A Modified Triangular Eccentric — known historically as the Paris Mint cam — is a non-circular eccentric whose profile combines three near-straight rise flanks with rounded apexes to give a coining press a controlled approach, a brief dwell at bottom-dead-centre, and a fast retract. It produces 80-120 strikes per minute on a typical screw-press conversion while holding peak striking force for 8-15 ms. The geometry exists to keep coin-blank impact loads predictable, and the Paris Mint adopted it on its monetary presses in the 19th century to lift coin quality and die life simultaneously.
Modified Triangular Eccentric Interactive Calculator
Vary the approach, dwell, and return cam phase angles and see the resulting single-lobe rotation, dwell share, and lobe count.
Equation Used
This calculator sums the Paris Mint cam phase zones for one lobe. The worked diagram shows a 70 deg approach, a 15-20 deg dwell, and a 30 deg return; using 20 deg dwell gives the stated 120 deg single-lobe profile and therefore three lobes per revolution.
- Angles are cam rotation degrees for one active lobe.
- The worked example dwell is set to 20 deg, the upper end of the stated 15-20 deg range, so 70 + 20 + 30 = 120 deg.
- The calculation is kinematic and does not include elastic deflection, die force, or wear.
Inside the Modified Triangular Eccentric (paris Mint)
The mechanism replaces a plain circular eccentric on the press crankshaft with a three-lobed profile that has been mathematically modified — the lobes are not equilateral arcs but blended curves chosen so the follower (the press ram) accelerates gently into the strike, decelerates into a near-zero velocity dwell, then snaps back. You get the high mechanical advantage of a knuckle-joint or toggle press near bottom-dead-centre without needing the full toggle linkage. If you cut the lobe radii wrong by even 0.2 mm on a 180 mm cam, the dwell collapses and you start seeing double-strike marks on the coin face because the ram bounces off the blank instead of pressing through it.
The ram follows the cam through a roller follower or a flat-faced shoe riding on hardened cam flanks — typically 58-62 HRC induction-hardened 4140 or a nitrided tool steel. Lobe spacing is 120° around the shaft, but the actual rise profile across each lobe is asymmetric: roughly 70° of approach, 15-20° of effective dwell at the apex, and 30° of fast return. This is what separates the Paris Mint cam from a plain eccentric — a circular eccentric gives you a pure sinusoidal ram motion with zero dwell and the worst possible force timing, where peak force happens for an instant and the rest of the rotation is wasted.
Failure modes are specific. If the apex radius wears flat, dwell duration grows uncontrollably and you start work-hardening the dies. If the approach flank pits — almost always from contaminated lubricant — you get chatter at 60-90° before BDC and the coin gets a faint radial witness mark. Out-of-phase mounting between the two cams on a twin-lobe press head produces uneven die loading and tapered coins, measured as a 0.03-0.05 mm thickness difference across the coin diameter.
Key Components
- Three-lobe cam disc: The hardened cam itself, typically 150-220 mm diameter, ground to a modified triangular profile with apex radii held to ±0.05 mm. Material is usually through-hardened D2 or A2 tool steel at 60-62 HRC because the cyclic Hertzian contact stress at the apex can reach 1,800 MPa during a strike.
- Roller or shoe follower: Transfers cam motion to the ram. Roller followers (40-60 mm diameter, needle-bearing supported) suit 80-120 SPM operation; flat shoes are used at lower speeds where you want maximum contact area to spread load. The follower face must match the cam hardness within 2 HRC points or the softer surface galls inside 50,000 cycles.
- Press ram and guide ways: The vertical slide carrying the upper die. Guide clearance is held to 0.02-0.04 mm per side on precision coining presses — any more and the ram cocks during strike, putting bending load into the cam follower and chipping the apex. Mass is typically 80-200 kg for medallion-size presses.
- Lower die bolster and toggle return: The fixed lower die plus the spring or pneumatic return that pulls the ram off the apex during the return stroke. Return force is sized at 1.5-2× ram weight so the follower never leaves the cam surface — separation causes percussive re-engagement that pits the cam flank within hours of running.
- Drive shaft and flywheel: Carries the cam disc and stores the kinetic energy needed for the strike. A typical 50-tonne coining cam press uses a 400-600 kg flywheel at 80-120 RPM, sized so shaft speed drops no more than 8% during the dwell phase. Bigger speed droop and you lose strike consistency between successive coins.
Who Uses the Modified Triangular Eccentric (paris Mint)
The Modified Triangular Eccentric earned its place on coining presses because no other simple cam gives you both controlled approach and a real dwell without resorting to a knuckle-joint linkage. You see it on historical mint machinery, modern medallion presses, and a handful of industrial niches where a short, repeatable dwell at peak force matters more than stroke length.
