A Triangular Eccentric is a curved-sided three-lobed cam — typically based on a Reuleaux-style profile — that rides under a flat-faced follower to convert continuous rotary input into intermittent reciprocating linear output. You'll find it inside small textile feeders, tablet press auxiliaries, and old-school postage cancelling machines. Its job is to give a follower three identical lift-and-dwell cycles per input revolution without using gears or ratchets. The result is reliable, low-cost, three-step indexing motion from a single shaft.
Triangular Eccentric Interactive Calculator
Vary the vertex spacing and flank arc radius to see the follower stroke and three-lift cam motion.
Equation Used
The calculator estimates peak follower lift from the difference between the reference Reuleaux-style flank height and the actual smaller arc-radius flank height. When the arc radius approaches the vertex spacing, the cam approaches constant width and the stroke trends toward zero.
- Three equal curved flanks with equal vertex spacing.
- Flat-faced follower remains in contact with the cam.
- Stroke is referenced to the ra = s constant-width case.
- Units are consistent and results are shown in mm.
How the Triangular Eccentric Works
The Triangular Eccentric, also called the Triangular Curved Eccentric in older British mechanism texts, works on a simple idea: instead of a round disc with an offset bore, you grind the disc into a three-sided curve where each side is an arc struck from the opposite vertex. As the cam rotates against a flat-faced follower, the follower rises smoothly while one curved side rolls under it, peaks at a vertex, and drops back to the next side. Three lifts per revolution. Three dwells. No gear teeth, no escapement, no ratchet pawl.
The geometry is what makes it work. If the three arcs share the same radius and that radius equals the distance between vertices, the shape is a Reuleaux triangle — a constant-width curve. A constant-width cam under a flat follower produces zero lift, which is the opposite of what we want here. So the Triangular Eccentric for intermittent reciprocating duty deliberately uses arcs slightly *smaller* than the vertex spacing, which breaks the constant-width property and produces a defined stroke. Get this wrong and you get one of two failure modes: too close to constant-width and the follower barely moves; too aggressive and the follower slams at each vertex transition, hammering the cam face and the follower edge.
Tolerance on the arc radius is tight. On a 40 mm vertex-spacing cam, we cut the arcs at 38.0 mm ±0.05 mm. Push the radius below about 37 mm and the vertex angle gets sharp enough that follower contact stress spikes — you'll see pitting on the cam face within a few thousand cycles. Above 39 mm and the stroke shrinks to almost nothing. The follower face also has to stay flat and parallel to the cam axis within 0.02 mm or the lift profile asymmetries between the three lobes, and you get a wobble in what should be three identical strokes.
Key Components
- Three-lobed cam disc: The driven element. Ground from hardened tool steel (typically O1 or A2 at 58-62 HRC) with three curved flanks meeting at three vertices. Vertex spacing and arc radius set the stroke length directly.
- Flat-faced follower: Rides on top of the cam, translating cam profile into linear motion. The face must be hardened to within 2 HRC of the cam to avoid one part wearing into the other. Width should exceed cam thickness by at least 1 mm per side to handle slight axial drift.
- Follower guide: A linear bushing or sliding block that constrains the follower to vertical motion only. Side play above 0.1 mm lets the follower cock under load and chew the cam edge at vertex transitions.
- Return spring or gravity load: Keeps the follower in contact with the cam during the descent phase. Spring rate must produce at least 1.5× the follower weight at minimum compression, otherwise the follower lifts off near peak velocity and slams back down.
- Drive shaft and key: Transmits torque from the input source. Key fit must be tight — any backlash here translates directly into timing error visible at the follower as inconsistent dwell phase between the three lobes.
Real-World Applications of the Triangular Eccentric
The Triangular Eccentric shows up wherever you need three discrete pushes per revolution without the cost or wear of an indexing gear. It's a niche cam, but where it fits, it's hard to beat on simplicity.
- Postal equipment: Older Pitney Bowes mail-cancelling drums used a triangular eccentric to drive the inking pad against the envelope flow three times per drum rotation.
- Textile machinery: Yarn lubrication applicators on Saurer and Schlafhorst-style winders use the Triangular Curved Eccentric to dab the yarn three times per cycle as it passes the lubricator wick.
- Pharmaceutical packaging: Auxiliary punch lifters in some rotary tablet presses use a Triangular eccentric for intermittent reciprocating action on dust-shield wipers — three wipes per upper-punch indexing rotation.
