An equal-link parallel ruler transfers a line direction while keeping its two bars parallel. At a fixed opening angle, each placement spans the same perpendicular distance. Calculate how many full placements reach a target distance and how far the final placement extends beyond it.
Transferring parallel lines
Hold one bar against a reference line and move the other while keeping the reference bar still. The links preserve the direction of the moving edge. Repeating an equal perpendicular step lets you compare the distance covered with a target; the final excess is unused coverage, not an estimate of drawing error.
Parallel-Line Placement Calculator
Enter bar pivot spacing, equal link length, opening angle and a target perpendicular transfer. The worksheet reports exact step geometry and ideal placement count.
Equation Used
- Both ruler bars are rigid with equal corresponding pivot spacing C.
- Both connecting links have exact equal pivot-center length L.
- Every ideal placement uses the same opening angle and perpendicular separation.
- The target is measured perpendicular to the parallel ruler edges.
- Handling error, clearance, friction, wear, compliance and accuracy are excluded.
Results use the entered opening angle, marked by the dashed bar. The moving linkage illustrates how the ruler remains parallel as it opens; the placement count describes repeated transfers at the selected angle.
Equal-link translation repeated in ideal steps
Hiscox movement 1513 uses two bars joined by two pieces of exactly equal pivot-center length at equal distances on the bars. The four pivots form a parallelogram, so the moving ruler receives one translation vector without rotation.
For a declared opening angle, the perpendicular component of that translation is L sin theta. Repeating that same ideal separation gives a transparent placement count.
Planning repeated parallel-line placements
The Fitzwilliam Museum defines the instrument as a pair of rulers connected by equal-length pivoting crosspieces so the rulers remain parallel, used for transferring parallel lines. EP0168948A1 likewise describes changing straight-edge separation without changing orientation.
The calculator counts equal geometric placements only; it does not model how an operator alternately holds and moves the physical bars.
Counting repeated placements
Coverage excess is covered minus target. It is simply the unused portion of the final full geometric step.
Declared transfer example
For L=90 mm, theta=60 degrees and a 600 mm target, each ideal placement spans 77.94 mm. Eight placements cover 623.54 mm, leaving 23.54 mm of geometric excess.
What the count omits
A real transfer sequence depends on pin clearance, member stiffness, edge straightness, friction and handling. Those quantities require measurements and cannot be represented by multiplying an assumed clearance by the number of steps.
The count assumes identical perpendicular transfers. Estimating accumulated error in a real drawing requires measurements of the instrument and its handling.
Repeated-transfer questions
Why round the placement count upward?
A whole number of full declared separations is required to reach or pass the target.
Is coverage excess an error?
No; it is only the unused part of the last full ideal step.
Does the model predict accumulated drift?
No.
Do the ruler bars rotate relative to each other?
Not in the ideal equal-link parallelogram.
Parallel-ruler references
- Gardner D. Hiscox, Mechanical Movements, movement 1513: exact equal link lengths and equal bar pivot spacing.
- Fitzwilliam Museum terminology, parallel ruler: equal pivoting crosspieces used to transfer parallel lines.
- European Patent EP0168948A1: variable separation without orientation change.
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