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A phrase such as linear output, empty-to-full or custom taper is not an engineering curve. Artwork cannot be reviewed until the physical input, electrical output, reference conditions, end behavior and interpretation between commanded points are explicit. This guide owns the upstream system-to-artwork requirement package. It does not choose optimum breakpoint spacing, calculate interpolation-error bounds, predict printed geometry or promise achieved accuracy. Those downstream decisions require their separate owners and supporting evidence after the command curve is agreed.
Key design decisions
- Define the physical input and electrical output with units, direction and reference state.
- Issue ordered command knots plus an interpolation and end-point rule, not a picture alone.
- Separate system allocation, card contribution and measurement uncertainty before assigning acceptance bands.
Name the independent and dependent variables
State exactly what drives the curve. The independent variable might be shaft angle, linear travel, liquid height, float-arm angle or another controlled coordinate. Record its units, positive direction, datum and usable interval. Do not interchange related quantities without a model: liquid volume is not generally proportional to height, and float angle is not automatically equal to contact angle. The dependent variable may be resistance between named terminals, a resistance ratio, voltage under a defined circuit or digital value after electronics. Name terminal pairs and excitation because the same card can produce different reported quantities.
Define the reference condition before selecting values. Temperature, motion direction, contact load, supply, external pull-up or divider resistance, settling time and measurement method can influence the observed output. If the command is intended to represent the card alone, use a card-level electrical quantity. If it represents a complete sender, include mechanism and contact interfaces explicitly. Mixing these levels causes later arguments about whether a deviation belongs to artwork or the surrounding system.
Issue ordered command knots
Represent the command as ordered pairs (x_k, y_k), where x_k is physical input and y_k is required electrical output at knot k. Sort the knots by x and prohibit duplicate x values unless a discontinuity is intentionally defined. Include enough knots to express real changes in slope, but do not create a dense table of false precision. Every number needs units and a tolerance or allocation rule. A graph can accompany the table for communication, yet the table remains the controlled numerical definition.
For a required monotonic curve, check (y_{k+1}-y_k)(x_{k+1}-x_k) >= 0 for increasing behavior or the corresponding nonpositive condition for decreasing behavior. This verifies command consistency, not manufacturability. A repeated y over an interval defines a plateau; a reversed increment defines a deliberate non-monotonic segment only if the system owner says so. Resolve accidental reversals before track synthesis because geometry optimization cannot repair an internally contradictory target.
Control interpolation between points
Two teams can implement the same knots differently unless interpolation is specified. Piecewise linear interpolation uses y(x) = y_k + (y_{k+1}-y_k)(x-x_k)/(x_{k+1}-x_k) within one interval. A step, spline, polynomial or lookup-table rule produces another command and must be named with boundary behavior. If software performs interpolation while artwork targets only sampled resistances, separate those functions. Avoid a high-order curve chosen solely because it passes through the knots; overshoot between points can violate monotonicity or create an impractical local slope.
Consider an illustrative interval from (20 degrees, 1.2 kOhm) to (50 degrees, 2.1 kOhm). Piecewise linear interpolation commands at 35 degrees: 1.2 + (2.1-1.2)(35-20)/(50-20) = 1.65 kOhm. This arithmetic is not a product specification. It demonstrates why units, interval and rule belong in the command. If another document reads 1.65 kOhm from a smoothed graph without naming its interpolation, the two definitions may coincide at one point but diverge elsewhere.
| Field | Required statement | Common ambiguity |
|---|---|---|
| Input x | Quantity, units, datum, direction and range | Height confused with volume |
| Output y | Terminal pair or defined circuit quantity | Resistance confused with divider voltage |
| Knots | Ordered numeric pairs and tolerances | Graph pixels treated as values |
| Between knots | Interpolation and end behavior | Uncontrolled smoothing or extrapolation |
Define electrical ends and unusable travel
Mechanical travel often extends beyond the useful electrical curve. Identify first valid input, last valid input, any dead zones, collector transitions, overtravel and stop tolerance. State whether output must clamp, continue by interpolation, become open, or remain unspecified outside the controlled interval. Do not let artwork software silently extrapolate beyond the first or last knot. An end pad or collector can occupy physical distance that contributes no commanded resistance change, and that distance must be reconciled with mechanism stops.