- Automatic stamping: Self-inking date stamps in industrial mailrooms use a small triangular cam to lift the stamp head three times per handle stroke for re-inking.
- Educational kinematics kits: MIT's mechanism teaching collection and the Cornell KMODDL archive both feature triangular eccentric cams as classroom examples of three-pulse intermittent motion.
- Antique mechanical music: Some 19th-century cylinder music boxes used triangular eccentrics to drive bellows or chime hammers at three-beat intervals from a single mainspring shaft.
The Formula Behind the Triangular Eccentric
The stroke of a Triangular Eccentric is set by the difference between the vertex circumradius and the inscribed circle radius of the three-arc profile. This is the number you need before you cut metal. At the low end of the typical operating range — small arc-to-vertex differences — the stroke is so short the follower barely registers a lift; at the high end, the vertex angle gets sharp and contact stress climbs into the territory where you need bearing-grade hardness on both surfaces. The sweet spot for most small mechanisms sits where the stroke is roughly 5-8% of the vertex spacing.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| h | Follower stroke (peak lift above the lowest point of the profile) | mm | in |
| Rv | Distance from cam centre to a vertex | mm | in |
| ra | Arc radius of each curved flank | mm | in |
| s | Side length between two vertices (chord across one arc) | mm | in |
Worked Example: Triangular Eccentric in a textile yarn-lubrication applicator
You're sizing a Triangular Eccentric for a yarn-lubricator dabber on a small bobbin winder running at 200 RPM input. Vertex spacing s = 40 mm, vertex radius Rv = 23.1 mm (centroid-to-vertex of an equilateral triangle with 40 mm sides), and you're choosing an arc radius near 38 mm. You need to know the stroke, the follower velocity, and where the design starts to fail.
Given
- s = 40 mm
- Rv = 23.1 mm
- ra (nominal) = 38.0 mm
- Input speed = 200 RPM
Solution
Step 1 — at the nominal arc radius of 38.0 mm, compute the lowest point of the cam profile (the perpendicular distance from cam centre to the midpoint of an arc):
Step 2 — but wait: dlow is measured from the arc centre, which sits on the opposite vertex, 23.1 mm from cam centre on the far side. So the actual radius from cam centre at the arc midpoint is:
The follower stroke is the difference between vertex radius and arc-midpoint radius:
Step 3 — at the low end of the practical range, ra = 39.5 mm (close to constant-width):
That's barely a flicker. The wick would touch the yarn but produce no real wiping motion — you'd see uneven lubrication along the bobbin. At the high end of the practical range, ra = 36.5 mm:
Big stroke, but at 200 RPM that's 600 lifts per minute, and the vertex transition becomes sharp enough that peak follower acceleration spikes above 80 m/s2. You'll hear it hammer. The 38.0 mm nominal sits in the sweet spot — enough lift to dab the yarn cleanly, smooth enough transitions that the follower stays in contact through every cycle.
Result
Nominal stroke at ra = 38. 0 mm is approximately 2.6 mm at 600 cycles per minute — enough to wet the yarn on every dab without the follower bouncing off the cam. At ra = 39.5 mm the stroke collapses to 0.6 mm and the lubricator misses contact intermittently; at ra = 36.5 mm the stroke jumps to about 5.1 mm but the cam vertices start hammering and you'll see edge-rolling on the cam face within 50,000 cycles. If your measured stroke is 30%+ below the predicted value, check three things: (1) cam-to-shaft key clearance — any rotational slop reduces effective lift, (2) follower-guide side play above 0.1 mm letting the follower tilt rather than translate, or (3) return spring preload too low so the follower separates from the cam near peak velocity and lands late.
