A two-shaft crank with slot for varying velocity is a linkage where a driving crank on one shaft carries a pin that rides inside a radial slot machined into a follower disk mounted on a second, offset parallel shaft. Variants of this mechanism appear in vintage Heidelberg platen presses and in cam-driven wire-forming machines like the Bihler RM35. The shaft offset forces the follower's angular velocity to swing above and below the driver's constant speed across each revolution. The result — a smooth, mechanically generated speed cycle ideal for indexing, dwell-and-snatch, and quick-return duties.
Two-shaft Crank with Slot Interactive Calculator
Vary the target speed variation and cycle time to see the required shaft offset ratio and fast/slow follower speeds.
Equation Used
The offset ratio e/Rp sets the velocity swing. For a requested fast-to-slow ratio V, the required eccentricity ratio is e/Rp = (V - 1)/(V + 1). The driver speed is 60/T rpm, and the follower reaches its maximum and minimum speeds when the pin is on the near and far sides of the offset.
- Parallel shafts with a straight radial slot in the follower disk.
- Ideal kinematics with no backlash, friction, or pin compliance.
- Eccentricity is less than pin radius, e/Rp < 1.
- One follower revolution occurs for each driver revolution.
How the Two-shaft Crank with Slot for Varying Velocity Works
The trick is the offset between the two shafts. The driver shaft turns at constant RPM and carries a pin at radius Rp. That pin lives inside a straight radial slot cut into a disk on the second shaft, which sits a distance e (the eccentricity) away. As the driver rotates, the pin slides up and down the slot — and because the geometric path from one shaft centre to the other changes with crank angle, the follower has to rotate faster when the pin is on the near side and slower when it's on the far side. You get a sinusoidal-ish velocity profile out of a steady input. No cams. No gearing. Just two shafts and a slot.
The geometry is unforgiving. If the slot is too wide for the pin you get backlash that eats your indexing accuracy — the follower rattles between slot faces every time the load reverses. We typically size the pin-to-slot clearance at 0.02 to 0.05 mm for a 12 mm pin, with the slot faces ground to Ra 0.4 µm or better. Run it loose and you'll see chatter marks on the slot walls within a few hundred thousand cycles. Run it too tight and you'll seize the moment a thermal cycle expands the disk.
What fails first? In our experience the pin galls before the slot does. The pin sees full Hertzian contact stress concentrated on a thin line as it slides, while the slot wall distributes wear over its full length. Hardened pin (58-62 HRC), nitrided slot, and a metered oil mist will get you past 10 million cycles. Skip the lubrication and you'll be replacing the pin every 200,000 cycles — easy to spot because the kinematic inversion produces an audible thump at the dead-centre positions.
Key Components
- Driver Shaft and Crank Arm: The constant-speed input. Carries the drive pin at a fixed radius Rp from the driver shaft centreline. Typical Rp sits between 25 mm and 80 mm depending on output torque demand, with the crank arm machined to ±0.05 mm true position on the pin bore.
- Drive Pin: The element that couples driver to follower through sliding contact in the slot. Hardened tool steel, 58-62 HRC, ground to h6 tolerance. Pin diameter typically 8-16 mm — undersize it and you'll bend it during overload; oversize it and the slot has to grow to match, which fattens the whole assembly.
- Slotted Follower Disk: Mounted on the second shaft, parallel to and offset from the driver. The radial slot is the working feature — straight, ground, and case-hardened or nitrided to HV 700+. Slot length must exceed the maximum pin excursion by at least 5 mm to prevent end-stop strikes.
- Follower Shaft and Bearings: Carries the output torque to whatever you're driving. Sized for the peak torque, which occurs near the small-radius position — not the average torque. We often see designers underspec this bearing because they sized for mean load, then watch it fail at the velocity peak.
- Eccentricity Frame: The structure holding the two shaft centrelines a distance e apart. Eccentricity ratio e/Rp typically runs 0.3 to 0.7. Below 0.3 the velocity variation is too mild to be useful; above 0.7 the slot length and pin loads become impractical.
Who Uses the Two-shaft Crank with Slot for Varying Velocity
You see this mechanism wherever a designer needs a non-uniform output cycle from a uniform input but doesn't want the cost or maintenance of a cam. It's compact, runs in oil, and makes its velocity profile out of pure geometry. Common in legacy printing, textile, and forming machines where a quick-return or dwell-snatch motion is the whole point of the machine cycle.
- Printing: Heidelberg Original Heidelberg cylinder press — slotted crank drives the gripper bar with the dwell-and-snatch profile needed to grab and release sheets at high speed.
