A double-crank mechanism is a four-bar linkage in which both the input link and the output link complete full 360° rotations about their fixed pivots, connected through a coupler. Agricultural machinery designers rely on it constantly — square balers, sickle drives and harvester pickup reels all use double-crank geometry. The shortest link sits as the ground link to satisfy the Grashof condition, which forces continuous rotation on both cranks. The output crank rotates non-uniformly relative to the input, giving you a controlled speed variation per revolution without clutches or gearing.
Double-crank Mechanism Interactive Calculator
Vary the four-bar link lengths and input RPM to check the Grashof double-crank condition and see the linkage motion.
Equation Used
The Grashof rule compares the shortest link plus the longest link against the two remaining links. A double-crank is obtained when this condition is satisfied and the shortest link is fixed as the ground link. For a valid double-crank, the output crank completes one full turn per input turn, so its average RPM matches the input RPM, even though its instantaneous speed varies.
- Shortest link is intended to be the fixed ground link.
- Links are rigid pin-jointed bars in a planar four-bar linkage.
- For a valid double-crank, the output crank completes one revolution per input revolution on average.
- Instantaneous output speed variation is not calculated; this calculator checks the central Grashof condition.
How the Double-crank Mechanism Actually Works
A double-crank, also called a drag-link mechanism, is one of three Grashof four-bar configurations. The Grashof rule says s + l ≤ p + q, where s is the shortest link, l is the longest, and p and q are the other two. To get a double-crank specifically, you fix the shortest link as the ground. Now both side links — input and output — can swing all the way around their pivots without locking. Get the link assignment wrong and you end up with a crank-rocker or double-rocker instead, and one of your cranks will stall at a dead point.
The coupler links the two crank tips and forces them to rotate at different instantaneous angular velocities. If you spin the input crank at constant 100 RPM, the output crank also averages 100 RPM over a full revolution, but speeds up and slows down within each revolution. This is the whole point — you get non-uniform rotation from a uniform driver. The ratio of fastest to slowest output speed depends on the link-length proportions, and you can tune it to match a load profile that a constant-speed shaft can't.
Tolerances matter here. Pivot bushing slop above about 0.1 mm radial play on a 250 mm crank starts showing up as audible knock at the dead-centre transition, because the coupler reverses load direction twice per revolution. If the shortest link is barely shorter than the next-shortest — say 99 mm vs 100 mm — you're sitting on the edge of the Grashof condition and any wear pushes you over the line into a double-rocker that jams. Build in at least 10% margin on link-length differences. Common failure modes are coupler-end bearing wear from the load reversal, and crank shaft fatigue near the keyway when the non-uniform torque pulse hits a resonance with the driveline.
Key Components
- Ground link (frame): The fixed reference link, and in a double-crank it must be the shortest of the four. Typical bore tolerance for the two fixed pivots is H7 on a hardened steel pin, with centre-to-centre spacing held to ±0.05 mm on a 200 mm baseline so the Grashof margin doesn't drift over the machine's life.
- Input crank: The driven link, connected to the motor or PTO shaft. Rotates 360° continuously. Typical sizes run 50-300 mm crank radius depending on application — a John Deere square baler plunger crank sits around 280 mm radius.
- Coupler (connecting rod): Joins the two crank tips and transmits the non-uniform motion. Carries the highest combined bending and tension loads in the linkage. Length is usually the longest link in the assembly, often 1.5-2.5× the input crank length.
- Output crank: The driven crank that rotates non-uniformly. Same 360° rotation as the input but with varying instantaneous angular velocity. Output bearing must handle reversing radial loads — sealed needle bearings rated for at least 2× peak calculated radial load.
- Pivot pins and bushings: Four pin joints, typically hardened ground steel pins running in bronze or composite bushings. Radial clearance held to 0.02-0.05 mm on a 20 mm pin. Wear past 0.1 mm produces visible coupler-end knock at the transition points.
Industries That Rely on the Double-crank Mechanism
Double-crank linkages show up wherever you need continuous rotation with a built-in speed variation, or where you want to drive two parallel shafts with a phase shift. They're cheap, robust, and need no electronics. The tradeoff is that the speed-variation profile is fixed by geometry, so they suit applications where the load cycle is predictable and repeats every revolution.
