Hiscox movement 1514 uses two equal crossed bars and sliding ends to keep a pair of ruler bars parallel. A common pivot joins the crossed bars at their midpoints. Explore the motion and calculate ruler separation, slot-end span and center-to-end distance.
Keeping the ruler bars parallel
Each cross bar has a pinned end and a sliding end on opposite rulers. As the bars rotate about their shared midpoint, the sliders accommodate the changing horizontal span. The slots are part of the mechanism: locking the sliding ends would prevent this parallel motion.
Hiscox 1514 Crossed-Bar Geometry Calculator
Enter ruler length, crossed-bar length and bar angle. The worksheet reports exact symmetric ruler separation, slot-end span and center-to-end length.
Equation Used
- Both crossed bars are rigid and have equal length L.
- The bars share one ideal central revolute pivot at their midpoints.
- Each bar has one pinned ruler end and one end constrained to slide along the opposite ruler.
- The two ruler centerlines remain parallel in the symmetric construction.
- Friction, clearance, stops, strength, wear, tolerance and accuracy are excluded.
The crossed bars keep a constant length as their angle changes. Numerical results describe the entered angle; the animation sweeps through a range of positions to show the sliding ends.
Hiscox movement 1514 uses slots
Hiscox identifies movement 1514 as a slotted parallel ruler that traverses in line. Two cross bars rotate about a common central pivot. Each cross bar is pivoted to a ruler at one end, while its opposite end slides in a slot in the other ruler.
The slots are essential: without them, simply crossing rigid links between swapped ruler pivots does not create the depicted one-degree-of-freedom parallel translation.
Crossed-bar parallel translation
The crossed bars provide a symmetric mechanism centered between the two rulers. US Patent 46,348 documents a historical crossed-lever parallel-ruler approach intended to avoid lateral deflection associated with ordinary diagonal-link rulers.
The calculator uses equal crossed bars with a shared midpoint pivot to show how their projections determine ruler separation and sliding-end positions.
Symmetric crossed-bar closure
Each rigid bar has horizontal projection L cos beta and vertical projection L sin beta. The central pivot bisects both bars.
Declared geometry example
For L=220 mm at beta=45 degrees, ruler separation and slot-end span are each 155.56 mm, and the center pivot is 110 mm from every bar end.
Slot travel and usable motion
Usable motion depends on actual slot length, bar/ruler interference and end stops. Hiscox supplies the topology but no universal percentage gain.
The ruler-length input changes the drawing; separation and slot-end span depend on crossed-bar length and angle. The calculator does not check slot-end stops or predict drawing accuracy.
Slotted-ruler questions
Why must two ends slide?
The moving slot coordinates accommodate the changing horizontal projection of the crossed bars.
Where is the central pivot?
At the shared midpoint of both equal crossed bars in this symmetric model.
Are the crossed bars a four-bar parallelogram?
No; the slots make this a different constrained mechanism.
Does the calculator predict accuracy?
No.
Slotted parallel-ruler references
- Gardner D. Hiscox, Mechanical Movements, movement 1514: crossed bars, central pivot, pinned ends and sliding ends in ruler slots.
- US Patent 46,348, Improvement in parallel rulers: historical crossed-lever construction designed to avoid lateral deflection.
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