Variable Crank Motion is a rotary-to-linear linkage where the effective crank radius can be changed during setup or while running, so the stroke and instantaneous velocity of the driven slider shift without altering input RPM. It solves the problem of needing different stroke lengths from one drive shaft. By repositioning the crank pin along a radial slot or T-slot, the operator changes throw, peak slider velocity, and the force-vs-displacement profile delivered to the load. Stamping presses, shapers, and metering pumps use it to retune output without swapping gear trains.
Variable Crank Motion Interactive Calculator
Vary the short and long crank-pin throw radii to compare the resulting slider strokes in an animated variable crank mechanism.
Equation Used
The crank pin throw radius r is the distance from the crank center to the adjustable pin. For a full revolution, the slider moves from one dead center to the other, so total stroke is S = 2r. Moving the pin farther out doubles that change in the final stroke.
- Crank completes a full 360 degree rotation.
- Stroke is measured between slider dead centers.
- Connecting rod length does not change the total stroke for full rotation.
The Variable Crank Motion in Action
The Variable Crank Motion, also called the Variable Power Transmitted from a Crank in older mechanism textbooks, works by mounting the crank pin in a slot or dovetail rather than at a fixed hole. You loosen a clamp, slide the pin closer to or further from the crank centre, and re-clamp. The effective crank radius r changes, so stroke = 2r changes with it. Input RPM stays the same, but the driven slider now sees a different peak velocity, a different acceleration profile, and a different mechanical advantage at top and bottom dead centre.
Why bother building it this way instead of just changing motors or gear ratios? Because you keep one drive train, one bearing set, one footprint. The press operator who needs a 50 mm stroke for one die and 110 mm for the next does not want to rebuild the machine — they want to crack a single bolt, slide the crank pin, and run. The compromise is mechanical: the slot weakens the disc, the clamp depends on friction, and the crank pin sees a bending moment proportional to its offset from the clamp face.
If the clamp friction is wrong, the pin walks under load. You see this as a stroke that slowly grows during a shift, with the slider over-travelling and hitting end stops. The classic failure modes are clamp-bolt preload below spec (typical requirement is a friction coefficient of 0.15 with 30-45 Nm preload on an M10 cap screw), galling on the slot face from running unlubed, and fatigue cracking starting at the slot end-radius if the radius is below 0.5 × slot width. Get those three right and the mechanism runs for decades — the Atlas 7B shaper used this exact principle on its bull gear from 1937 onward.
Key Components
- Crank Disc with Radial Slot: Carries the crank pin and provides the adjustment range. The slot end-radii must be - 0.5 × slot width to avoid stress concentrations that crack under reversed loading. Typical slot length is 60-70% of disc radius.
- Adjustable Crank Pin: The hardened pin that translates rotary motion into the connecting-rod throw. Pin diameter is sized for the maximum stroke condition, not nominal — at full offset, bending stress at the clamp face can be 2-3× the nominal value.
- Clamp Block and Bolt: Locks the crank pin at the chosen radius. Preload typically 30-45 Nm on an M10 grade 8.8 bolt, giving roughly 18 kN clamp force. Below this the pin migrates under cyclic load and the stroke drifts.
- Connecting Rod: Couples the crank pin to the slider. Length-to-throw ratio (L/r) should stay above 4:1 to keep the slider velocity profile near-sinusoidal and limit second-order acceleration spikes.
- Slider or Ram: The driven element that delivers reciprocating output. Guideway clearance must stay below 0.05 mm per side or the slider chatters at the end of stroke when the connecting rod transitions through its angular extremes.
- Calibrated Scale or Index: Engraved on the disc face so the operator can set repeatable throw without trial and error. Resolution of 0.5 mm is standard on toolroom-class machines.
Who Uses the Variable Crank Motion
Variable Crank Motion shows up wherever a single drive shaft must produce different stroke lengths on demand. The Variable Power Transmitted from a Crank principle lets the same input torque deliver different output force-stroke combinations — shorter throw means higher mechanical advantage at the slider, longer throw means more displacement per cycle. That trade is what makes the mechanism worth the extra complexity over a fixed crank.
- Metalworking machine tools: The bull gear on an Atlas 7B or South Bend shaper carries a sliding block with a T-slot, letting the operator dial in stroke from about 25 mm up to 175 mm to match the workpiece length being planed.
