Equally-traversing rollers via slotted bar is a linkage that forces a row of rollers to slide along a common shaft so their spacing stays equal at every position. A single slotted bar pinned to each roller carriage at proportional distances drives the whole set with one input, holding pitch error typically below 0.5 mm across a 600 mm spread. We use it where a row of nip rollers, idlers, or guide rollers must expand and contract uniformly — for example on Bobst sheet-fed presses where the cross-web roller bank must reset for different sheet widths without drift.
Equally-traversing Rollers via Slotted Bar Interactive Calculator
Vary carriage count, bar span, swing angle, and slot clearance to see proportional roller travel and accumulated pitch error.
Equation Used
The slotted bar makes each carriage move in proportion to its index position. For carriage i, travel equals i times the per-step travel, where per-step travel is (s / N) * sin(theta). The outer carriage travel x_N is therefore s * sin(theta). The clearance estimate is a simple worst-case stack-up for pin-to-slot play.
- Straight slotted bar with equally spaced pin stations.
- Carriages move on a straight guide rail with negligible bearing friction.
- Swing angle theta is entered in degrees and converted to radians in the calculation.
- Slot clearance stack is estimated linearly as clearance per pin times carriage count.
Inside the Equally-traversing Rollers via Slotted Bar
The principle is geometric, not driven by gears or belts. You have a fixed guide rail and a set of N roller carriages riding on it. A single slotted bar sits at an angle to the rail, and each carriage carries a pin that engages the slot. As the bar swings or translates, every pin slides along the slot, but because the pins sit at proportional spacings along the bar, every carriage moves by an amount proportional to its index position. Carriage 1 moves by Δ, carriage 2 moves by 2Δ, carriage 3 moves by 3Δ, and so on. The result is uniform pitch — the synchronised roller traverse you need when a row of nip rollers has to open and close together.
The geometry only stays clean if the slot is straight, the pins are a tight sliding fit, and the bar pivots about a fixed point on the rail. If the slot has 0.2 mm of clearance on each pin and you have 8 carriages, you can stack 1.6 mm of cumulative pitch error across the row. That is why we spec the pin-to-slot fit at H7/g6 — a slip fit with roughly 10-20 µm clearance — and why the slotted bar itself needs to be ground flat, not milled. A milled slot with 50 µm of waviness will telegraph straight into roller spacing error and you will see web wander on a paper line within minutes.
Common failure modes are predictable. If a pin seizes from contamination, that one carriage stops moving and the rest of the row goes out of pitch — you see it as one nip closing late or a single guide roller sitting proud of the others. If the slot wears oval near the high-use pins (usually the outermost ones, because they travel the furthest), pitch accuracy drops first at the ends of the row. And if the bar pivot loosens, the whole equal-spacing relationship breaks down because the proportional distances stop being proportional.
Key Components
- Linear guide rail: A precision-ground rail (typically a hardened steel shaft 20-30 mm diameter, or an INA/Schaeffler profile rail) that constrains every roller carriage to a single axis of motion. Straightness must hold below 0.05 mm per metre or the carriages bind.
- Roller carriages: Each carriage carries one roller plus a drive pin that engages the slotted bar. Carriages run on linear bushings or recirculating ball blocks with less than 0.02 mm radial play, otherwise the pin geometry pulls the roller axis off-square.
- Slotted drive bar: A flat bar with one continuous straight slot, ground to flatness within 20 µm over its length. The bar pivots at one end and the carriage pins ride in the slot at indexed positions corresponding to roller numbers 1, 2, 3 ... N.
- Drive pins: Hardened dowel pins (typically 6-10 mm diameter, 60 HRC) press-fit into each carriage. Pin-to-slot fit is held at H7/g6 — about 10-20 µm clearance — so the carriage slides cleanly without backlash.
- Pivot bearing: A single needle roller bearing or precision shoulder bolt anchoring the slotted bar to a fixed point on the frame. Any axial or radial play here multiplies into spacing error at the far end of the bar.
- Input actuator: A handwheel, leadscrew, or Linear Actuator that swings or translates the slotted bar. A FIRGELLI FA-150 with 200 mm stroke at 7 mm/s is a typical fit for a 6-roller bank with 400 mm total spread.
Who Uses the Equally-traversing Rollers via Slotted Bar
You see this mechanism wherever a row of rollers, fingers, or carriages must change spacing in unison without independent control of each one. It shows up in printing, packaging, textile, and material handling lines where width changeovers happen often and operators need a single hand-crank or actuator to reset the whole row. It is mechanically simpler and cheaper than giving each carriage its own servo, and the equal-spacing relationship is enforced by geometry — there is no software to drift, no encoders to calibrate.