- Coin minting: Paris Mint (Monnaie de Paris) historical Thonnelier-style coining presses, where the cam profile let a single operator strike 60-80 coins per minute with consistent relief depth.
- Commemorative medallion striking: Schuler MRH-series medal presses use a modified-eccentric cam stack to produce high-relief medals at 40-60 SPM with 800-tonne strike force.
- Powder metallurgy compaction: Small-tonnage PM compaction presses for sintered bronze bushings, where the dwell phase lets powder de-aerate before the final compaction stroke.
- Cold heading and upset forging: Single-blow cold headers for fastener heads, where the modified profile reduces tool shock compared with a plain eccentric and extends die life by 30-40%.
- Watch case stamping: Swiss watch-case finishing presses using small modified-triangular cams (60-90 mm diameter) for final coining of bezels and case backs.
- Token and badge production: Industrial token presses for casino chips and transit tokens, running 100-150 SPM with the cam profile tuned for the specific blank alloy.
The Formula Behind the Modified Triangular Eccentric (paris Mint)
What you really care about is ram velocity at the moment of impact and how long the dwell holds. The formula below gives you peak follower velocity as a function of cam speed, throw, and the modification factor that flattens the apex. At the low end of the typical 60-120 RPM range, ram velocity stays gentle and the coin fills the die slowly — good for high-relief work but slow output. At the high end you maximise throughput but the dwell window shrinks toward the elastic recovery time of the press frame, and beyond that you simply can't hold peak force long enough to fully form the coin. The sweet spot for most medallion work sits at 80-100 RPM.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| vpeak | Peak ram velocity during approach phase | m/s | in/s |
| ω | Cam shaft angular velocity (2π × N / 60) | rad/s | rad/s |
| e | Cam eccentricity (half the total ram throw) | m | in |
| km | Modification factor → ratio of modified-profile peak velocity to a pure circular eccentric (typically 0.85-0.95 for Paris Mint geometry) | dimensionless | dimensionless |
| N | Cam shaft speed | RPM | RPM |
Worked Example: Modified Triangular Eccentric (paris Mint) in a 30-tonne commemorative medallion press
You are commissioning a modified-triangular cam on a 30-tonne medallion press striking 38 mm bronze medallions at a target output of 90 SPM. The cam has a throw of 24 mm (so eccentricity e = 12 mm = 0.012 m), and the profile gives a modification factor km of 0.90. You need to know peak ram velocity at nominal speed, what happens when you slow the press for high-relief proofs, and what happens when production wants to push throughput.
Given
- Nnom = 90 RPM
- e = 0.012 m
- km = 0.90 dimensionless
- Cam diameter = 180 mm
- Ram mass = 120 kg
Solution
Step 1 — convert nominal cam speed to angular velocity:
Step 2 — compute peak ram velocity at nominal 90 SPM:
This is the sweet spot for 38 mm bronze medallions — fast enough to keep flywheel droop under 8% and slow enough that the coin fills the die during the 12 ms dwell. You'll feel a clean, single thump at each strike with no audible bounce.
Step 3 — at the low end of the practical operating range, 60 SPM for high-relief proof striking:
At 0.068 m/s the ram approaches the blank gently — exactly what you want for high-relief work where metal needs time to flow into deep die cavities. Output drops to 60 medallions per minute but reject rate on relief depth falls below 1%.
Step 4 — at the high end of the practical operating range, 120 SPM for production tokens:
In theory you get 33% more throughput. In practice the dwell window collapses from 12 ms toward 8 ms, the press frame's elastic recovery starts eating into the peak-force hold time, and on bronze you'll see a 3-5% reject rate from incomplete relief on the high points of the design. Above ~110 SPM most operators back off unless the design is shallow.
Result
Peak ram velocity at the nominal 90 SPM operating point is 0. 102 m/s, with an effective dwell of around 12 ms at bottom-dead-centre. At the 60 SPM low end you drop to 0.068 m/s — gentle enough for high-relief proof work — and at the 120 SPM high end you theoretically reach 0.136 m/s but the dwell window shrinks below the press frame's recovery time and reject rate climbs above 3%. If you measure 0.085 m/s at nominal instead of the predicted 0.102 m/s, the most common causes are: (1) flywheel speed droop exceeding 12% because the flywheel was undersized for the strike energy, (2) follower roller bearing drag from contaminated grease adding 5-10% rotational resistance, or (3) cam apex wear of more than 0.1 mm flattening the profile and reducing the effective km below 0.90.