Choosing the Triangular Eccentric: Pros and Cons
The Triangular Eccentric is one of several ways to get intermittent reciprocating motion from a continuous rotary input. The Triangular Curved Eccentric competes mainly against the Geneva drive, the snail cam, and the simple offset-disc eccentric. Each has a different cost-vs-precision-vs-cycle-life profile.
| Property | Triangular Eccentric | Geneva Drive | Snail Cam |
|---|---|---|---|
| Pulses per input revolution | 3 (fixed by geometry) | Typically 4-6 (set by slot count) | 1 per revolution |
| Practical input speed | Up to 600 RPM with hardened steel pair | Up to 300 RPM before pin-slot impact wear dominates | Up to 1500 RPM |
| Stroke repeatability | ±0.05 mm with ground cam | ±0.02 mm (positively constrained) | ±0.1 mm (depends on follower spring) |
| Manufacturing cost (small batch) | Low — single ground disc | High — driver, driven wheel, locking arc | Low — single profile cut |
| Service life at typical load | 5-10 million cycles before edge wear | 10+ million cycles | 2-5 million cycles |
| Best application fit | Three-pulse-per-rev light-load reciprocation | Precision indexing tables, film advance | Single sharp drop-and-reset, e.g. trip hammers |
| Complexity | Two parts (cam + follower) | Three to four parts plus locking geometry | Two parts (cam + follower) |
Frequently Asked Questions About Triangular Eccentric
Nine times out of ten the cam itself is fine and the problem is the mounting. If the cam bore is even 0.05 mm off the geometric centroid of the three arcs, one lobe sits closer to the follower than the others and you get a tall-tall-short pattern. Pull the cam, set it on a surface plate with a height gauge against each vertex in turn, and confirm all three vertices are within 0.02 mm of the same radius from the bore.
Second cause: shaft runout. A bent shaft or worn bushing will show as a slow drift in stroke height that cycles once per revolution rather than three times. Indicate the shaft directly — anything above 0.03 mm TIR is your problem.
Yes, and that's actually a different mechanism — a constant-width cam under a flat follower gives no reciprocating output, which is the whole reason the Triangular Eccentric breaks the constant-width geometry. If you accidentally cut a true Reuleaux profile (arc radius exactly equal to vertex spacing) and bolt it under a flat follower, the follower will sit motionless while the cam spins underneath it. Useful demo. Useless mechanism.
Geneva wins if you need positive locking between dwells — the locking arc holds the output rigidly stationary, which matters for things like film cameras or assembly fixtures where the load can push the output back during the dwell. Triangular Eccentric wins on cost and parts count, but the dwell is geometric — the follower is held by the cam profile, not locked. If anything pushes the follower during the dwell phase it will move.
Rule of thumb: load on the output during dwell exceeds 20% of the cam-driving force, go Geneva. Below that, the triangular cam is half the price and half the part count.
The spring rate is sized for static load, not dynamic. At each vertex transition the follower decelerates hard — at 600 RPM on a 3 mm stroke that's tens of g's of peak acceleration. If the spring's pre-load force is below the follower mass times peak deceleration, the follower goes ballistic and lands back on the cam late, producing a click and an irregular stroke.
Quick fix: measure the spring force at minimum compression (follower at top of stroke). It must exceed follower mass × peak acceleration with at least 1.5× safety factor. For a typical small build that means a stiffer spring than your intuition will suggest.
Yes. The terms Triangular Eccentric, Triangular Curved Eccentric, and Triangular eccentric for intermittent reciprocating motion all refer to the same three-arc cam under a flat follower. The 'curved' qualifier emphasises that the flanks are arcs (not straight lines, which would make it a true triangle and produce impact loading at every vertex). Older British texts and 19th-century kinematic atlases tend to use the longer name; modern usage drops the qualifier.
Aim for Ra 0.4 µm or better on the cam flanks and the follower face. Above Ra 0.8 µm the asperity contact stress at vertex transitions punches through any boundary lubrication you can apply, and you'll see pitting start at the vertices within the first 100,000 cycles. Polish below Ra 0.2 µm and you stop seeing finish-related wear entirely — the failure mode shifts to bulk fatigue, which is what gives you the 5-10 million cycle life.
Match hardness within 2 HRC between cam and follower — if one part is significantly softer it will carry all the wear and the harder part will plough through it.
The formula assumes a flat follower face contacting the cam at a single point along the centreline of motion. In practice the follower face has a small radius break on its edges (intentional, to prevent corner-loading the cam), and that radius effectively shortens the lift by however deep the break is. A 0.5 mm radius break on a 2.6 mm stroke knocks roughly 0.15 mm off the measured stroke.
Second source of mismatch: cam axis not perpendicular to follower travel. A 1° tilt on a 40 mm cam costs you about 0.7 mm of effective stroke through cosine error. Indicate both axes square before you blame the math.
References & Further Reading
- Wikipedia contributors. Cam. Wikipedia
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
