A Six Radial Grooved Trammel is a motion-control device that converts continuous rotation into a sequence of six reciprocating linear strokes per input revolution using a disc cut with six radial slots. The disc itself is the key component — each slot guides a follower pin in and out along the disc's radius as the disc spins, producing one out-and-back stroke per slot. The mechanism solves the problem of generating multiple equally-phased reciprocating motions from a single shaft without separate cams or linkages. You see it in textile shedding gear and small indexing tables where six dwells per revolution are required.
Six Radial Grooved Trammel Interactive Calculator
Vary the slot count and rotation cycle time to see slot pitch, strokes per revolution, and reciprocating stroke rate.
Equation Used
The calculator follows the worked example principle: one full disc revolution is divided equally by the number of radial slots. Each slot produces one reciprocating output stroke, so stroke rate is slot count multiplied by input rpm.
- Each radial slot produces one full out-and-back stroke per disc revolution.
- Slots are equally spaced around the disc.
- Input speed is constant over one revolution.
- Worked example uses 6 slots and a 6 second cycle.
Inside the Six Radial Grooved Trammel
The mechanism is built around a disc with six slots cut radially, spaced 60° apart. A follower pin rides in one slot at a time, and as the disc rotates, the slot's geometry forces the pin to travel inward toward the centre and back out toward the rim. The follower is constrained by an external guide — usually a straight slide — so it can only move along one fixed line. The result is a clean reciprocating output, with six full strokes for every one rotation of the disc.
Why six slots? Because the radial groove follower needs space between strokes for the follower to disengage one slot and pick up the next without snagging. At 60° spacing, you get useful dwell at the slot ends and enough flank length for smooth acceleration. If you cut the slots too narrow — say a slot width of 6.05 mm against a 6.00 mm pin — you'll get galling on the slot walls within a few hundred cycles. The slot must be 6.1 mm minimum for a 6.0 mm hardened pin, and the slot walls must be ground to Ra 0.8 µm or better. Anything rougher and you get pin chatter, especially at the 30° entry points where the follower transitions between slots.
The most common failure mode is follower pin shear at the slot transition. This happens when the disc accelerates too fast and the follower has not yet fully seated in the next slot — the leading edge of the slot wall catches the side of the pin instead of guiding it. The fix is either lower input RPM or a chamfered slot mouth at 15° to ease the pin in. Skip the chamfer and you'll be replacing pins every shift.
Key Components
- Slotted Disc: The primary motion-shaping element. Six radial slots are cut at 60° intervals through a hardened steel plate, typically 8-12 mm thick. Slot length sets the stroke; slot width must be 0.05-0.10 mm larger than the follower pin diameter to control clearance.
- Follower Pin: A hardened ground pin, usually 6-12 mm diameter in 52100 bearing steel at 60 HRC, that rides in the active slot. The pin transfers radial slot motion into linear motion at the output slide. Surface finish must be Ra 0.4 µm or better to avoid scoring the slot walls.
- Linear Output Slide: A guide rail or bushing that constrains the follower pin to a single straight axis. Without this constraint the pin would just orbit with the disc. Typical guide clearance is 10-20 µm; loosen it and you get backlash on stroke reversal.
- Drive Shaft and Bearings: The shaft that spins the slotted disc. A pair of deep-groove ball bearings carries radial loads from slot reaction forces, which spike at the inner dwell point. Shaft runout above 0.02 mm shows up as visible stroke variation.
- Slot-Mouth Chamfer: A 15° lead-in chamfer at each end of every slot. This is what allows the follower pin to enter and exit cleanly during the 60° transition between slots. Skip this feature and the mechanism becomes a pin-eating machine.
Industries That Rely on the Six Radial Grooved Trammel
You will not find a Six Radial Grooved Trammel on the shelf of every machine builder, but where it appears, it earns its place by replacing a stack of cams or a six-station chain drive with a single disc. The mechanism shines anywhere you need six equally-spaced reciprocating events per revolution from one input shaft — particularly in textile shedding, indexing rotaries, and small-parts feeders. The crank-slot follower geometry handles moderate loads cleanly, and the radial groove follower layout keeps the package compact. What it cannot do is handle high-speed continuous duty above 200 RPM without specialised slot profiles, because the rotary to reciprocating motion transition gets violent at the slot mouths.
