A slotted-arm rectilinear variable is a linkage that converts rotary input into reciprocating linear output whose stroke length you can change on the fly by sliding a crank pin along a slotted lever. Typical units run 30 to 300 cycles per minute and deliver strokes adjustable from near-zero up to roughly 200 mm. The geometry lets one drive cover a range of throw lengths without swapping cranks, which is why textile loom takeup motions, knitting machine yarn guides, and adjustable-feed strip rolls have used it for over a century.
Slotted-arm Rectilinear Variable Interactive Calculator
Vary crank radius, lever geometry, pin position, and speed to see the adjustable output stroke and moving linkage.
Equation Used
The calculator estimates adjustable stroke from the slotted-lever ratio. The crank creates a peak-to-peak drive motion of 2r at the drive block; moving the output pin farther from the pivot multiplies that motion by Lout/Lin. Slot use flags when the output pin is pushed toward the far end of the slot.
- Small-angle lever-ratio stroke estimate.
- Output pin and drive block distances are measured from the lever pivot.
- Output slide motion is treated as sinusoidal for peak speed.
- Clearance, backlash, rod angularity, and quick-return effects are ignored.
The Slotted-arm Rectilinear Variable in Action
The mechanism takes a rotating crank and couples it through a sliding block to a lever that has a long radial slot machined down its centreline. As the crank rotates, the block travels back and forth inside the slot, forcing the lever to rock through an arc. A connecting rod off the far end of the lever — or off a second pin riding in a parallel slot — converts that rocking arc into clean rectilinear reciprocation at the output. The whole point of the slotted-lever architecture is that you can reposition the output pin along the slot, changing the effective lever ratio and therefore the stroke, without disturbing the crank or the input shaft.
Geometry sets everything. The slot must be straight, parallel-sided, and hardened — typical industrial units run a 50 HRC slot face with the sliding block ground to a 0.02 to 0.05 mm running clearance. Run it looser and the block hammers at every stroke reversal, beating the slot edges into a trumpet shape within a few hundred hours. Run it tighter and the block galls under side load. The crank pin centre-distance, the slot length, and the lever pivot location together define the variable stroke range — push the output pin past about 85% of the slot length and the velocity profile turns nasty, with a pronounced quick-return characteristic that hammers the connecting rod bearings.
Failure modes are predictable. Worn slot faces show up as backlash at top and bottom dead centre, which the operator hears as a faint click at each reversal. Sliding block wear flats cause the output stroke to come up short by 1 to 3 mm. And if the lever pivot bushing gets sloppy beyond about 0.1 mm radial play, the rectilinear output picks up a sideways wobble that shreds whatever guide bushing the connecting rod runs in.
Key Components
- Driving Crank: Rotates at constant input speed, carrying the sliding-block pin at a fixed radius from the crank centre. Crank radius is typically 20 to 80 mm and the pin runs in a needle-roller bearing rated for the full input torque, since this pin sees the highest cyclic load in the assembly.
- Sliding Block: A hardened steel shoe that rides inside the slot. Ground to a running clearance of 0.02 to 0.05 mm against the slot faces. Loses 0.1 to 0.2 mm per side over 5,000 hours of typical service before stroke accuracy drifts out of spec.
- Slotted Lever: The rocking arm with a straight radial slot machined into it. Slot faces are induction-hardened to 50 HRC minimum, parallel within 0.03 mm over the full slot length. The lever pivots on a bushing or roller bearing that must hold radial play under 0.05 mm.
- Adjustable Output Pin: Locates in the slot at a chosen radius from the lever pivot, which sets the lever ratio and therefore the output stroke. Locked in place by a clamp screw rated for the full output reaction load — usually 5 to 50 kN clamp force depending on stroke.
- Connecting Rod: Couples the rocking output pin to the rectilinear slide. Length is set so that at mid-stroke the rod runs perpendicular to the slide axis, which minimises side loading on the slide bushing. A 5 to 10 degree cosine error here is normal and absorbed by the slide guide.
- Output Slide and Guide: Constrains the final motion to a straight line. Typically a linear bushing or a pair of V-rails. Must accept the small sinusoidal side-load component left over from the connecting rod arc — usually 5 to 15% of the axial output force.
Where the Slotted-arm Rectilinear Variable Is Used
The slotted-arm rectilinear variable shows up wherever a machine has to reciprocate something at a stroke length that changes by job, by pattern, or by product size — and where a servo would be overkill. The variable stroke is the whole reason you choose this linkage over a fixed slider-crank. Operators love it because a single hand-wheel adjustment changes throw on a running machine, and the mechanism keeps timing locked to the main shaft.