- Mechanical metering pumps: Milton Roy and ProMinent diaphragm dosing pumps use an adjustable eccentric on the worm gear output to vary discharge volume from 10% to 100% of rated flow without changing motor speed.
- Stamping and coining presses: Bench-top toggle presses building electrical terminals use an adjustable crank to retune stroke when switching from a stripping die to a forming die, keeping the same flywheel and clutch.
- Textile machinery: Older Cocker and Jacquard loom take-up motions used a variable crank on the let-off shaft to tune fabric feed per pick when changing weave patterns.
- Test rigs and fatigue machines: Instron and MTS mechanical fatigue rigs that predate servo-hydraulic actuators used a variable-throw crank to set displacement amplitude on coupon testing, typically over a 0-25 mm range.
- Reciprocating compressors: Capacity-variable air compressors in legacy industrial plants used a variable crank on the lay shaft so a single-speed motor could deliver multiple displacement settings to match downstream demand.
The Formula Behind the Variable Crank Motion
The core formula relates crank radius to slider stroke and peak slider velocity. At the low end of the typical adjustment range — say 20% of maximum throw — the slider moves slowly with high mechanical advantage at the load, ideal for forming or coining where you need force not speed. At the nominal middle setting, you get a balanced velocity profile and the connecting-rod L/r ratio is comfortably above 4:1. Push to the high end of the range and stroke maxes out, peak slider velocity climbs linearly with r, but the second-order acceleration term gets worse because L/r drops — so the slider sees harsher reversal loads and the crank pin bending stress climbs faster than linearly. The sweet spot for most variable-crank machines sits between 50% and 80% of maximum throw.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| S | Slider stroke (peak-to-peak displacement) | m | in |
| r | Adjustable crank radius (throw) | m | in |
| vpeak | Peak slider velocity through mid-stroke | m/s | in/s |
| ω | Crank angular velocity | rad/s | rad/s |
| L | Connecting rod length (centre-to-centre) | m | in |
Worked Example: Variable Crank Motion in an Adjustable-Stroke Briquette Press
You are retuning the variable crank on a Komarek B-050 roll-fed briquette press at a charcoal plant in Mariveles, Philippines. The press uses an adjustable crank on the feed-screw drive to vary the powder charge per stroke. Connecting rod length L is 240 mm, the drive runs at 90 RPM steady, and you need to know slider stroke and peak velocity at three throw settings: 20 mm (low end), 45 mm (nominal recipe), and 75 mm (max throw used for the largest briquette mould).
Given
- L = 240 mm
- N = 90 RPM
- rlow = 20 mm
- rnom = 45 mm
- rhigh = 75 mm
Solution
Step 1 — convert input speed to angular velocity:
Step 2 — at the nominal 45 mm throw, compute stroke and peak slider velocity:
That 90 mm stroke at 0.5 m/s is the recipe sweet spot — the L/r ratio is 5.3, so the slider velocity profile stays close to sinusoidal and the connecting-rod bearing sees manageable reversal loads.
Step 3 — at the low end, 20 mm throw:
This is the gentle setting used for fine powder where you want minimum impact at fill. The slider creeps in and out at roughly 0.2 m/s — you can comfortably watch it reverse with the naked eye, and the L/r ratio is 12, so motion is almost pure sinusoid.
Step 4 — at the high end, 75 mm throw:
Stroke nearly doubles versus nominal, but peak velocity nearly doubles too. L/r drops to 3.2, below the 4:1 rule, so the second-order acceleration term grows and the slider snaps through bottom dead centre. You will hear it as a sharper thud per cycle and the connecting-rod little-end bearing temperature climbs 15-20 °C above the nominal setting after an hour of running.
Result
Nominal slider stroke is 90 mm with peak velocity 0. 50 m/s — the recipe sweet spot the press was designed around. The low-end 20 mm setting gives a gentle 40 mm stroke at 0.20 m/s suitable for fine fill, while the high-end 75 mm setting pushes 150 mm of stroke at 0.93 m/s but drops the connecting-rod L/r ratio to 3.2 and you can feel the harsher reversal in the machine frame. If you measure stroke drifting during a shift instead of holding constant, the most likely causes are: (1) clamp-bolt preload below 30 Nm letting the crank pin walk in its T-slot, (2) galling on unlubed slot faces giving a false stick-slip lock that releases under load, or (3) connecting-rod little-end bushing wear past 0.10 mm radial clearance, which adds parasitic stroke that scales with throw setting.
