established by this worksheet.
| Step | Record | Acceptance basis | If unavailable |
|---|---|---|---|
| 1. Inspect and install | Serials, bolt pattern, preload, cable routing and origin | Supplier mounting instructions and safe load envelope | Resolve drawings and limits before loading |
| 2. Stabilize and survey | Temperature at arm and sensor; loaded coordinate survey | Defined stability criterion and uncertainty allocation | Continue stabilization or qualify a narrower range |
| 3. Load and reverse | Zero before/after, ascending/descending loads, repeated placements | Pre-agreed drift/repeatability limits | Investigate reactions, creep and routing |
| 4. Compare and document | Measured error, complete U, k, assumptions and decision rule | Laboratory-approved criterion | Record inconclusive; improve evidence or use an external lab |
Source basis: JCGM 100:2008 — Guide to the expression of uncertainty in measurement · ILAC-G8:09/2019 — Decision rules and statements of conformity. Engineering recommendations are the site’s interpretation; no source endorses this worksheet.
Illustrative calculations and decision paths, not customer test records. Assumptions and omitted effects are stated so you can reproduce each example.
Premise: For the 100 N, 250 mm moment example above, compare assumed aluminum α=23.4 ppm/K with Invar α=1.2 ppm/K over ±2 K. The same ±20 µm rectangular location tolerance and u(F)=0.010 N apply.
Calculation / Process: Invar thermal half-range is 0.6 µm. Standard arm u is sqrt((20/√3)²+(0.6/√3)²)=11.55 µm; its geometry moment contribution is 0.001155 N·m.
Interpretation / Next Step: The two-term k=2 subtotal changes from 0.00567 N·m to 0.00551 N·m. Location and reference uncertainty dominate; changing material alone gives only a small improvement. Obtain actual CTE and geometry evidence before spending on Invar.
Premise: For one 1000 N full-scale force channel with tolerance ±0.2% FS, the tolerance half-width is 2 N. Assume independent standard components: reference 0.10 N, alignment 0.20 N, compliance 0.05 N and residual transfer 0.03 N.
Calculation / Process: u_c=sqrt(0.10²+0.20²+0.05²+0.03²)=0.2311 N; U(k=2)=0.4622 N; indicative TUR=2/0.4622=4.33.
Interpretation / Next Step: This subtotal meets the worksheet planning target. Adding omitted sensor repeatability u=0.20 N raises U to 0.6112 N and lowers the ratio to 3.27. A favorable fixture subtotal is insufficient for accepting a sensor.
Premise: A deadweight fixture has mass and arm certificates, but the site gravity value and mass convention are missing. The tool cannot quantify the remaining reference bias.
Calculation / Process: Leave the correction confirmations off and calculate: the estimate is marked incomplete. Request site gravity, density and the mass-convention details, or use a force transfer standard with suitable certificate evidence.
Interpretation / Next Step: No certificate or pass/fail claim is issued. Retain the worksheet as a design memo, collect the missing references, then repeat the load/reversal protocol and agree the complete decision rule with the lab.
Not automatically. Compare thermal expansion with location, force reference and alignment contributions. Example 1 shows that location and reference uncertainty can dominate even after lowering CTE. The CTE values here are illustrative; verify the material and operating temperature range.
Possibly, if measured parasitic reactions fit the budget. Contact type alone cannot predict the residual wrench. Check reversal hysteresis, joint freedom, stiffness and mounting constraints. The calculator factors are sensitivity assumptions, not bearing specifications.
Set an allowed angular or linear displacement, then use kθ=M/θ or k=F/δ with consistent units. For 500 N and 0.1 mm, k=5000 kN/m. Include force-offset moments and verify loaded geometry; no one stiffness threshold suits every rig.
It assumes Mx uses Ly, My uses Lx and Mz uses max(Lx,Ly); Lz only affects the illustrative mass estimate. These are simplified independent channel envelopes, not a solved spatial load path. For an actual fixture, survey every signed coordinate and apply M=r×F.
No. Use the certificate value, coverage factor, load range and conditions. Convert U to standard u=U/k and convert to percent of reading at the test point. Reference class labels alone do not establish the complete uncertainty of the applied force.