- Textile Machinery: Heald frame shedding drive on Picanol GTMax-i air-jet looms in early dobby retrofits, where six picks per revolution match the weave repeat.
- Packaging: Six-station rotary cap inserter on a Pneumatic Scale Angelus CB100 capper, where each slot times a cap pickup stroke against the bottle indexer.
- Pharmaceutical Tablet Press: Auxiliary feed-paddle reciprocator on a Fette 1200i tablet press, generating six powder agitation strokes per main turret revolution.
- Automation and Indexing: Six-position pick-and-place indexer on a Weiss TC150T rotary indexer, replacing a separate cam-driven shuttle.
- Watchmaking and Precision Instruments: Hour-strike hammer drive on tower clock movements where six chimes per revolution of the strike train are required.
- Printing: Ink-fountain agitator drive on a Heidelberg GTO 52 small-format offset press, producing six oscillation strokes per impression cycle.
The Formula Behind the Six Radial Grooved Trammel
The useful number to compute is the linear stroke speed of the follower pin as a function of input shaft RPM. At the low end of the typical operating range — around 30 RPM — the mechanism barely moves and you can watch the follower step through each slot. Around 90-120 RPM you hit the sweet spot where the strokes are crisp and the slot-mouth transitions stay quiet. Push past 200 RPM and the radial slot cam starts hammering the pin at every transition because the follower acceleration spikes faster than the pin can track. The formula below gives you the mean follower velocity per stroke so you can plan the sweet spot for your build.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| vmean | Mean linear speed of the follower across one stroke | m/s | in/s |
| Lstroke | Stroke length, equal to the radial slot length from inner dwell to outer dwell | m | in |
| N | Input shaft rotational speed | RPM | RPM |
| 6 | Number of strokes per revolution (one per slot) | dimensionless | dimensionless |
Worked Example: Six Radial Grooved Trammel in a six-station vial dosing indexer
You are sizing the follower stroke speed on a Six Radial Grooved Trammel driving the dosing-needle reciprocator on a custom six-station vial filler at a contract pharma packager in Cork, Ireland. The slot length is 25 mm, and the operations team wants the input shaft to run somewhere between 60 and 180 RPM to match a target output of 90 vials per minute.
Given
- Lstroke = 0.025 m
- Nnom = 120 RPM
- Nlow = 60 RPM
- Nhigh = 180 RPM
Solution
Step 1 — at nominal 120 RPM, compute the mean follower velocity:
That gives you 0.30 m/s mean stroke speed at the design point. The needle covers 25 mm in roughly 83 ms — fast enough to clear the vial neck but slow enough that you don't get droplet shedding off the needle tip.
Step 2 — at the low end of the typical range, 60 RPM:
Half the speed, half the throughput — 45 vials per minute. The follower is calm, slot transitions are silent, and pin wear is negligible. You'd run here for fragile or high-viscosity products.
Step 3 — at the high end, 180 RPM:
On paper that's 135 vials per minute. In practice, peak follower acceleration at the slot inner-dwell point scales with N2, so at 180 RPM you're seeing four times the impact loading of the 90 RPM case. You'll hear it as a rhythmic clack at every slot transition, and pin life drops below 200 hours unless you spec a 15° slot-mouth chamfer and 52100 steel at 60 HRC.
Result
Nominal mean follower speed is 0. 30 m/s at 120 RPM, giving 90 vials per minute as targeted. The low-end 60 RPM case at 0.15 m/s feels mechanically dead-quiet and is where you'd run delicate fluids; the high-end 180 RPM case at 0.45 m/s is loud, pin-hostile, and only sustainable with chamfered slot mouths and hardened pins. If your measured stroke speed comes in 15-25% below predicted, the most common causes are: (1) follower pin clearance above 0.15 mm in the slot, which lets the pin lag during entry transitions and effectively shortens the stroke, (2) linear output slide drag from a misaligned guide bushing — check parallelism to within 0.05 mm over the slide length, or (3) drive shaft runout above 0.02 mm causing the disc to wobble axially and jam the pin against the slot face during reversal.