- Wire forming: Bihler RM35 stamping and forming machine — offset slotted crank generates the variable-velocity slide stroke that lets the tooling close slowly and retract fast.
- Textile machinery: Sulzer projectile loom picking mechanism — the picking lever uses a two-shaft slotted crank to accelerate the projectile sharply through a short angular sweep.
- Packaging: Bosch CUT 120 sachet cutter — slotted crank drives the knife carriage with a slow cut stroke and fast return, increasing throughput without raising input RPM.
- Metalworking: Shaper machines like the Cincinnati 24-inch — the classic Whitworth quick-return is geometrically a two-shaft slotted crank, giving the cutting stroke twice the duration of the return.
- Bookbinding: Müller Martini Presto perfect binder — slotted crank operates the spine-roughening head with a dwell at the working position before snapping back clear.
The Formula Behind the Two-shaft Crank with Slot for Varying Velocity
The follower's angular velocity ω2 as a function of the driver's constant ω1 tells you the whole story — peak speed, minimum speed, and where in the cycle they happen. At low eccentricity ratio (e/Rp ≈ 0.2) the variation is gentle, around ±25%, and the mechanism behaves almost like a 1:1 coupling. At a moderate ratio of 0.5 (the sweet spot for most machine designs) you get a 3:1 ratio between peak and minimum follower speed — enough to make the quick-return useful without crippling the pin loads. Push e/Rp above 0.7 and the peak velocity climbs steeply but so does the pin reaction force, and the slot length runs away with you.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| ω2 | Instantaneous angular velocity of the slotted follower | rad/s | rad/s |
| ω1 | Constant angular velocity of the driver crank | rad/s | rad/s |
| Rp | Drive pin radius from the driver shaft centreline | m | in |
| e | Eccentricity — centre-to-centre distance between driver and follower shafts | m | in |
| θ | Driver crank angle measured from the line through the two shaft centres | rad | rad |
Worked Example: Two-shaft Crank with Slot for Varying Velocity in a corrugated sheet creasing machine
Sizing the two-shaft slotted crank that drives the creasing roller carriage on a Latitude Machinery LM-1000 corrugated converter at a packaging plant in Guadalajara. The driver runs at 180 RPM constant, Rp = 50 mm, and the design eccentricity is e = 25 mm (e/Rp = 0.5). You need to know the follower's peak and minimum angular velocity so the carriage acceleration profile stays inside the linear-rail dynamic load rating.
Given
- ω1 = 18.85 rad/s (180 RPM)
- Rp = 0.050 m
- e = 0.025 m
Solution
Step 1 — at the nominal operating angle θ = 0° (pin at far side, slot longest), evaluate the follower velocity:
That's 120 RPM — the slow phase. In the LM-1000 application this is when the creasing roller carriage is actually pressing the corrugated board, so a slow stroke means a clean crease without tearing the liner.
Step 2 — at θ = 180° (pin at near side, slot shortest), the high-end of the follower's instantaneous velocity:
That's 360 RPM — three times the slow speed, and this is the return stroke. The carriage snaps back to its start position in a third the time it took to advance, doubling the effective cycle rate compared to a constant-velocity drive.
Step 3 — at the low end of the eccentricity range you might consider, e = 0.010 m (e/Rp = 0.2), the velocity ratio shrinks dramatically:
Only a 1.5:1 ratio — not enough quick-return benefit to justify the mechanism. At the high end, e = 0.035 m (e/Rp = 0.7), the ratio jumps to (0.085/0.015) = 5.67, which is aggressive but punishes the pin: peak side load roughly doubles compared to e/Rp = 0.5, and slot length must grow to 105 mm. The 0.5 ratio is the sweet spot — meaningful 3:1 quick-return without forcing oversized pins or slot length.
Result
The follower's nominal velocity range runs from 120 RPM at the slow phase to 360 RPM at the fast phase, a 3:1 ratio set by the e/Rp = 0. 5 geometry. In practical terms, the LM-1000 carriage creases for 0.22 seconds of each cycle and returns in 0.07 seconds — operators see a clean board feed with no return-stroke choke point. Compare this to e/Rp = 0.2 (only 1.5:1, not worth the complexity) and e/Rp = 0.7 (5.67:1 but doubled pin loads), and the 0.5 ratio is clearly the design sweet spot. If you measure the follower peak speed below predicted — say 320 RPM instead of 360 — check first for slot wear opening the working clearance beyond 0.05 mm (you'll hear a tick at top-dead-centre), second for pin shaft deflection under the higher transient torque (caliper the pin runout under load), and third for driver shaft coupling slip if you're running through a taper-lock bushing that wasn't torqued to spec.