- Sheet-fed printing: Cross-web idler roller banks on Bobst Masterflex folder-gluers — operators reset roller pitch for different blank widths in one motion.
- Textile finishing: Selvedge guide roller arrays on Monforts Montex stenters where edge guides must equalise across a 2400 mm fabric width.
- Corrugated converting: Slitter-scorer head spacing on BHS and Fosber corrugator lines, where multiple slitting heads must redistribute evenly across the web for new order widths.
- Paper rewinders: Idler roller banks on Goebel-IMS slitter-rewinders that handle multiple narrow rolls — the pantograph spacing logic equalises gaps between rewind shafts.
- Solar cell stringing: Cell-pickup finger arrays on Schmid stringer machines, where 6 to 12 vacuum fingers must spread evenly across a half-cut module pitch.
- Bottling lines: Lane divider finger sets on Krones Modulpalm palletisers where bottle lanes must reset for different pack counts.
The Formula Behind the Equally-traversing Rollers via Slotted Bar
The formula gives you the displacement of each carriage as a function of the input bar swing angle and the carriage's index position along the bar. At small input angles you get fine adjustment — useful for trim corrections on a running line. At large angles you cover the full width changeover range, but the relationship stays linear in pin position only if you drive the bar in pure translation; pure rotation introduces a cosine error that grows past about 15° of swing. The sweet spot for most production builds is a translating slotted bar with ±50 mm input stroke driving 6-10 carriages over a 300-600 mm total spread.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| xi | Displacement of carriage i along the guide rail | mm | in |
| i | Carriage index, counting from the pivot end (1, 2, 3 … N) | dimensionless | dimensionless |
| s | Length of the slotted bar between pivot and the outermost pin | mm | in |
| N | Total number of carriages on the bar | dimensionless | dimensionless |
| θ | Swing angle of the slotted bar from its rest position | degrees | degrees |
Worked Example: Equally-traversing Rollers via Slotted Bar in a corrugated slitter-head spacing bar
Sizing the slotted-bar synchroniser for a 6-head slitter on a BHS corrugator line. The slitter heads must space evenly across a 1200 mm web, which means a maximum end-to-end spread of 1000 mm (to leave 100 mm edge trim each side). The slotted bar is 1100 mm long from pivot to outer pin, carries 6 carriages at indexed positions, and the input is a FIRGELLI Linear Actuator swinging the bar through a typical operating range of 10° to 30° of arc.
Given
- s = 1100 mm
- N = 6 carriages
- θnom = 20 degrees
- θlow = 10 degrees
- θhigh = 30 degrees
Solution
Step 1 — compute the per-index spacing factor at nominal 20° swing. This tells you how far each unit of carriage index moves the carriage along the rail:
Step 2 — compute carriage 6 displacement at nominal. This is the outermost head, which moves the most:
That sets the spread between the innermost and outermost slitter head at 376 mm — a useful mid-range setting for narrow-box production.
Step 3 — at the low end of the typical operating range, 10° swing:
At 10° you get a tight 191 mm spread between heads 1 and 6 — fine adjustment territory. Operators use this band for small order changeovers, trimming a few millimetres at a time. At 30° (the high end of typical), the geometry opens up:
550 mm is full-width territory for a 1200 mm web — exactly what you size the mechanism around. Push past 30° and the slot length on each carriage starts demanding extra travel along the bar axis, which means a longer slot, more pin-to-slot wear, and the cosine term begins eating real accuracy. Above 40° we typically swap to a translating bar instead of a swinging one.
Result
Nominal carriage-6 displacement is 376 mm at 20° swing, giving a clean 62. 7 mm pitch between heads. In practice that means an operator turning the input crank one quarter turn sees the slitter heads fan open across the web in perfect proportion — heads 2, 3, 4, 5 land exactly where head 6 says they should. The range from 10° to 30° covers 191 mm to 550 mm of total spread, with the 20-25° band being the sweet spot where slot wear, pin loading, and accuracy all sit in balance. If you measure a real-world spread that disagrees with the calculation, look at three things first: (1) pivot bearing radial play above 50 µm — it shifts the effective pivot location and skews every carriage by a different amount, (2) slot waviness from a milled rather than ground slot causing carriage 6 to lag carriage 1 by 0.5-1.0 mm at full extension, and (3) thermal growth of the bar itself if the line runs hot — a 1100 mm steel bar grows about 0.13 mm per 10°C, which shows up as proportional pitch drift across the row.