- Textile Machinery: Yarn guide traverse on a Karl Mayer warp knitting machine where stroke changes with fabric width
- Packaging: Adjustable indexing pusher on a Bosch Pack 102 horizontal flow wrapper sized to product length
- Strip Feeding: Variable-feed roll lifter on a coil-fed punch press at a Heidelberg fastener plant, throw adjusted to part pitch
- Printing: Ink fountain agitator stroke on a Heidelberg GTO 52 offset press, set to ink viscosity
- Bottle Filling: Adjustable nozzle dive depth on a Krones Sensometic linear filler running multiple bottle heights on the same line
- Woodworking: Sander oscillation throw on a Costa Levigatrici brush sander adjusted to grain orientation
The Formula Behind the Slotted-arm Rectilinear Variable
The output stroke depends on the radius at which the output pin sits inside the slot, the crank radius, and the slot/pivot geometry. At the low end of the adjustment range — output pin sitting close to the lever pivot — you get a tiny stroke with low output force amplification and very smooth acceleration. At the high end, with the pin near the far end of the slot, the stroke is long but the velocity curve picks up a quick-return asymmetry and the slot block sees its peak side load. The sweet spot for most industrial setups sits at 40 to 70% of full slot extension, where the output is approximately sinusoidal and the slot block load stays manageable.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| Sout | Peak-to-peak output stroke at the connecting rod end | mm | in |
| Rc | Crank radius — distance from crank centre to sliding-block pin centre | mm | in |
| Lp | Output pin radius — distance from lever pivot to adjustable output pin | mm | in |
| Ls | Slot pin radius — distance from lever pivot to sliding block at mid-stroke | mm | in |
Worked Example: Slotted-arm Rectilinear Variable in a Karl Mayer warp knitting yarn guide traverse
You are setting up the variable-stroke yarn guide traverse on a Karl Mayer HKS 3-M warp knitting machine running synthetic warp at 1800 courses per minute. The crank radius is fixed at 35 mm. The sliding block runs at a mid-stroke radius of 140 mm from the lever pivot. You need to dial in three output stroke settings to match three fabric widths the line is running this week — narrow trim, nominal, and wide selvedge.
Given
- Rc = 35 mm
- Ls = 140 mm
- Lp,nom = 200 mm
- Lp,low = 120 mm
- Lp,high = 280 mm
- Input speed = 1800 cycles/min
Solution
Step 1 — at the nominal pin setting of 200 mm, compute the output stroke:
That 100 mm peak-to-peak gives the yarn guide a clean traverse for the standard fabric width. At 1800 cycles/min the peak guide velocity works out to roughly 9.4 m/s — fast, but well inside what a properly lubricated guide eyelet handles without yarn fray.
Step 2 — at the low end of the adjustment range, output pin pulled in to 120 mm:
60 mm of throw is what you'd run for narrow trim fabric. The motion feels noticeably gentler — peak velocity drops to about 5.7 m/s and the connecting rod barely loads the slide bushing. The downside is that a small adjustment error here translates to a big percentage stroke error, so the operator needs to set the pin to within 0.5 mm of nominal or the fabric edge wanders.
Step 3 — at the high end, output pin pushed out to 280 mm:
140 mm sounds great for wide selvedge work, but here is where the geometry bites. The output pin now sits well past the slot block radius, so the velocity profile picks up a quick-return characteristic — return stroke roughly 15% faster than forward stroke. Peak velocity climbs to about 13.2 m/s and the slide guide bushing sees a side-load spike at each reversal. Most Karl Mayer field techs cap the pin radius at around 240 mm in continuous service to keep bushing life above the 6000-hour service interval.
Result
Nominal output stroke is 100 mm at the 200 mm pin setting, which is the design sweet spot for this Karl Mayer setup. The yarn guide traverses smoothly with peak velocity around 9.4 m/s and the slide bushing runs cool. Pulling the pin in to 120 mm shrinks the stroke to 60 mm with much gentler dynamics, while pushing it out to 280 mm gives 140 mm of throw but introduces a quick-return asymmetry and shortens bushing life. If your measured stroke comes up short by 1 to 3 mm, suspect (1) wear flats on the sliding block faces, which take 0.1 to 0.2 mm per side out of effective travel, (2) clamp screw on the output pin slipping under reversal load and letting the pin creep inward, or (3) lever pivot bushing radial play above 0.05 mm bleeding off motion at each reversal.