Use separate terms for nominal end value, permissible end error and guaranteed valid-travel window. A system may require a value at the hard stop while the card design needs margin so the contact does not leave the intended surface. That conflict must be resolved in the mechanism-card interface, not hidden by moving the first knot. Include assembly and wear-related position uncertainty in the review while leaving actual wear life to its own validation owner.
Allocate error to the right contributors
A system output band usually contains contributions from mechanism position, card transfer, contact behavior, external circuit, measurement and calibration. Write an error model before assigning the card a tolerance. For a voltage divider, the sensitivity to card resistance depends on the external resistance and supply, so a fixed resistance error does not produce a fixed voltage error across the range. Use derivatives or bounded evaluations from the actual circuit; do not convert a system percentage into a blanket printed-resistor tolerance.
Keep systematic shape error apart from repeatability, hysteresis and short interruptions. A curve can match knots on average yet have direction-dependent error. Another can be repeatable but offset because a datum is displaced. Measurement uncertainty also consumes part of an observed acceptance band. Define whether limits apply to individual points, interval slope, maximum absolute error, integrated error or a filtered output. The choice affects artwork optimization and validation sampling, so it must be owned by the system requirement.
Translate the command into artwork inputs
Once the curve is controlled, provide the artwork engineer with the allowed card outline, active path, terminal and collector geometry, contact footprint, sheet-resistance information supported for the selected material route, trim strategy if applicable, and forbidden regions. The command curve is an input to synthesis, not the artwork itself. Local track width, path length and segmentation may be adjusted to approximate commanded increments while respecting printing, contact and clearance constraints. Do not demand an impossible local slope without allowing geometric or calibration alternatives.
Preserve traceability between every artwork station and its command coordinate. If a rotary design uses angular stations, identify the same pivot datum used by the mechanism. For linear motion, define whether distance follows the housing, card edge or contact carrier. When the target curve derives from tank geometry or linkage kinematics, keep that upstream model under revision control. A changed tank profile can alter command knots even though the resistor-card drawing envelope remains unchanged.
Measure the implemented transfer curve
Validate at commanded knots and at points between them that challenge slope changes, plateaus and electrical ends. Use a position reference with resolution and uncertainty appropriate to the error allocation. Approach points from both directions and record raw position-output pairs, temperature state, contact load, supply and timing. A fitted summary is useful, but retain residuals so localized departures are visible. If output is voltage, measure the actual external circuit or use its controlled equivalent.
Compare observed output to the command produced by the specified interpolation, not to a visually drawn trend line. Report residual e(x)=y_measured(x)-y_command(x), along with direction and condition. A repeating spatial feature can indicate artwork or local track effects; a direction-dependent separation suggests mechanism or contact hysteresis; an end-only error points toward stops, collectors or invalid extrapolation. These patterns guide investigation but do not prove cause without a discriminating comparison.
Release one authoritative curve package
The controlled package should include variable definitions, units, datums, direction, valid interval, ordered knots, interpolation, extrapolation prohibition or rule, tolerances, end behavior and the allocation between card and system. Include the source requirement revision and the drawing or model that relates system input to card position. Machine-readable data should accompany the human-readable graph so rounding and pixel extraction cannot create another version. If a correction is issued, replace the table and identify affected artwork and validation records.
For a project review, send the physical-input definition, commanded output, terminal or circuit configuration, knot table, interpolation rule, valid travel, end requirements, mechanism mapping, contact geometry, environment, error budget and calibration concept. Existing measurements should include raw coordinates and both directions. A drawing-specific review can assess consistency and propose an artwork/validation route. Final achievable tolerance, durability and production release remain conditional on selected materials, geometry and representative verification.
Review a commanded resistive sensor output curve
Send the numeric transfer requirement and its physical/electrical interfaces before artwork synthesis begins.
- Independent variable, units, datum, direction and valid range
- Dependent output, terminal pair or complete circuit definition
- Ordered command knots, tolerance and interpolation rule
- End regions, overtravel, dead zones and stop tolerances
- Mechanism-to-contact coordinate mapping
- Contact footprint and available card geometry
- Error budget, environment, calibration and validation requirements
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