A triangular eccentric can produce a repeating rise and fall as it rotates beneath a follower. This calculator explores a Reuleaux triangle of constant width, giving its centroid support limits, ideal lift and threefold repetition rate.
Equal-Arc Triangular Eccentric Calculator
Enter constant width and shaft speed. The worksheet reports the centroid support limits, ideal support lift and three-cycle repetition rate for the declared Reuleaux construction under an ideal translating flat follower. It does not reproduce an unidentified historical cam or rate a real valve or press.
Equation Used
- The illustrated profile is a Reuleaux triangle formed by three radius-w arcs centered on the vertices of an equilateral triangle of side w.
- The shaft passes through the profile centroid and the follower is an ideal horizontal flat translating vertically.
- The reported support limits are exact centroid support-function extrema for the declared equal-arc profile.
- Dynamics, dwell, force, material, stress, manufacture, valve timing and historical dimensional fidelity are excluded.
The numerical model uses three equal circular arcs and a shaft through the centroid. It calculates support height for an ideal flat follower, without predicting contact loads or historical cam dimensions.
Historical triangular eccentric and the model used here
Brown's movement 91 describes a triangular eccentric used in France for steam-engine valve motion. The model here uses a Reuleaux triangle of constant width w rotating about its centroid. Its calculated vertical support height represents an ideal flat follower; the round moving marker in the diagram indicates that height and is not a solved roller contact.
Geometry study, not a machine rating
Use this calculator to examine the support range and repetition of the declared equal-arc construction. Applying any triangular eccentric to a valve, press or other machine requires the actual measured profile, follower geometry, speed, acceleration, force, stress, lubrication and clearance.
Exact support limits for the declared construction
Declared-geometry example
For w=100 mm, the centroid support ranges from 42.3 mm to 57.7 mm, for 15.5 mm ideal support lift. At 60 rpm the threefold support function repeats 180 times per minute.
Limits of the equal-arc model
The equal-arc geometry defines its own support motion. It does not establish the dimensions of a historical valve cam, a finite dwell interval, press force, contact stress or service life. Those results require the actual cam profile, follower and operating conditions.
Triangular-eccentric questions
What profile does the calculator use?
A Reuleaux triangle formed by three equal circular arcs, rotating about its centroid. It is an ideal geometry model, not a measured historical cam.
Does a constant-width profile create true dwell?
Not by itself under the illustrated centroid and flat-follower arrangement; the support function varies three times per revolution.
Can this size a steam valve or coining press?
No.
Triangular-eccentric references
- Henry T. Brown, Five Hundred and Seven Mechanical Movements, movement 91: identifies a triangular eccentric for intermittent reciprocating valve motion in France; no profile dimensions or Paris Mint application are given.
- Cornell University Library scan of Brown's mechanical movements: independent historical scan of the source work.
- Wolfram MathWorld, Reuleaux Triangle: equal-arc construction and constant-width geometry used for the explicitly declared model.
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