A parallel ruler transfers the direction of a line using two equal pivoted links. Calculate the perpendicular and longitudinal components of one ideal transfer, then multiply the perpendicular component by a chosen number of identical transfers.
Repeating a parallel transfer
Moving one ruler bar while holding the other preserves the reference direction. For the calculation below, each transfer has the same link length and opening angle. The pivot spacing changes the length of the ruler linkage but does not change the perpendicular step produced by those links.
Parallel-Ruler Transfer Calculator
Enter equal bar pivot spacing, equal link length, opening angle and completed walks. The worksheet reports exact per-walk components and total ideal perpendicular advance.
Equation Used
- The ruler bars are rigid and have equal corresponding pivot spacing C.
- Both connecting links have exact equal pivot-center length L.
- Every completed walk repeats the same opening angle and translation vector.
- The bars remain parallel in the ideal planar parallelogram.
- Handling, pin clearance, mismatch, compliance, friction, wear and navigation accuracy are excluded.
The animation opens the linkage between 15 degrees and the selected angle. Numerical results use the selected angle for every transfer; the count multiplies this fixed perpendicular step.
One equal-link translation, repeated
Hiscox movement 1513 uses two ruler bars joined by two pieces of exactly equal pivot-center length at equal distances on the bars. The four pivots form a parallelogram, so one ruler receives a translation without rotation.
An ideal walk repeats that same translation. The geometric sequence is exact under the declared assumptions; it is not a model of how a person grips and advances a physical instrument.
Ideal alternating parallel-line transfer
The Fitzwilliam Museum defines a parallel ruler as equal-length pivoting crosspieces joining two rulers so the rulers remain parallel, used for transferring parallel lines. EP0168948A1 likewise describes changing straight-edge separation without changing relative orientation.
The walk counter is useful for visualizing repeated equal transfers only.
Ideal walk geometry
Both moving pivots receive the same vector, so the moving ruler's ideal angular error is zero.
Declared sequence example
For L=90 mm, theta=55 degrees and N=10, each ideal walk advances 73.72 mm perpendicularly and shifts 51.62 mm longitudinally. Ten identical walks total 737.24 mm of ideal perpendicular advance.
What the ideal sequence excludes
A real walking technique can accumulate effects from unequal links, clearance, edge straightness, out-of-plane motion, stiffness, wear and handling. Those effects require measurements and a specified operating method.
Use the total as a geometric transfer distance. It does not include the repositioning and handling errors of a real instrument.
Walking-sequence questions
Is total advance a measured path?
No; it is N identical ideal perpendicular translations.
Why is ideal angle error zero?
Equal corresponding link vectors translate the moving ruler without rotating it.
Does the model predict accumulated drift?
No.
Can it specify a manufacturing tolerance?
No; that requires a physical accuracy requirement and measured construction data.
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 and parallel-line transfer.
- European Patent EP0168948A1: variable straight-edge separation without orientation change.
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