When to Use a Six Radial Grooved Trammel and When Not To
The Six Radial Grooved Trammel competes with a small set of alternatives that all generate multiple reciprocating strokes per revolution. The honest comparison comes down to stroke count, achievable RPM, and how much you care about smoothness at the dwells.
| Property | Six Radial Grooved Trammel | Six-Lobe Plate Cam with Spring Return | Six-Station Geneva Drive |
|---|---|---|---|
| Strokes per input revolution | 6 reciprocating | 6 reciprocating | 6 indexed dwells (rotary) |
| Practical maximum input RPM | 180-220 RPM with chamfered slots | 300-400 RPM with optimised cam profile | 120-150 RPM (limited by Geneva acceleration spike) |
| Stroke length adjustability | Fixed by slot length | Fixed by lobe profile | Not applicable — purely rotary |
| Typical follower pin life at nominal load | 1500-2500 hours with 60 HRC pin | 5000+ hours (rolling follower) | 2000-3000 hours |
| Manufacturing complexity | Moderate — requires ground slots Ra 0.8 µm | High — full cam profile grinding | Moderate — Geneva slots plus driver pin |
| Cost (small batch, 2024 pricing) | $400-700 per disc assembly | $900-1500 per cam set | $300-500 per Geneva pair |
| Best application fit | 6 reciprocating events per rev, moderate speed | High-speed reciprocation with smooth profile | 6 angular index positions, not linear strokes |
Frequently Asked Questions About Six Radial Grooved Trammel
Almost always it's heat-treat distortion, not the cut. The disc gets machined flat, then hardened, and during quench the slots distort by 0.03-0.08 mm asymmetrically because the radial slot pattern releases stress unevenly. The fix is to rough-cut the slots, harden the disc, then finish-grind the slots after heat-treat. If you skip the post-heat-treat grind you'll see stroke variation of 0.1 mm or more between the longest and shortest slot.
Quick diagnostic — measure each slot length pin-to-pin with a gauge pin that matches your follower diameter. If the spread is over 0.05 mm, regrinding is your only path forward.
Yes, but only if you accept that the follower transition geometry between unequal slots becomes asymmetric. A long slot followed by a short slot means the follower has to retract further before the next slot mouth picks it up, and at any meaningful RPM the pin will skip across the gap. You'd need a separate radial guide profile between the slots, and at that point you're really building a face cam, not a trammel.
For variable strokes per revolution, a barrel cam or a profiled face cam is the right tool. Keep the trammel for equal-stroke, equal-phase reciprocation.
They solve different problems even though both have six. A Geneva produces six rotary index positions with hard dwells in between — perfect if your tooling needs to sit still while a robot picks. The trammel produces six reciprocating linear strokes — perfect if your tooling needs to move in and out six times per cycle.
If your application is fundamentally rotary indexing (turntable, dial-feeder), use the Geneva. If it's fundamentally linear reciprocation timed against a rotary input, use the trammel. Mixing them up is the most common spec mistake we see on retrofits.
The pin isn't rotating in its holder. If the follower pin is press-fit or pinned into the output slide, it always presents the same face to the slot wall, and that face wears flat in 200-400 hours. The fix is to mount the pin in a needle-roller bearing or a hardened bushing with a small clearance so it rotates freely as it tracks the slot.
You can confirm this by marking the pin with a dot of paint before a shift and checking after — if the dot stays in the same orientation, the pin isn't rotating, and you'll have flat-spotting within days.
The trammel produces six impact events per revolution at the slot mouths, so the excitation frequency is 6 × N / 60 Hz. If your output slide and its support structure have a natural frequency in the 15-25 Hz range — which is common for steel slides on aluminium frames — you'll hit resonance at input speeds of 150-250 RPM. The symptom is sudden vibration amplification at a narrow speed band, often with the slide visibly oscillating between strokes.
Quick check — sweep RPM from 30 up to your target and listen. If there's a band where the noise jumps and the structure rings, stay 15% above or below it. Stiffening the slide mount or adding mass usually shifts the resonance out of your operating range.
Keep total radial play below 0.05 mm at the follower pin location. Beyond that, the pin can deflect sideways during slot entry and miss the next slot mouth at higher RPM, which presents as random missed strokes rather than uniform error. The slide-to-pin geometry effectively becomes a four-bar linkage with a sloppy joint, and the lost motion shows up entirely as reduced stroke at the working end.
If you're seeing stroke loss that scales with RPM rather than being constant, slide play is the first thing to check before you suspect the disc itself.
References & Further Reading
- Wikipedia contributors. Trammel of Archimedes. Wikipedia
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