An eidograph is a precision drawing-copying instrument that reproduces a figure at a chosen scale using two parallel bars connected by a central pivot beam and a pulley-and-cord drive. Unlike the older pantograph, which uses four jointed bars in a parallelogram, the eidograph uses two bars kept parallel by equal pulleys linked by a crossed cord. It exists to give draughtsmen cleaner reductions and enlargements with less linkage slop. William Wallace invented it in 1821, and it became the standard scaling tool in 19th-century survey and engineering offices.
Eidograph Interactive Calculator
Vary the tracer and pencil graduations to see the copied length and scale ratio produced by the eidograph linkage.
Equation Used
The eidograph scale is set by the pencil graduation divided by the tracer graduation. A 1:2 setting gives S = 1/2, so every copied length is half the original length when the crossed cord keeps the two arms parallel.
- Equal pulleys with crossed cord keep both arms parallel.
- Cord does not slip or stretch during tracing.
- Tracer and pencil graduations are read directly as scale settings.
- Drawing distortion from wear, bow, or backlash is neglected.
Inside the Eidograph
The eidograph rests on a single fulcrum pin pressed into the drawing board. From that pin a central beam carries two equal pulleys at its ends, and each pulley anchors a long arm — one carrying the tracer point, the other carrying the pencil. A crossed cord (or thin steel band on later instruments) wraps both pulleys so that when one arm rotates, the other rotates by the exact same angle in the opposite sense. That kinematic constraint is what keeps the two arms parallel through every position on the board. Move the tracer along the original drawing and the pencil traces a geometrically similar figure on the copy.
The scale ratio is set by sliding the tracer arm and pencil arm in their tubular sleeves and locking them at matching graduations on the beam. If both arms sit at the same numbered division, the copy comes out at that ratio of the original — 1:2, 1:3, 2:3, and so on. The graduations are cut on the beam itself, typically to 0.1 mm precision on a quality Stanley or Elliott Brothers instrument, and the cord tension must stay high enough that the pulleys cannot slip under the side load of a steady tracing pass.
If the cord stretches, slips, or the pulleys differ in diameter by even 0.05 mm, the copy starts to drift — straight lines on the original come out as gentle arcs on the copy, and a closed polygon will fail to close. Worn fulcrum bushings cause a different symptom: the whole copy shifts laterally as you press harder on the tracer. The classic failure mode is a glazed cord that has lost its grip on the brass pulley grooves, which shows up as the pencil lagging behind the tracer on quick direction changes.
Key Components
- Central beam: The horizontal bar carrying both pulleys and the fulcrum socket. Graduated along its length, usually to 0.1 mm, so the tracer and pencil arms can be locked at matched scale divisions. Beam straightness is the master reference — bow above 0.05 mm over 300 mm and your scale ratio drifts across the working area.
- Equal pulleys: Two brass pulleys of identical diameter mounted at the beam ends. Their diameters must match within 0.02 mm, otherwise the arms will not stay parallel and the copy will skew. The pulley grooves are V-cut to grip the cord without crushing it.
- Crossed cord or steel band: Wraps both pulleys in an X-pattern so a clockwise rotation of one pulley forces a clockwise rotation of the other through equal angle. Silk cord on early Wallace instruments, replaced by phosphor-bronze ribbon on late-19th-century Stanley models for zero stretch.
- Tracer arm: Carries the tracer point that follows the original drawing. Slides in a sleeve on its pulley so the user can set the scale division precisely. The point itself is a polished steel pin, never a pencil — too much friction would torque the arm.
- Pencil arm: Mirror of the tracer arm, fitted with a sprung pencil holder so the lead maintains constant contact pressure (typically 30–60 g) without digging into the paper. Slides and locks at the same graduation as the tracer arm.
- Fulcrum pin and weight: A vertical pin set in a heavy lead-filled brass weight that sits on the drawing board. The whole instrument pivots around this pin. The weight must hold position under a 200 g side load from a brisk tracing pass — anything lighter and the copy walks across the board.
