A section liner repeatedly advances a guided rod and attached ruling blade so a drafter can draw evenly spaced parallel hatch lines. This calculator resolves the selected number of line intervals, signed cumulative pitch error, guide travel and spacing projected normal to the ruled lines.
Section Liner Indexing Geometry
Explore a section liner's repeated guide advance, signed accumulated pitch error and projected hatch spacing.
Equation Used
- The carriage advances once for each new line after the first.
- Pitch error is a signed constant error per interval.
- The ruling blade stays parallel throughout the sequence.
- Backlash, compliance, skipped indexes and operator variation are excluded.
The first ruled line is the starting position, so N lines contain N−1 indexed intervals.
Lever-indexed ruling blade
The reviewed visual follows the arrangement documented in historical section-liner patents: a fixed bed, an endwise movable rod, an angular ruling blade, an advancing lever and a hold that prevents backward motion.
Each cycle advances the carriage by the selected actual step. The blade remains parallel to itself, and the hatch field grows one line at a time.
What the calculator determines
Select nominal guide step, total line count, signed error per interval and blade angle measured from the vertical reference. With N lines there are N−1 intervals.
The Smithsonian describes the section liner as an instrument for drawing closely spaced parallel cross-hatching and identifies a mechanism that controls a rod carrying an optional ruler. U.S. Patent 669,239 documents an endwise movable rod, angular ruling blade, intermittent advancing lever, return spring and backward-motion lock.
Indexing and projected spacing
Let m = max(0,N−1), nominal step p, signed step error e and blade angle θ from vertical. Actual guide step is p+e. Guide travel is x = m(p+e), cumulative drift from nominal is Δ = me, normal line spacing is q = (p+e)cosθ, and normal hatch span is mq.
Selected-input arithmetic
For 50 lines, 2 mm nominal step, +0.05 mm error per interval and a 45° blade angle, there are 49 intervals. Actual guide travel is 100.45 mm, cumulative drift is +2.45 mm, and normal line spacing is about 1.45 mm.
Model boundary
The result is deterministic selected-step geometry. A real instrument may have backlash, nonuniform tooth errors, compliance, skipped indexes, blade straightness error and operator variation; these are not inferred from the four inputs.
The former formula used N steps for N lines and the former tolerance percentage assumed an unsupported 0.05 mm reference. Both are removed.
Questions
Why are there N−1 intervals?
The first line establishes the starting position; each additional line requires one advance.
Can pitch error be negative?
Yes. Negative error means each actual step is shorter than nominal.
Does the angle rotate during indexing?
No. The ruling blade remains parallel to itself.
Does this predict drafting quality?
No. It reports selected geometry only.
References & Further Reading
- Wikipedia contributors. Technical drawing tool. Wikipedia
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