A triangular eccentric can be represented by a threefold curved form rotating about a central axis. This calculator evaluates one restricted dimension construction; it does not calculate an actual cam profile or follower motion.
Comparing a separate actuator-driven motion
The height comparison below does not calculate a cam motion profile or size an actuator. A separate actuator-driven mechanism needs its complete output motion and loads defined; linkage geometry can change speed and mechanical advantage through the stroke.
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.
The mechanism may also change speed as the linkage angle changes. A constant actuator extension speed does not always create constant output speed, so timing should be checked at the actual output point.
- 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.
Triangular Eccentric Interactive Calculator
Enter vertex spacing s and arc radius ra. Valid inputs satisfy s/2 <= ra <= s. Outputs are derived dimension comparisons and a symmetry count, not lift, dwell, force or design performance.
Equation Used
- s and ra are positive lengths expressed in the same unit.
- The model uses only the stated right-triangle square-root construction.
- The valid domain is s/2 <= ra <= s.
- The constant three is a symmetry count, not a measured lift-cycle result.
- No exact boundary curve, follower geometry, contact, displacement law, dwell, velocity, acceleration, force, stress, wear or structural limit is modeled.
Threefold Curved Form
Curved polygons with threefold symmetry can be used in mechanisms, but their properties depend on the exact boundary construction. U.S. Patent 12,122,196 distinguishes fixed-diameter and variable-diameter triangular or Reuleaux-type follower surfaces; that distinction matters when interpreting motion.
The animation is therefore schematic. It rotates a threefold form to identify symmetry but does not claim that the drawn outline produces the calculator's height difference as follower travel.
What This Calculator Represents
The tool evaluates two right-triangle heights that share half of the entered vertex spacing, then subtracts them. It also reports that difference relative to spacing, the normalized spacing-minus-radius difference and the form's threefold symmetry count.
Those quantities can help inspect the entered construction. They do not define a manufacturable cam, constant-width body or follower displacement diagram.
Restricted Height-Difference Arithmetic
arc height = sqrt(ra²-(s/2)²)
derived height difference = reference height - arc height
difference / spacing = 100 Delta h/s
spacing-minus-radius ratio = 100(s-ra)/s
The accepted domain is s/2 <= ra <= s. Below s/2 the arc-height square root is not real; above s the two reported differences change sign, outside this page's restricted construction.
Worked Construction Example
For s=40 mm and ra=38 mm, the reference height is about 34.64 mm and the arc height is about 32.31 mm. Their difference is about 2.33 mm, or 5.83% of s. The spacing-minus-radius ratio is 5.0%.
Model Boundary
- Calculated: two square-root heights, their difference and two normalized dimension ratios within an explicit domain.
- Illustrated: threefold symmetry only.
- Not calculated: exact curved boundary, constant-width behavior, eccentric offset, follower position, lift, dwell, velocity, acceleration, pressure angle, contact stress, torque, wear, fatigue, tolerances, material choice, manufacturability or safety.
Frequently Asked Questions
Is the height difference the follower stroke?
No. It is only the difference between two stated geometric heights.
Why must ra be at least s/2?
Otherwise ra²-(s/2)² is negative and the real-valued construction is undefined.
Why is ra restricted to no more than s?
The chosen construction compares nonnegative height and radius differences. An arc radius above s falls outside that stated domain.
Does threefold symmetry prove three lifts per revolution?
No. Actual follower motion depends on the exact curve, axis and follower arrangement.
Is the illustrated form a dimensioned cam profile?
No.
Can this calculator size or validate a mechanism?
No.
References
- U.S. Patent 12,122,196, Follower surface and related mechanisms: triangular and Reuleaux-type follower surfaces and the distinction between fixed and variable diameter.
- European Patent EP 0 282 166 B1, Rotary piston engine: curved polygon and tri-lobe geometry described through uniform or essentially uniform diameter.
- National Bureau of Standards, Curves of Constant Width: mathematical treatment including the Reuleaux triangle.
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