Real-World Applications of the Eidograph
The eidograph found its home wherever draughtsmen needed to copy a drawing at a different scale without redrawing it by hand. It outlived the pantograph in survey and engineering offices because the parallel-bar geometry produces less linkage backlash than four jointed bars, and the central pivot gives a wider working envelope on a small board. You still find working examples in archive conservation, map reproduction, and museum draughting departments where digitising a fragile original is not appropriate.
- Cartography: Ordnance Survey draughtsmen used Stanley eidographs to reduce field plane-table sheets to publication scale through the 19th century, particularly for the 1:2500 county series.
- Mechanical engineering drawing offices: James Watt & Co's drawing office in Birmingham used Wallace-pattern eidographs to produce reduced general-arrangement drawings from full-size detail sheets.
- Archive conservation: The British Library uses period eidographs to produce facsimile copies of fragile 18th and 19th-century estate plans without putting the original under a digital scanner light.
- Museum draughting: The Science Museum in London holds and occasionally uses Elliott Brothers eidographs to produce display-scale copies of original patent drawings.
- Naval architecture: Admiralty draughting offices reduced full-size lofted hull lines to 1:48 builder's drawings using long-beam eidographs through the late 1800s.
- Geology and mining surveys: Mining surveyors copied underground workings from the original 1:500 face plans down to 1:2500 plan sheets for company records, particularly in Scottish coalfield offices.
The Formula Behind the Eidograph
The scale ratio of an eidograph copy is set entirely by the ratio of the tracer-arm distance to the pencil-arm distance, both measured from their pulley centres. At the low end of the typical operating range — say a 1:5 reduction — the pencil arm sits very close to its pulley and the copy comes out small but the system is forgiving of cord stretch. At the high end of the typical range, around 5:1 enlargement, the pencil arm is fully extended and any error in cord tension or pulley diameter is amplified by the same factor. The sweet spot for a 600 mm-beam instrument sits between 1:2 and 2:1, where arm extensions stay balanced and the linkage runs cleanly.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| S | Scale ratio of copy to original | dimensionless | dimensionless |
| Lpencil | Distance from pencil pulley centre to pencil point | mm | in |
| Ltracer | Distance from tracer pulley centre to tracer point | mm | in |
Worked Example: Eidograph in a Victorian botanical illustration archive
A botanical illustration archive at the Royal Botanic Garden Edinburgh is producing 1:3 reduction copies of a set of 1840s pressed-plant drawings using a restored Wallace-pattern eidograph with a 600 mm graduated beam. The tracer arm is set to 240 mm from its pulley centre. The team needs to confirm the pencil arm setting and check what happens at the limits of the instrument's range.
Given
- Ltracer = 240 mm
- Snom = 1/3 dimensionless
- Beam length = 600 mm
Solution
Step 1 — at the nominal target reduction of 1:3, rearrange the formula to find the pencil arm length:
Step 2 — at the low end of the typical operating range, a gentle 1:2 reduction, the pencil arm extends further from its pulley:
This is the sweet spot for the instrument — both arms run at balanced lengths, cord tension stays even, and a 200 mm-long line on the original comes out as a clean 100 mm line on the copy with no perceptible bow.
Step 3 — at the high end of the practical range, a 1:5 reduction:
At 48 mm the pencil arm sits almost on top of its pulley. Any cord stretch of even 0.1 mm now translates to a measurable angular error at the pencil — a 200 mm original line will close-off short by roughly 0.4 mm on the copy, and a closed polygon noticeably fails to meet itself. Pushing past 1:6 is technically possible but the copy quality falls off a cliff.
Result
The pencil arm sets at 80 mm for the nominal 1:3 reduction. In practice that produces a clean copy where a 150 mm leaf on the original comes out as a 50 mm leaf on the copy with line weight that the sprung pencil holder can hold consistently. Comparing the three points: 1:2 gives the most forgiving operation, 1:3 is comfortable working territory, and 1:5 is the practical limit before cord and pulley errors start showing as polygon-closure failures. If the actual copy comes out the wrong size — say 52 mm instead of 50 mm on a known-length feature — the most common causes are a pencil arm that has crept in its sleeve under tracing pressure (check the locking screw torque), a stretched silk cord that has lost 1–2% of its original length and let the pulley ratio drift, or a worn fulcrum bushing letting the whole beam shift between strokes.