When to Use a Equally-traversing Rollers via Slotted Bar and When Not To
The slotted-bar synchroniser is one of three common ways to enforce equal spacing across a row of carriages. Each has a clear operating window — the right choice depends on how often you change widths, how tight the pitch tolerance must be, and how much budget you have per axis.
| Property | Slotted-bar synchroniser | Lazy-tongs (pantograph) | Independent servo per carriage |
|---|---|---|---|
| Pitch accuracy across 6 carriages | ±0.3 mm (ground slot, H7/g6 pins) | ±0.5-1.0 mm (joint slop accumulates) | ±0.05 mm (encoder-limited) |
| Cost per carriage (relative) | Low — 1.0× | Lowest — 0.7× | High — 4-6× |
| Changeover time | 2-5 s with one Linear Actuator | 5-10 s manual crank typical | Under 1 s, fully programmable |
| Maintenance interval | 12-24 months (re-grease pins, check slot wear) | 3-6 months (many joints) | 24+ months (sealed servos) |
| Maximum carriages practical | 8-12 before slot length gets unwieldy | 20+ joints possible but slop multiplies | Unlimited |
| Failure on single-point fault | One seized pin disrupts whole row | One worn joint disrupts whole row | Single carriage fails alone |
| Best application fit | Width changeovers on web/sheet lines | Manual or low-duty fixtures | High-mix production with recipe recall |
Frequently Asked Questions About Equally-traversing Rollers via Slotted Bar
Almost always slot waviness, not pin clearance. A milled slot — even a good one — has 30-80 µm of waviness along its length. That error multiplies with index position, so carriage 1 sees almost no shift but carriage 6 sees 6× the local slot deviation summed along its travel path.
The fix is to grind the slot, not mill it. Surface grinding holds 10-15 µm flatness over 1 metre and pulls carriage-6 lag back under 0.2 mm. If grinding is not an option, hand-stoning the slot with a fine India stone after milling cuts the waviness roughly in half.
Translating gives you cleaner linearity. A swinging bar adds a sin(θ) term that goes nonlinear past 15-20°, so you lose proportional response at the extremes of stroke. Translating the bar parallel to itself — usually with two parallel guides and a Linear Actuator at one end — keeps the relationship purely linear regardless of stroke.
Swing is fine if your total angular travel stays under 25° and you only need ±0.5 mm accuracy. For tighter accuracy or longer travel, go translating. The mechanical penalty is one extra guide rail and a little more frame width.
Sum three loads: carriage friction (linear bushing or block drag, typically 5-15 N each under normal preload), roller bearing drag (1-3 N each at moderate speed), and any process force on the rollers themselves (nip pressure, web tension reaction, etc.). Multiply by N carriages and divide by sin(θ) to refer the load back to the actuator.
For a 6-carriage bank with 10 N drag per carriage at 20° swing, that's 60 N / sin(20°) ≈ 175 N at the actuator. A FIRGELLI FA-150 with 150 lbf capacity has plenty of headroom. Do not skimp here — undersizing the actuator means slow, jerky changeovers and the bar will stall partway through stroke.
You can, but you have to phase the two bars exactly. The usual mistake is to drive each bar with its own actuator and rely on synchronised commands — even 50 ms of timing skew at 1 m/s means 50 mm of differential travel between the two bar sections, and you'll see one carriage row leading the other.
The robust solution is a single mechanical input — one leadscrew, one actuator, one hand-crank — that drives both bars through a rigid coupling shaft. We've used this on 16-carriage banks where one bar handled carriages 1-8 and the other handled 9-16, with a single shaft tying them together. Pitch accuracy stayed under 0.5 mm across the full 16-carriage row.
Thermal growth of the slotted bar. A 1 metre steel bar grows about 12 µm per °C. If your machine room sits at 18°C and the bar runs at 35°C after warm-up, that's a 17°C rise and roughly 0.2 mm of bar length change. Because every carriage's position scales linearly with bar length in the formula, the outermost carriage drifts the most.
If thermal stability matters, switch the bar to Invar (1.2 µm/°C — about 10× more stable than steel) or design the bar with one end fixed and the other end on a sliding mount so growth doesn't propagate as pitch error. We do not recommend aluminium bars for this — they grow at twice the rate of steel.
Around 10-12 carriages. Beyond that, three problems compound: the bar gets long enough that thermal and bending effects dominate, the outermost pin sees so much slot travel that wear localises and pitch accuracy degrades at the ends, and the actuator force scales with N so you need bigger drives.
Above 12 carriages we typically split the row into two or three slotted-bar sections driven from a common shaft, or move to independent servo control if pitch tolerance demands it. The crossover point on cost favours servos around 16+ carriages with frequent recipe changes.
References & Further Reading
- Wikipedia contributors. Scotch yoke. Wikipedia
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