When to Use a Modified Triangular Eccentric (paris Mint) and When Not To
The choice between a Modified Triangular Eccentric, a plain circular eccentric, and a knuckle-joint linkage comes down to dwell quality, cost, and what you're striking. Here's how they compare on the dimensions that actually matter when you're specifying a press.
| Property | Modified Triangular Eccentric (Paris Mint) | Plain Circular Eccentric | Knuckle-Joint Toggle |
|---|---|---|---|
| Operating speed (SPM) | 60-120 | 100-300 | 40-80 |
| Effective dwell at BDC | 8-15 ms (real dwell) | <1 ms (instantaneous) | 20-40 ms (longest dwell) |
| Peak strike force (relative) | 1.0× (reference) | 0.6-0.7× | 1.5-2.0× |
| Cam/linkage cost | Medium — ground tool steel | Low — turned eccentric | High — multiple precision pivots |
| Maintenance interval | Inspect cam apex every 500k cycles | Inspect bearing every 1M cycles | Re-shim pivots every 200k cycles |
| Service life (cycles to overhaul) | 3-5 million | 5-10 million | 1-2 million |
| Best application fit | Coining, medallion, light forging | High-speed stamping, blanking | Heavy coining, cold heading |
| Mechanical complexity | Medium — single ground cam | Low — single eccentric | High — 3-bar linkage with toggle |
Frequently Asked Questions About Modified Triangular Eccentric (paris Mint)
This almost always points to ram tilt, not the cam profile. If the upper die is bolted to a ram running with more than 0.05 mm guide clearance per side, the ram cocks slightly during the strike and one die face contacts the blank a fraction of a millisecond before the other. The cam delivers the same total energy but it's distributed unevenly across the die.
Check guide-way clearance with a feeler gauge at top-dead-centre and bottom-dead-centre. If clearance is fine, look at die parallelism — a 0.02 mm difference in die height across the 38 mm coin diameter is enough to produce visible relief asymmetry on bronze.
Lower km (0.85) means a more aggressive profile modification — you flatten the apex more, get a longer dwell, but you also lose some peak velocity and the approach flank gets steeper. This suits powder compaction and high-relief medallion work where dwell time matters more than throughput.
Higher km (0.95) keeps the profile closer to a pure circular eccentric — shorter dwell, higher peak velocity, better throughput. This suits token and badge production where the relief is shallow and you care about strikes per minute. For general-purpose 38-50 mm coining, 0.90 is the well-proven middle ground.
The follower roller is rotating during the rise and return phases, but during the dwell at the apex the roller can momentarily stop rotating because there's no surface speed differential — the cam apex is essentially flat for those 10-15 ms. If the same patch of roller surface lands on the apex every cycle (which happens when roller circumference and cam circumference share a simple ratio), you get repeated Hertzian contact on one spot.
The fix is to use a slightly non-integer ratio between roller and cam diameters — for example, a 47 mm roller on a 180 mm cam instead of a 45 mm roller. The roller indexes around its own axis over many strikes and wear distributes evenly.
Knuckle joints win when you need strike force above roughly 100 tonnes and dwell time above 20 ms — heavy coining of large medallions, cold heading of bolt heads above M10, or any application where the work requires sustained pressure to flow metal. The toggle linkage gives you mechanical advantage approaching infinity right at BDC.
The Modified Triangular Eccentric wins below 80 tonnes where simplicity, lower cost, higher SPM, and easier maintenance matter more. Once you cross into multi-pivot toggle territory, you also accept shorter cycles between re-shimming and a more skilled maintenance burden.
Velocity isn't your problem — dwell duration is. Peak velocity tells you how fast the ram arrives at the blank, but coin fill on high-relief features is governed by how long peak force is maintained while metal flows into the die cavity. If your cam apex radius has worn or was originally cut wrong, the dwell collapses even though approach velocity stays correct.
Measure the cam profile with a coordinate-measuring machine or even a dial indicator on a rotary fixture. Look for apex radius differing from spec by more than 0.1 mm or asymmetry between the three lobes greater than 0.05 mm. Either condition cuts effective dwell roughly in half and produces exactly the symptom you describe.
That witness ring almost always traces back to follower separation during the return stroke. If the ram return spring or pneumatic cylinder has weakened, the follower briefly leaves the cam surface near top-dead-centre and crashes back onto the approach flank a few degrees later. The crash imparts a small secondary impact to the ram that prints as a faint ring on the next strike.
Check return-side preload — it should be 1.5-2× ram weight. On a 120 kg ram you want 1,800-2,400 N of return force minimum. Anything less and the follower starts skipping at higher SPM. A stethoscope on the cam housing makes the skip audible as a soft tick at the same crank angle every revolution.
References & Further Reading
- Wikipedia contributors. Cam. Wikipedia
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