This page now isolates the exact ideal geometry of a four-point proportional divider. It removes fabricated clamp-slip, accuracy, tolerance, deployment and maintenance claims that cannot be inferred from the selected dimensions.
Proportional-Compass Pivot-Setting Explorer
Enter a point-to-point leg length, transfer ratio and long-side opening. The connected view keeps both legs straight and equal, locates the common pivot exactly, and reports the corresponding short-side opening.
Equation Used
- Both straight legs have the same declared point-to-point length D.
- One ideal common pivot divides each leg into short distance a and long distance b.
- Corresponding openings are measured between like points on opposite sides of the pivot.
- The declared transfer ratio is r=b/a=B/S.
- The animation varies the included angle while preserving point-to-point length and pivot position.
- Clamp construction, slot geometry, point shape, clearance, friction, compliance, wear, accuracy, scale engraving and safe handling are excluded.
Replaces fabricated clamp-slip and accuracy claims with exact ideal pivot-setting and similar-triangle transfer geometry.
Four points share one adjustable crossing pivot
The Smithsonian describes proportional dividers as two pointed legs opening in an X, with a screw and nut that slide along the legs to select a proportion. The two pairs of points share the same included angle, so their openings are proportional to their pivot distances.
The connected animation preserves two straight equal-length legs and one common pivot.
Use this page to audit ideal pivot geometry
The worksheet locates the pivot for a declared leg length and ratio, then converts a declared long-side opening to the corresponding short-side opening.
It cannot predict accuracy, repeatability, clamp behavior, point wear or instrument quality.
Set the pivot from the required ratio
The pivot distances sum to the point-to-point leg length, and the opening ratio follows directly from similar triangles.
A transparent pivot-setting example
For D=400 mm and r=3, the pivot is 100.00 mm from the short points and 300.00 mm from the long points. A 90 mm long-side opening corresponds to a 30.00 mm short-side opening and a 0.3333 reduction factor.
No tolerance or physical accuracy follows.
Ideal geometry is not instrument accuracy
Real transfer results depend on the instrument's manufactured scale, pivot construction, point condition, friction, stiffness, setup and reading technique. Those require instrument-specific documentation or measurement.
The former numerical accuracy, slot tolerance, point-angle, named deployment, slip-error, maintenance and troubleshooting claims are removed.
Proportional-compass questions
Why does the ratio stay constant?
The corresponding triangles share an included angle and remain similar.
Does this model clamp slip?
No.
Does it predict transfer accuracy?
No.
Can any opening be used?
The equation is ideal; a real instrument's physical range must come from its documentation.
Proportional-compass references
- Smithsonian Institution, Proportional Dividers: four points, sliding screw-and-nut pivot and scale-drawing use.
- Industrial Drawing and Geometry: reducing and enlarging drawing lines in a required proportion.
- Museo Galileo, Double Compasses: intersecting four-point legs with fixed or variable hinge for enlarging and reducing drawings.
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