Two-shaft Crank with Slot for Varying Velocity vs Alternatives
The two-shaft slotted crank competes with a few alternatives whenever a designer needs non-uniform output. Each option trades cost, complexity, and maintenance interval differently. Here's how they line up on the dimensions that actually matter on the shop floor.
| Property | Two-shaft slotted crank | Geneva drive | Disc cam with follower |
|---|---|---|---|
| Typical operating speed | Up to 600 RPM input | Up to 300 RPM input | Up to 1500 RPM input |
| Velocity profile flexibility | Sinusoidal-ish, fixed by geometry | Fixed dwell + indexing only | Arbitrary — designer-specified |
| Indexing accuracy | ±0.5° at slot wear limit | ±0.05° at engaged dwell | ±0.1° with ground cam |
| Cost per unit (small batch) | Low — two shafts and a slot | Medium — precision indexing teeth | High — ground cam profile |
| Maintenance interval | Pin/slot inspection every 1-2M cycles | Roller and slot inspection every 5M cycles | Cam follower replacement every 10M cycles |
| Lifespan with proper lubrication | 10-20 million cycles | 20-50 million cycles | 50-100+ million cycles |
| Best application fit | Quick-return strokes, dwell-snatch | Pure indexing with dwell | Custom motion laws, high speed |
Frequently Asked Questions About Two-shaft Crank with Slot for Varying Velocity
Axial wobble in a parallel-shaft slotted crank almost always traces back to the pin not being perpendicular to the slot face. If the pin axis tilts even 0.5° relative to the driver shaft, the contact point between pin and slot wall walks back and forth along the pin as the crank rotates, and that introduces an axial force component the follower bearing has to absorb.
Check the crank-arm pin bore for squareness with a dial indicator on the pin while the driver is fixtured. Anything above 0.05 mm of indicated runout per 100 mm of pin length is your culprit. Skim-cut the pin bore square and the wobble disappears.
No — the slot length doesn't drive the velocity ratio. The ratio is set entirely by e/Rp. Lengthening the slot just gives the pin more room to travel, but if you don't increase e the pin still sweeps the same range and the velocity profile is unchanged.
This is a common design mistake. We've seen builders cut a 200 mm slot expecting a more aggressive quick-return, then wonder why nothing changed. If you want more velocity variation, increase e relative to Rp — but accept the corresponding rise in pin reaction force and bearing load.
The Whitworth IS a two-shaft slotted crank, geometrically — same equations, same kinematics. The decision is mechanical packaging. Whitworth puts the slot on a long arm that swings around the driven shaft, which gives you a longer effective stroke at the output, useful for shapers cutting 600 mm strokes.
The plain slotted disk version is more compact and better suited to rotary-output applications like indexing rollers or feeder cranks. If you need linear stroke at the output, go Whitworth. If you need rotary motion with a velocity asymmetry, the disk version is simpler to build.
If the velocity peak shifts away from θ = 180°, the line connecting the two shaft centres isn't aligned with where you think it is. Either the driver shaft has moved in its mount (loose pillow block, taper-lock slip) or the follower bearing housing is cocked relative to the frame.
Drop a dial indicator on each shaft and verify the centre-to-centre line against the frame datum. A 30° angular phase error in the velocity peak corresponds to roughly a 30° rotation of the centre line — usually one of the two shaft housings has rotated in its mounting bolts after the foundation shifted.
For most machine duties, e/Rp between 0.45 and 0.55 is the practical sweet spot. You get a velocity ratio of 2.6:1 to 3.4:1, which is enough quick-return benefit to be worth the mechanism, while pin reaction force stays within reasonable bounds — typically 1.5× the average tangential load.
Below 0.3 the quick-return effect is too mild to justify the complexity over a simple constant-velocity drive. Above 0.65 the peak pin force climbs sharply (it scales roughly with 1/(Rp − e)) and you'll start chasing pin galling and slot deformation within a few months of production running.
The closed-form formula assumes the pin slides without friction inside the slot. In reality, friction does two things: it dissipates energy at the slow phase (where sliding velocity along the slot is highest) and it briefly stores elastic energy in the pin and arm that releases at the fast phase. The result is a measured peak that overshoots the rigid-body prediction by 5-15%.
If your measured peak is HIGHER than predicted, that's normal and the math is fine. If your measured peak is LOWER than predicted, look for slot pickup (galling debris narrowing the working clearance) or a flexible coupling on the driver introducing windup that smooths out the velocity peak.
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