Choosing the Slotted-arm Rectilinear Variable: Pros and Cons
The slotted-arm rectilinear variable competes with two main alternatives when you need adjustable reciprocating motion: a fixed slider-crank with swappable cranks, and a servo-driven linear actuator. Each wins on different axes — the slotted-arm sits between them on cost, complexity, and adjustability.
| Property | Slotted-arm rectilinear variable | Fixed slider-crank with swappable cranks | Servo-driven linear actuator |
|---|---|---|---|
| Stroke adjustment time | 30 seconds, on running machine | 10 to 30 minutes, machine stopped, crank swap | Under 1 second, programmable |
| Maximum cycle speed | 300 cpm | 600 cpm | 120 cpm at full stroke |
| Stroke repeatability | ±0.2 mm | ±0.05 mm | ±0.01 mm |
| Capital cost (typical industrial unit) | $800 to $2500 | $300 to $900 plus crank set | $3000 to $12000 |
| Service life before rebuild | 8000 to 15000 hours | 20000+ hours | 30000 hours, electronics dependent |
| Side-load tolerance at output | Moderate, 5 to 15% of axial | Low, near-zero side load | Low, depends on guide |
| Best fit application | Frequent stroke changes between jobs | Single-stroke production runs | Programmable multi-stroke recipes |
Frequently Asked Questions About Slotted-arm Rectilinear Variable
Slot deflection. When you push the output pin out near the end of the slot, the lever sees its highest bending moment, and a slot-arm machined from mild steel rather than 4140 will flex visibly under load. A 1 mm tip deflection at the output pin translates directly to 2 mm of lost peak-to-peak stroke.
Check the lever material certificate. If it's anything below 4140 pre-hardened or equivalent, you'll see this loss climb with stroke. The fix is either a stiffer lever blank or capping the maximum pin radius at 70% of slot length so the bending moment stays manageable.
The Scotch yoke gives you a pure sinusoidal output and dead-simple geometry, but the stroke is fixed by the crank radius — change stroke and you swap the crank. The slotted-arm wins when stroke needs to change between jobs without tearing the machine down.
Rule of thumb: if you change stroke more than once a week, slotted-arm pays back the extra complexity within months in changeover time. If stroke is fixed for the life of the machine, Scotch yoke is mechanically superior and cheaper.
Geometry. When the output pin radius equals the sliding-block radius (Lp ≈ Ls), the lever effectively swings symmetrically about the crank centre line and you get near-sinusoidal output. When the output pin sits significantly outside the slot block radius, the lever spends unequal time on each side of dead centre, which shows up as faster return than forward stroke.
If you need a symmetric profile at long strokes, you have to redesign with a longer slot so the block can run further out — not push the output pin further out.
Three checks in this order. First, sliding block clearance in the slot — anything above 0.08 mm clearance produces an audible reversal click and grows fast once it starts. Pull the block, mic it, and replace if the wear flat exceeds 0.15 mm.
Second, crank pin needle bearing. A spalled needle clicks at every revolution but loudest at peak load near the dead centres. Third, the output pin clamp — if the clamp screw torque has dropped below spec, the pin micro-moves at each reversal and produces a sharp tick rather than the duller click of slot wear.
No, and the manufacturer rating sheets bury this. Maximum stroke ratings are quoted at moderate speed, and maximum speed ratings are quoted at moderate stroke. The product of stroke and speed squared drives the dynamic load on the sliding block, and that load is what kills the slot face.
Practical rule: if you need full stroke, derate speed to 60% of catalogue maximum. If you need full speed, derate stroke to 70%. Run both at maximum and you'll be replacing the slot lever inside 2000 hours.
The mid-stroke centre point of the rectilinear output is set by the geometry of the connecting rod and the lever neutral angle — when you slide the output pin along the slot, the lever pivot stays put but the connecting rod attachment point moves to a new arc, which shifts the rod's mean position by a few millimetres.
If your downstream process can't tolerate that shift, you need a parallel adjustment on the slide stop or a centring linkage between the output pin and the connecting rod. Most operators just zero the downstream process after each stroke change.
Force at the output drops in inverse proportion to the lever ratio you set for stroke. If you doubled the stroke by moving the output pin from Ls to 2×Ls, output force at the slide is now half of what the crank pin sees, but the side load on the sliding block is unchanged.
The block side load is the limiter. Most industrial units rate the slot face for 8 to 15 kN sustained block load. Above that you yield the slot edges, and once those edges roll over you've lost the block running fit permanently.
References & Further Reading
- Wikipedia contributors. Linkage (mechanical). Wikipedia
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