A disk-and-pin alternate rectilinear mechanism is a rotary-to-linear converter where a pin offset from a rotating disk's centre engages a slotted yoke, driving the yoke back and forth along a straight guideway. Textile traverse machinery relies on it to lay yarn across a bobbin face. The pin slides freely inside the slot as the disk rotates, so each full revolution produces one complete reciprocating cycle with a stroke equal to twice the pin offset. The result is smooth sinusoidal reciprocation from a single rotating shaft — no cams, no return springs, no dead points.
Disk-and-Pin Alternate Rectilinear Interactive Calculator
Vary the required stroke and disk angle to see the pin offset, yoke position, and slot sliding motion.
Equation Used
The required crank pin offset is one half of the required stroke. At any disk angle, the yoke position is the horizontal component of the pin circle, x = r cos(theta), while the vertical component is absorbed by sliding in the slot.
- Ideal disk-and-pin geometry with no backlash or elastic deflection.
- The yoke is constrained to horizontal rectilinear motion only.
- Theta is measured from the right-hand stroke end position.
How the Disk-and-pin Alternate Rectilinear Actually Works
The geometry is simple but the behaviour is worth understanding before you scale it up. A disk rotates about a fixed centre. A pin presses into the disk at a radial offset r — that offset is the crank radius. The pin engages a transverse slot machined into a yoke, and the yoke is constrained by linear guides so it can only move along one axis. As the disk rotates, the pin traces a circle, but only the component of that circle parallel to the yoke's travel axis produces useful motion. The perpendicular component is absorbed by the pin sliding inside the slot. That sliding action is the whole trick — without the slot you'd lock the mechanism solid in under 90° of rotation.
The motion is pure sinusoidal. Position follows x = r × cos(θ), velocity peaks at mid-stroke, and acceleration peaks at the stroke ends. This is identical to a scotch yoke, and many engineers treat the disk-and-pin as a scotch yoke variant — the difference is that the disk-and-pin places the pin on a flat rotating face rather than a crank arm, which makes it more compact axially and easier to balance. Stroke length equals 2r exactly, so if you need a 50 mm stroke you set the pin offset to 25 mm. No linkage geometry, no correction factors.
Tolerances matter more than people expect. The pin-to-slot clearance directly governs backlash at stroke reversal. A typical hardened pin running in a bronze-bushed slot wants 0.02 to 0.05 mm diametral clearance — go below 0.02 and the pin binds at temperature, go above 0.05 and you get an audible knock at each reversal as the yoke snaps from one slot face to the other. Pin wear is the dominant failure mode: at high cycle rates the pin sees fully reversing side load, and if you skip the case-hardening or run it dry, you'll see the slot wear into an oval shape within a few hundred thousand cycles. Misaligned linear guides are the second-biggest killer — any cocking of the yoke turns the slot into a wedge and chews the pin in days.
Key Components
- Drive Disk: The rotating element that carries the offset pin. Typical disk diameter runs 1.5× to 3× the pin offset for stiffness. Face flatness should be within 0.05 mm to keep the pin perpendicular to the slot.
- Crank Pin: A hardened steel pin pressed or threaded into the disk at radial offset r from centre. Pin diameter is normally 8 to 20 mm depending on side load. Surface hardness 58-62 HRC and ground finish Ra ≤ 0.4 µm.
- Slotted Yoke: The driven member with a transverse slot that captures the pin. Slot length must exceed 2r plus pin diameter plus 2-3 mm clearance, otherwise the pin bottoms out at top-dead-centre and the mechanism stalls.
- Slot Bushing or Wear Plates: Replaceable bronze or hardened steel inserts lining the slot working faces. These take the wear so you don't have to scrap the yoke. Diametral clearance to pin held at 0.02-0.05 mm.
- Linear Guideway: Constrains the yoke to single-axis travel. Linear bearings, profile rails, or plain ways all work. Parallelism to the disk face must be within 0.1 mm over the stroke length to avoid yoke cocking.
- Drive Shaft and Bearing: Carries the disk and absorbs the reaction force from the pin's side load. Reaction equals m × ω² × r at top and bottom dead centre — size the bearing for that, not just the average load.
Where the Disk-and-pin Alternate Rectilinear Is Used
The disk-and-pin shows up wherever you need cheap, reliable reciprocation from a single rotating input and you can tolerate sinusoidal motion. It dominates in textile machinery, small pumps, sieves, and material-handling shakers. You'll find it where a scotch yoke would also work, but where the designer wanted a balanced rotating face rather than an exposed crank arm — easier to guard, easier to enclose in oil.
- Textile machinery: Yarn traverse drives on cone winders such as the Schlafhorst Autoconer 6, where the disk-and-pin lays filament across the package face at controlled stroke.
