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A precisely printed track can still be sampled at the wrong coordinate when the card, housing, shaft and contact carrier reference different features. Datum stack-up is the signed relative displacement between the printed curve and the moving contact after assembly. Its electrical consequence depends on local curve slope, so the same geometric offset can be harmless in one region and serious in another. The analysis must preserve shared datums and correlations rather than adding every drawing tolerance as though it were independent.
Key design decisions
- Select the functional system datum that defines indicated position.
- Build separate signed chains to the track and the moving contact.
- Convert relative displacement through the released local output slope.
Choose a datum that follows the controlled motion
Begin with the shaft axis, linear guide or mechanism surface whose position the system intends to measure. External substrate edges are convenient inspection features only if the mounting scheme transfers their location to that functional reference. Identify primary, secondary and tertiary contacts that constrain the card, including clearance directions and seating force. A circular track additionally needs centre and angular-zero datums; a linear track needs origin and travel direction. State the assembly state, because a loose card before fastener torque does not occupy the same datum structure as the final unit.
Subtract the contact chain from the printed-track chain
Write one coordinate chain from the system reference to a chosen track feature and another to the contact centre or controlling footprint edge. Their difference is the sampling offset. Shared housing or fixture dimensions cancel when they appear with the same sign; treating them as separate worst-case terms overstates error. Rotations should be converted at the local radius or through a sensitivity matrix when they create both tangential and lateral movement.
Δx_rel=Σ a_i d_i-Σ b_j q_j; Δy≈s(x)Δx_rel
- d_i are dimensions locating the printed feature from the system datum.
- q_j are dimensions locating the contact from the same datum.
- a_i and b_j are signed geometric sensitivity coefficients.
- s(x) is connected-output slope at the reviewed track coordinate.
Small offsets, a fixed seated assembly state and a locally differentiable output curve.
Calculate an offset without losing direction
For an illustrative linear assembly, the track origin lies 12.40±0.10 mm from a housing datum. The contact centre at mechanical zero lies 12.18±0.08 mm from that datum. Nominal relative offset is +0.22 mm. Arithmetic extremes give a range from +0.04 to +0.40 mm. At a local slope of 0.55 V/mm, the nominal output shift is +121 mV and the geometric range corresponds to +22 through +220 mV before other electrical errors. These values explain the sign and conversion; they are not released tolerances or capability.
Convert centre and angular errors for rotary tracks
For a rotary card, shaft-centre eccentricity changes radial placement while angular-zero error moves the contact tangentially. Project centre-offset vectors onto the track tangent at each angle; the contribution varies sinusoidally around the arc. Angular print registration produces a more uniform phase shift. Contact-arm rotation can also alter footprint orientation and effective radius. Report radial tracking margin separately from tangential output error, because adequate electrical phase does not prove the contact remains fully on the intended wear band.
| Contributor | Geometric effect | Review output |
|---|---|---|
| Card mounting location | Track translation or rotation | Relative sampling coordinate |
| Print registration | Active curve versus substrate datum | Local output phase |
| Shaft or guide location | Contact carrier location | Assembly zero shift |
| Contact footprint | Leading, centre and trailing positions | Engagement and averaging |
Respect correlation, material condition and assembly sequence
Worst-case arithmetic is suitable for a guaranteed bound when all adverse directions can coexist. Statistical methods require distributions and correlations supported by process evidence. Print-to-substrate and substrate-to-housing terms may not be independent if the same fiducials or nests control them. Hole clearance permits a range determined by seating direction, not a centred normal distribution. Thermal expansion, fastener torque and compliant seals create state-dependent shifts that should enter as named load cases instead of an arbitrary environmental multiplier.
Use error shape to distinguish datum shift from curve distortion
A nearly constant position phase shift is consistent with an origin offset. A sinusoidal rotary residual can indicate centre eccentricity. A localized feature repeating at the same card coordinate points toward print geometry or contact surface rather than whole-card location. Direction-dependent displacement may involve seating, clearance or backlash. Measure independent contact and track coordinates rather than fitting output alone; refitting gain and offset can conceal the datum evidence. Inspect witness surfaces and fastener state, but do not declare root cause from appearance without controlled dimensional confirmation.
Validate the assembled coordinate chain, not isolated dimensions only
Measure substrate datums and printed fiducials, then locate the contact or carrier relative to the same system reference in the assembled state. Capture connected output while moving through controlled positions from both directions. Compare measured relative offset with the stack prediction at several locations. Fixture datums must be traceable and should not constrain the assembly differently from service. Record torque, seating direction, specimen identity, temperature, metrology uncertainty and raw coordinates. A coordinate measurement on an unassembled card validates print registration but not the complete sampling location.
Put functional datum ownership on the drawings
The card drawing should control print origin, orientation, active boundaries and contact path relative to inspectable substrate features. The assembly drawing should show how those features seat to the housing and how the shaft or guide locates the carrier. The interface requirement should allocate relative-position and output error. ChipSimple can review and manufacture the drawing-controlled ceramic and thick-film features; housing, shaft and completed sensor accuracy require customer-controlled evidence. Reopen the stack after changes to artwork, outline, holes, mount, fasteners, carrier, contact, shaft, receiver or software conversion.
Close the remaining implementation and validation risks
A card located tightly by several holes or edges can be over-constrained; manufacturing variation then produces bending or unpredictable seating rather than a simple coordinate offset. Identify intended locating contacts and provide clearance elsewhere. Verify that terminals, seals and harness loads do not become unintended datums after assembly. Inspect minimum contact overlap as well as output phase, because a software offset cannot repair lateral departure from the track. Repeat measurements after permitted thermal and mechanical load states to distinguish reversible movement from permanent seating change. If a proposal tightens an easy-to-measure edge while leaving the functional print-to-contact chain unchanged, it adds cost without reducing output error.
Send both sides of the functional datum chain
Datum review requires card artwork and assembly mechanics tied to one reference coordinate.
- Card outline, holes, fiducials and print-registration tolerances.
- Housing, shaft or guide, carrier and contact datum dimensions.
- Assembly seating, torque, clearance, temperature and load states.
- Output curve, local slopes, permitted error and validation plan.
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