It states that these corrections were handled outside the tool and that residual contributions are included in reference u. The tool does not calculate g or density. Unconfirmed corrections leave the estimate incomplete rather than substituting a generic bias.
Convert at each test load. For example U=0.2 N, k=2 at F=100 N gives standard u=0.1 N, or 0.1% of reading. An FS-based percentage cannot be used unchanged as a reading-based percentage. Use a point-specific certificate value.
JCGM 100 supplies uncertainty propagation principles; ILAC-G8 and JCGM 106 explain decision rules and risk. OIML R111 addresses mass standards. ComTraForce provides multicomponent and dynamic metrology context. The references below are linked directly and reviewed on November 4, 2026.
No. The 4:1 band here is a design planning choice. Accreditation, uncertainty and a statement of conformity require evidence beyond a ratio. ILAC-G8 explains documenting and agreeing the decision rule. No fixed false-acceptance probability can be inferred from this tool.
All-zero loads return an input error. An individual unloaded channel shows its estimated receiving-channel effects but no TUR. Per-axis loads above the entered full scale are rejected. Passing those checks does not verify the manufacturer combined-load envelope.
No. It is an assumed coverage factor here. Coverage depends on distributions and effective degrees of freedom. A lab must evaluate whether that approximation is justified. The worksheet assumes independent components and does not include covariance.
Only the loaded axis with the minimum indicative TUR is used. Each component variance is divided by that axis total variance. Force variances in N² are never added to moment variances in (N·m)². Unmodeled effects are absent from the chart.
No. For fixed r, M=[r]×F, so gravity-generated wrenches have at most three independent inputs. With an on-axis center of mass, Mz is always zero. Change offsets or apply independent couples to check missing moment modes; validate the robot frame convention before use.
It depends on rank and the model. A three-level, six-factor full factorial has 729 points; 27 points describes three factors. Selected designs can use fewer points, but must demonstrate rank, conditioning, repeats and independent validation. There is no automatic condition number from point count.
Define measured stability and gradient criteria for the assembly and uncertainty budget. A fixed 45- or 60-minute soak is not established here. Record temperatures at the sensor and arm and verify drift before loading. Static results do not establish dynamic frequency response.
Send the design memo, sensor ranges, load-point drawing and reference certificates through the inquiry form. Availability, scope, deliverables and any accredited calibration must be confirmed separately. This page does not establish a supplied fixture product, certified performance or medical approval.
Prepared and reviewed by HexaForce Metrology & Robotics. Repository record created ; public publication date is unverified. Review again by May 4, 2027, or sooner if the cited standards change.
Standards and metrology review: . Source scope was checked against JCGM 100, ILAC-G8, JCGM 106, OIML R111 and the ComTraForce final report. Worksheet thresholds and residual coefficients are illustrative assumptions, not prescribed standard limits.
Sections 4–6 explain standard uncertainty, sensitivity coefficients, covariance and coverage factors. This worksheet assumes independent contributions; it is not a complete application of the GUM.
Sections 2–5 discuss agreement on decision rules, acceptance limits and risk. A numerical TUR alone does not establish accreditation or conformance.
Explains how conformance risk depends on the measurement model, results, distributions and decision rule. No fixed false-pass probability is claimed here.
Mass class requirements and nominal mass matter. A class label is not a universal force uncertainty; use certificate values and gravity/buoyancy corrections.
Research on force traceability, static/continuous/dynamic measurements, multicomponent methods and temperature effects. It supplies context, not performance ratings for the illustrative rigs on this page.
Material CTEs and effective friction/transfer factors are illustrative assumptions without a verified grade, bearing or rig dataset. The static worksheet excludes covariance, sensor response, arm self-weight and actual load-point geometry. Verify these before making a calibration decision.
Return to the fixture error budget calculator. For certificate auditing and sensor data sheets, visit 6-axis force sensor calibration certificate review. For overall sensor design, see 6-axis load cell design and calibration.
Share the load envelope, mounting drawing, reference certificates and design estimate for an engineering discussion. Scope, availability and any accredited calibration service must be confirmed separately.
Explore related guides: axis and sign checks, cable force compensation, or engineering resources.