- Mineral processing: Drive units for laboratory test sieves like the Retsch AS 200, converting motor rotation into vertical reciprocation of the sieve stack.
- Small fluid pumps: Diaphragm metering pumps in the KNF NF series, where the disk-and-pin reciprocates the diaphragm at fixed stroke for repeatable dosing volume.
- Packaging machinery: Horizontal pouch-fill machines using a disk-and-pin to reciprocate the seal-jaw carriage in time with film advance, common on Bosch SVE form-fill-seal lines.
- Laboratory equipment: Reciprocating shaker tables for sample agitation, such as the IKA HS 260 basic, where balanced sinusoidal motion is required to avoid splashing reagents.
- Automotive: Windshield wiper linkages on older commercial vehicles, where a disk-and-pin drove the wiper arm directly from a gearmotor before four-bar linkages took over.
The Formula Behind the Disk-and-pin Alternate Rectilinear
What you need to know is the linear velocity of the yoke at any disk angle, because peak velocity governs seal speed, traverse rate, or fluid flow depending on application. At the low end of the typical operating range — say 30 RPM on a lab shaker — the motion is gentle enough that you barely register acceleration. At nominal mid-range speeds around 200-400 RPM, the mechanism hits its sweet spot: smooth motion, manageable inertia loads, predictable wear. Push past 800-1000 RPM and the acceleration at stroke ends starts hammering the pin, the yoke guides take a beating, and you'll see fatigue cracks at slot corners within months. The formula below gives you instantaneous yoke velocity as a function of disk angle and rotation speed.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| v(θ) | Instantaneous linear velocity of the yoke at disk angle θ | m/s | in/s |
| r | Radial offset of pin from disk centre (crank radius) | m | in |
| ω | Angular velocity of the drive disk | rad/s | rad/s |
| θ | Disk angular position from top-dead-centre | rad | rad |
| vmax | Peak yoke velocity, occurring at θ = 90° and 270°, equal to r × ω | m/s | in/s |
Worked Example: Disk-and-pin Alternate Rectilinear in a glass-bottle washer reciprocating spray manifold
You are sizing the disk-and-pin drive for the reciprocating spray manifold inside a Krones Lavatec bottle washer, where the manifold sweeps across a row of inverted bottles to rinse them. Stroke length must be 80 mm to cover four 20 mm bottle pitches in a single sweep. The line runs at a nominal 240 manifold cycles per minute, with operating range from 120 to 480 cycles per minute depending on bottle size changeover. Compute the peak manifold velocity so you can size the flexible hose loop and check spray nozzle dwell time.
Given
- Stroke = 80 mm
- r (pin offset) = 40 mm
- Nnom = 240 cycles/min
- Nlow = 120 cycles/min
- Nhigh = 480 cycles/min
Solution
Step 1 — convert nominal cycle rate to angular velocity. One cycle equals one full disk revolution, so 240 cycles/min = 4 rev/s.
Step 2 — compute peak yoke velocity at nominal speed. Peak occurs at θ = 90°, where sin(θ) = 1.
That's a brisk but controllable manifold sweep. The hose loop moves at roughly walking pace at mid-stroke, and a spray nozzle passing a bottle mouth gets about 20 ms of effective dwell — enough for the rinse jet to fully wet the inside surface.
Step 3 — low-end of operating range, 120 cycles/min during large-format bottle runs.
At this rate the manifold drifts slowly enough that you can watch a single bottle get rinsed in real time. Dwell roughly doubles to 40 ms — which is generous, but operators sometimes complain about water carryover because the manifold lingers over each bottle.
Step 4 — high end, 480 cycles/min during small-format glass.
Now you're moving fast. Peak acceleration at stroke ends jumps to ω² × r = (50.27)² × 0.040 = 101 m/s² — over 10 g. The pin sees roughly 4× the side load it sees at nominal, the hose loop whips visibly, and unless you've specified a hardened pin with bronze slot inserts you'll see measurable slot wear inside 500 hours.
Result
Peak manifold velocity at nominal 240 cycles/min is 1. 005 m/s. In practice that means the spray header sweeps the bottle row in about 0.125 s per stroke, giving spray nozzles enough dwell to wet bottle interiors without flooding the conveyor. At the low end (120 cycles/min) velocity halves to 0.503 m/s and dwell doubles, while at the high end (480 cycles/min) velocity quadruples to 2.011 m/s and acceleration loads on the pin go up 16-fold — the sweet spot sits right around the 240 cycles/min nominal where wear and dwell are both acceptable. If you measure peak velocity below the predicted 1.005 m/s, check first for drive belt slip on the gearmotor pulley, second for an undersized pin offset (a 38 mm offset instead of 40 mm gives 0.955 m/s and is a common machining error), and third for excessive slot clearance — anything beyond 0.08 mm diametral lets the yoke lag the pin at reversal and shaves 5-8% off measured peak speed.