Eidograph vs Alternatives
The eidograph competes mainly with the pantograph and, in modern offices, with the photographic or digital reduction. Each one trades off accuracy, working envelope, and operator skill in different ways. The choice depends on copy fidelity, original-document handling restrictions, and how often the operator changes scale ratios.
| Property | Eidograph | Pantograph | Photographic reduction |
|---|---|---|---|
| Typical scale accuracy | ±0.2% over working area | ±0.5% over working area | ±0.05% with calibrated lens |
| Working envelope on a 600 mm beam | ~500 mm radius around fulcrum | ~300 mm offset between tracer and pencil | Limited only by camera bed |
| Time to change scale ratio | 30–60 seconds (slide and lock) | 2–3 minutes (re-pin joints) | Minutes to hours (re-set lens or rescan) |
| Handles fragile originals | Yes, no light or pressure | Yes, no light or pressure | Marginal — light exposure and contact |
| Linkage backlash | Low (single pivot, cord drive) | Higher (4 jointed bars) | None (no linkage) |
| Capital cost (period instrument) | £200–£800 restored | £80–£300 restored | £2,000+ for archival camera setup |
| Operator skill required | Moderate — steady hand on tracer | Lower — geometry is intuitive | Low — push button after setup |
Frequently Asked Questions About Eidograph
That is almost always a pulley diameter mismatch. If the two pulleys differ by even 0.02 mm in working diameter — common after years of cord wear cutting into the brass groove — the two arms no longer rotate by exactly equal angles, and a rectangle on the original prints as a parallelogram on the copy. Measure both pulley grooves with a vernier and compare. The fix is to either re-cut both grooves to a matched dimension or replace the cord with a thinner one that rides higher on the worn groove.
At 1:5 you are at the practical edge for a typical 600 mm-beam eidograph — the pencil arm gets so short that pulley and cord errors dominate. A pantograph at 1:5 actually performs comparably because its linkage error scales differently with ratio. The deciding factor is usually working envelope. The eidograph copies anywhere within a circle around the fulcrum, so it suits roughly square originals. The pantograph reaches further in one direction but has a dead zone, so it suits long, narrow originals like canal or railway alignment plans.
Check the beam itself for bow. A 600 mm beam that has developed even 0.05 mm of bow over its length will swing the pulleys through slightly different arcs as the instrument rotates around the fulcrum, and straight lines on the original come out curved on the copy. Lay the beam on a surface plate and check with a feeler. The other suspect is an off-centre fulcrum hole — if the pin hole has worn oval, the beam shifts laterally during tracing and produces the same arcing symptom.
That is cord slip on the pulleys. A glazed silk cord that has hardened with age cannot grip the brass groove under sudden angular acceleration, so the pencil pulley rotates a fraction of a degree behind the tracer pulley until the cord catches. The diagnostic check is to trace a sharp zigzag — if the corners come out rounded only on the copy and not on the original, you have cord slip. Replace the cord with a fresh waxed silk or, better, a phosphor-bronze ribbon as fitted to late Stanley instruments.
Yes, but you swap which arm carries the tracer and which carries the pencil. For a 3:1 enlargement, the pencil arm sits at three times the tracer arm length. The practical limit is roughly 5:1 because the pencil arm runs out of beam, and because any tremor in your tracing hand is multiplied by the scale factor — a 0.1 mm wobble at the tracer becomes a visible 0.5 mm wobble on the copy. For enlargements above 3:1 most draughtsmen would brace the tracing hand on a rest.
The cord must be tight enough that you cannot slip it on the pulley by thumb pressure, but not so tight that it deflects the beam or loads the pulley bearings. A working rule is roughly 5–8 N of tension on a 1.0 mm silk cord. Over-tensioning is the more common mistake on restorations — it bows the beam slightly toward the cord side, and you get a systematic scale error along one axis of the copy. If your copies are accurate in one direction but consistently 0.5% off in the perpendicular direction, slack the cord by a quarter turn of the tensioner.
References & Further Reading
- Wikipedia contributors. Eidograph. Wikipedia
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