This cyclograph draws a circular arc when its center is inaccessible. Two crossed straight rules are clamped at a fixed angle and held rigid by a third rule. Sliding this frame against two fixed guide pins makes the pencil at the crossing follow the circle. Enter the pin spacing and arc rise to calculate the required geometry.
Linear actuator checks for Cyclograph (form 1) Mechanism
An actuator-driven version of cyclograph (form 1) mechanism should be reviewed for stroke, linkage angle, and peak force. The mechanism may feel light through most of the travel and still bind or spike in force at one position.
For cam-driven motion, look for dwell, rapid lift, and shock loading. A linear actuator may simplify positioning, but it will not naturally reproduce a cam profile unless the control system is designed for it.
If the application needs synchronized motion, feedback should be treated as a requirement rather than an accessory. Two open-loop actuators wired together can drift apart when friction, load, or mounting geometry differs between sides.
- Map actuator stroke to the actual output travel before choosing a model.
- Check for binding, changing leverage, and peak load near the ends of travel.
- Decide whether timed motion is acceptable or position feedback is required.
For a FIRGELLI design review, calculate the load case with the FIRGELLI actuator force calculator and plan the switching or controller arrangement with the linear actuator wiring diagram generator. If an actuator or cylinder is already installed, the linear actuator replacement finder helps keep the comparison tied to real dimensions.
Cyclograph Form 1 Arc Interactive Calculator
Set the distance between the two guide pins and the required arc rise. Watch the rigid three-rule frame trace the corresponding circle.
Equation Used
- Rigid frame with two straight rule directions and fixed brace.
- Two ideal point guide pins at chord endpoints.
- Positive rise selects the arc on the shown side of the chord.
- No pin-radius, pencil-offset or clearance correction.
Ideal point pins and straight rule directions. Full arc dimensions; animated sweep stops short of pin endpoints.
A rigid angle slides against two pins
Brown movement403 shows two sloping rules fixed together with a cross brace. The guide pins define the ends of the chord. At the central setup position, the pencil lies above the chord by the required rise, also called sagitta.
During tracing, each rule remains on its guide pin while the braced frame moves as one rigid body. The included angle is constant. By the inscribed-angle relationship, the pencil therefore traces a circular arc through the two pins.
Set an arc without reaching its center
The guide can represent a shallow large-radius curve whose center lies well beyond the drawing sheet. The calculator draws the local arc and guide arrangement without shrinking it to include that distant center.
Pin spacing and rise are the design inputs. The illustrated rule length is selected to cover the shown sweep; it is not an optimized stock length or a physical end-stop design.
Chord, sagitta and the rule angle
For chord c and positive sagitta h, the circle radius is R=(c²/4+h²)/(2h). Let φ=2 atan(2h/c). The specified arc’s central angle is 2φ, and its arc length is 2Rφ with φ expressed in radians.
The angle between the two guide rules is π−φ. This stays constant as the pencil moves along the selected arc. A rise greater than half the chord selects a major arc, whose central angle exceeds 180 degrees; the calculation does not silently switch to the shorter arc.
400 mm chord with 80 mm rise
For c=400 mm and h=80 mm, the radius is 290 mm. The central arc angle is approximately 87.206 degrees, the full arc length is 441.388 mm, and the included angle between the rules is approximately 136.397 degrees.
These results describe the complete specified arc. The animation deliberately stops short of the two endpoints, because pencil and guide-pin coincidence would make the ideal construction indeterminate.
Ideal point guides and straight rule edges
The geometric model treats the pins as points and the rule guidance as ideal lines. Real pin radius, pencil offset, clearance, rule-edge straightness and clamp rigidity affect a built tool and are not included in the result.
The prior page depicted a cylindrical-surface tracer with paper-drive slip. That was a different instrument. This rebuild restores the three-rule circular-arc construction and replaces the unrelated length-transfer calculation with its chord-and-rise geometry.
Cyclograph setup questions
Where is the pencil?
At the intersection of the two sloping rule directions, marked in gold.
Which points remain fixed?
The two blue pins defining the chord. The entire braced rule frame moves.
Why is the center not shown?
The tool is useful when that center is distant or inaccessible. The local guide geometry is enough to construct the arc.
Are all requested input combinations drawable?
Positive chord and rise define a circle, including major arcs. Practical rule reach and physical interference still need checking in a real tool.
Reference
Henry T. Brown, 507 Mechanical Movements, movement403, original drawing and description of the crossed-rule cyclograph for an inaccessible circle center. The chord-and-sagitta equations and constant-angle verification are derived from elementary circle geometry.
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