When to Use a Variable Crank Motion and When Not To
Variable Crank Motion competes with several other ways to get adjustable reciprocating output. Each alternative wins on some axes and loses on others — pick by what the machine actually has to do day to day, not by which mechanism is theoretically prettier.
| Property | Variable Crank Motion | Scotch Yoke with Adjustable Throw | Servo-driven Ball Screw |
|---|---|---|---|
| Typical operating speed | 50-300 RPM | 30-200 RPM | 0-3000 RPM equivalent |
| Stroke adjustment time | 1-3 min, manual | 2-5 min, manual | instant, software |
| Stroke repeatability after re-clamp | ±0.3 mm with engraved scale | ±0.2 mm | ±0.01 mm |
| Capital cost (relative) | 1.0× | 1.3× | 5-10× |
| Maintenance interval | regrease pin and slot every 500 hr | regrease yoke every 300 hr | ball-screw lube every 2000 hr |
| Load capacity per kg of mechanism | high — direct steel linkage | high | moderate — limited by screw column buckling |
| Best application fit | recipe-change presses, shapers, dosing pumps | valve actuators, simple linear strokes | servo-controlled motion profiles |
Frequently Asked Questions About Variable Crank Motion
Almost always slot-face contamination, not bolt failure. Powder, oil mist, or paint flakes on the slot mating surface drop the friction coefficient from the assumed 0.15 down to 0.08 or lower. The clamp force is unchanged, but the resistive friction force halves. Each load reversal nudges the pin outward by a few microns — over thousands of cycles you measure visible drift.
Pull the pin, degrease the slot with brake clean, lightly stone any high spots, and reassemble dry. Lubrication on the clamp face is wrong — it slips. Lubrication on the pin shank where it slides during adjustment is right.
Three questions decide it. First, how often does stroke change — once per recipe, once per shift, or every cycle? If every cycle, you need a servo. If once per recipe, the crank wins on cost. Second, what is your repeatability requirement? Below ±0.05 mm a manual clamp will not hold consistently and you need a servo. Third, what is the duty cycle and load? At 200+ RPM with multi-tonne reversal loads, the variable crank's all-steel linkage is more honest than any ball screw.
Rule of thumb we use: under 50 stroke changes per day and tolerance loose enough for an engraved scale, build the variable crank. Above that, spend the money on a servo.
The simple vpeak formula only captures the first-order velocity. The acceleration profile contains a second-order term proportional to (r/L) × ω2, and that term grows nonlinearly as r approaches L/3. At nominal settings with L/r above 5, you do not feel it. At maximum throw with L/r near 3, the slider acceleration peak near top dead centre can be 30-40% higher than the pure sinusoidal value.
If your machine vibrates noticeably worse at max throw, it is not a fault — it is the geometry. Either accept the duty restriction at high throw or lengthen the connecting rod to keep L/r above 4 across the full range.
Minimum 0.5 × slot width, ideally 0.6 × slot width, with a polished finish (Ra below 0.8 µm). Square-cut slot ends are the single most common reason these discs crack — the stress concentration factor at a sharp inside corner runs 3-4×, and reversed bending finds it within a few million cycles.
If you are restoring an old shaper or press disc, inspect the slot ends with dye penetrant before putting it back in service. Hairline cracks at the slot ends are not optional repairs — they grow.
No. The crank-slider geometry is inherently sinusoidal — slider velocity is zero at top and bottom dead centre and peaks near mid-stroke. Changing crank radius scales the whole velocity curve up or down but does not flatten it.
If you need constant velocity over a working stroke, you need a different mechanism: a Scotch yoke gives a pure sinusoid (still not constant), but a cam with a constant-velocity rise profile or a servo-driven linear actuator are the right tools. People misuse the variable crank for this and then complain the part quality varies through the stroke — it is not the mechanism's fault, it is the wrong mechanism for the job.
Yes. Variable Power Transmitted from a Crank is the older textbook name, used in 19th-century mechanism catalogues like Brown's 507 Mechanical Movements. It emphasises the force-stroke trade — short throw means high force at the slider, long throw means more displacement per turn. Modern machine-tool and packaging engineers usually call it Variable Crank Motion or simply an adjustable-throw crank.
Both phrases describe the same kinematic device: a crank disc with a slot or dovetail letting the crank pin sit at variable radius from the rotation axis.
References & Further Reading
- Wikipedia contributors. Crank (mechanism). Wikipedia
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