When to Use a Disk-and-pin Alternate Rectilinear and When Not To
The disk-and-pin competes with a handful of other rotary-to-linear converters. Each one has a place — choosing well depends on whether you need pure sinusoidal motion, dwell, or constant velocity. Here's how the disk-and-pin stacks up against a slider-crank and a cam-and-follower for typical reciprocating duty.
| Property | Disk-and-pin alternate rectilinear | Slider-crank | Cam-and-follower |
|---|---|---|---|
| Motion profile | Pure sinusoidal | Near-sinusoidal with second-harmonic distortion | Fully programmable (dwell, constant velocity, custom) |
| Practical speed range | 30-1000 RPM | 30-3000 RPM | 10-2000 RPM |
| Stroke accuracy | ±0.05 mm with ground pin and slot | ±0.1 mm typical (linkage stack-up) | ±0.02 mm with precision-ground cam |
| Side load on driven member | High — pin slides in slot under load | Low — connecting rod handles side load | Moderate — depends on follower type |
| Relative cost | Low | Low to moderate | High (cam grinding) |
| Lifespan at nominal load | 10-50 million cycles | 50-200 million cycles | 20-100 million cycles |
| Best application fit | Compact reciprocators, traverse drives, sieves | High-speed pumps, engines, presses | Indexing, dwell-required motion, packaging |
| Maintenance interval | Inspect pin and slot every 2000 hr | Inspect rod bearings every 4000 hr | Inspect cam profile every 5000 hr |
Frequently Asked Questions About Disk-and-pin Alternate Rectilinear
Almost always slot wear, not pin wear. The pin sees side load that fully reverses twice per revolution, and the slot faces take that load on alternating sides. As the slot bushing wears from its initial 0.03 mm clearance to about 0.10 mm, the yoke briefly free-floats at each reversal until the pin hits the opposite slot face — that impact is the knock you hear.
Pull the yoke and measure slot width with a bore gauge. If it's grown more than 0.05 mm beyond pin diameter, replace the bushing or wear plates. Don't just shim it — the wear pattern is rarely symmetric and shimming makes the binding worse on the unworn side.
Upsizing the pin handles bending stress but doesn't fix the real problem at high speed: peak acceleration at stroke ends scales with ω², so doubling RPM quadruples the inertia force on the yoke. That force is reacted by the pin pressing on the slot face, and contact stress scales with force divided by pin diameter — a bigger pin helps, but only linearly.
Rule of thumb: keep ω² × r below about 200 m/s² for plain bushings, or 500 m/s² for needle-rolled slot followers. Above that you need to switch to a roller-follower scotch yoke or accept a much shorter service life.
For a 50 mm stroke and any reasonable speed below 600 RPM, the disk-and-pin wins on packaging — the rotating face is balanced, the pin sits flush, and you can enclose the whole thing in an oil-filled housing without an exposed crank arm flailing around. A traditional scotch yoke with an offset crank arm needs more axial space and more guarding.
Pick the offset-crank scotch yoke only if your pin offset is so large (>50 mm) that disk diameter becomes unwieldy, or if you need to access the pin for adjustment without removing the disk.
Two usual suspects. First, slot end-clearance: if the slot is only just long enough to fit pin diameter plus 2r, thermal expansion or any pin-position error shaves usable stroke off both ends. Always machine the slot at least 3 mm longer than 2r + pin diameter.
Second, yoke guideway end-stops or limit switches positioned tighter than the mechanism's natural travel. A linear bearing block bottoming on its end-stop will steal stroke silently — you'll hear a faint tick at top-dead-centre that operators usually mistake for normal mechanism noise.
The pin and any pin-collar mass create a rotating imbalance equal to mpin × r. Drill a balancing pocket diametrically opposite the pin, sized so the removed mass times its centroid radius equals the pin's mass times its offset. For a typical 15 mm steel pin at 40 mm offset, you're looking at roughly 8-12 g of material to remove from a 25 mm-radius pocket.
What this doesn't fix is the reciprocating imbalance of the yoke itself — that's a linear force along the stroke axis and you can only cancel it with a counter-rotating mass or a second yoke 180° out of phase. Above 600 RPM with heavy yokes, that secondary balancing matters more than the disk balance.
Asymmetric noise almost always points to non-perpendicularity between the disk face and the yoke slot axis. If the disk axis is tilted by even 0.5° relative to the yoke guide, the pin presses harder against one slot face on the upstroke than the downstroke, and the louder direction is the one with the higher contact load.
Check it with a dial indicator on the disk face while rotating slowly — you want runout under 0.05 mm across the pin's working radius. If runout is fine, look at yoke guide parallelism; the yoke cocking by 0.1 mm over its travel produces the same audible asymmetry.
References & Further Reading
- Wikipedia contributors. Scotch yoke. Wikipedia
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