This form of cyclograph is a flexible drawing rule arched by a central adjustment screw. Its ends are retained by rollers on a straight bar. Enter the guide spacing and target rise to calculate the desired circle, then enter screw lead to estimate the adjustment from a 5 mm reference rise.
Flexible-Rule Cyclograph Arc Calculator
Set guide spacing, target rise and screw lead. See the center screw adjust the arch while the flexible rule slides through fixed roller guides.
Equation Used
- Symmetric circular target through two ideal point guides and the central rise.
- Fixed guide spacing; rule ends can slide through their retainers.
- No backlash or elastic deflection in the adjustment screw.
- Variable-depth rule is schematic; intermediate real shapes need not be circular.
Target circle geometry, not an elastic spring analysis. Results describe the selected target; animation cycles from a 5 mm reference rise.
A screw arches a flexible rule
Brown movement404 shows an elastic arched rule above a straight supporting bar. A screw through the middle of the support raises the rule at its center. Retainers with small rollers guide the ends while allowing sliding as the arch changes.
The original design uses a rule whose depth at the ends is half its depth at the middle. Its shape is chosen so the outer edge is circular at the greatest intended bend. This does not establish that every intermediate setting is an exact circle.
Set a curve from three points
The two guide points and the center rise define a target circle without locating its distant center. A shaped flexible rule can serve as a drawing edge for that curve.
The animation shows the support, roller retainers, screw and flexible rule directly. Ends feed through the guides as the central arch grows. Target circular geometry is shown for clarity; a manufactured rule needs verification against the required curve.
Target circle and screw adjustment
For guide spacing c and rise h, radius R=(c²/4+h²)/(2h). The half-angle is φ=2 atan(2h/c), so the central angle is 2φ and the arc between guides is 2Rφ with angles in radians.
An ideal screw of lead l moves its pad by l per revolution. Adjustment from the illustrated 5 mm reference rise is (h−5)/l turns. This is geometric travel, not a screw-torque or spring-force calculation.
400 mm guide spacing and 60 mm rise
The target radius is 363.333 mm, and the arc angle is approximately 66.797 degrees. A screw with 1 mm lead requires 55 turns to move from the 5 mm reference rise to 60 mm.
Changing screw lead changes the required turns without changing the selected arc. Changing guide spacing or target rise changes the circle geometry.
What the drawing model does and does not predict
The animation preserves a constant illustrative outer-edge stock length: the central target arc grows while the straight overhangs shorten. This explains end sliding without showing the rule stretching.
The real elastic shape depends on the initial profile, depth distribution, material, guide contacts and screw loading. Circular arcs and ideal point guides are construction targets here, not an elastic-beam solution. Roller radius, rule thickness offsets and bending stress are not included.
Flexible-rule cyclograph questions
Is this a wheel that measures curved lines?
No. Brown404 is a screw-adjusted drawing guide. The former wheel-diameter and indicated-distance calculation described a different instrument and has been replaced with this guide’s arc geometry.
Why do the ends slide?
With guide spacing fixed, a higher arch requires more rule length between the guides. Material feeds in from the overhangs.
Does the animation prove the spring will be circular?
No. It displays the desired circular geometry. The real rule must be shaped and checked for the intended bend range.
Why does screw lead affect only turns?
The target rise is already specified. Lead determines how many turns produce that travel.
Reference
Henry T. Brown, 507 Mechanical Movements, movement404, original flexible-rule cyclograph drawing and description. Circle dimensions and ideal screw travel are derived from geometry; no material properties are inferred from the historical sketch.
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