- Agricultural machinery: Plunger drive on a New Holland BB9000 square baler — the double-crank gives a slow compression stroke and a fast return, matching the bale-chamber load profile.
- Locomotives: Coupling rods between driving wheels on a steam locomotive — the LMS Stanier Class 5 4-6-0 uses what is functionally a series of parallel double-crank linkages to keep all driving wheels in phase.
- Textile machinery: Beat-up motion on a Sulzer projectile loom, where the reed must accelerate forward quickly and dwell at the front of the stroke.
- Marine engineering: Quick-return drives on slotting machines and shaper feed mechanisms — the cutting stroke moves slowly under load while the return stroke whips back fast.
- Printing presses: Sheet-feeder drives on a Heidelberg Speedmaster, where intermittent grip-and-release timing benefits from a non-uniform rotation profile.
- Packaging machinery: Carton-erecting flight conveyors on a Bosch Sigpack, where the flight bars need to dwell briefly at the loading station.
The Formula Behind the Double-crank Mechanism
The instantaneous angular velocity ratio between the output crank and the input crank is what every double-crank designer cares about. At the low end of the operating range — say a baler running at 30 RPM input — the absolute speed difference is small but the timing matters because the load is high. At nominal speed (typically 100-120 RPM for ag drives), you hit the design sweet spot where the velocity ratio swings cleanly between its minimum and maximum without inducing resonance. Push past the high end of the typical range and centrifugal loads on the coupler start to dominate, and the linkage begins flexing enough to throw off your designed velocity profile.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| ωout | Output crank angular velocity | rad/s | rev/min |
| ωin | Input crank angular velocity | rad/s | rev/min |
| rin | Input crank length | mm | in |
| rout | Output crank length | mm | in |
| θin | Input crank angle from ground link | rad | deg |
| θout | Output crank angle from ground link | rad | deg |
| θcpl | Coupler angle from ground link | rad | deg |
Worked Example: Double-crank Mechanism in a vineyard pruning-shear oscillator drive
A boutique vineyard equipment maker in Mendoza is building a tractor-mounted twin-blade pruning oscillator for pinot noir vines. The double-crank takes a 540 RPM PTO input geared down to 120 RPM at the input crank, and drives an output crank that swings a pair of opposing blades. Link lengths are: ground 80 mm (shortest), input crank 110 mm, coupler 180 mm, output crank 130 mm. They need to know the output crank's velocity ratio swing — the ratio between fastest and slowest output speed in one revolution — to size the blade-shaft bearings and confirm the cutter sees a clean slicing stroke without snatch.
Given
- Lground = 80 mm
- rin = 110 mm
- Lcoupler = 180 mm
- rout = 130 mm
- ωin = 120 RPM
Solution
Step 1 — confirm the Grashof double-crank condition. The shortest link must be the ground, and s + l ≤ p + q must hold:
That's a problem. The proposed link set does not satisfy Grashof — it would behave as a non-Grashof linkage with dead points. The designer must shorten the coupler or lengthen the side links. Adjust the coupler to 160 mm:
Step 2 — at the nominal 120 RPM input with corrected geometry, compute the maximum and minimum output velocity ratios. These occur when the input crank is collinear with the coupler. By geometric analysis the ratio extremes for these proportions work out to:
So at nominal 120 RPM input, peak output speed = 1.46 × 120 = 175 RPM, and slowest output speed = 0.58 × 120 = 70 RPM. The blade swings fast through the cut and dwells slower at the reversal — exactly what you want for a clean slicing action.
Step 3 — at the low end of the typical PTO operating range, around 60 RPM input (idle PTO), peak output drops to 88 RPM and slow point to 35 RPM. The blade barely accelerates enough to slice cleanly through 8 mm vine wood, and you'll see crushing instead of cutting. At the high end, 180 RPM input, peak output hits 263 RPM:
Above 3 m/s tip speed the coupler bearing inertial loading starts producing visible flex in a 180 mm-long mild steel coupler, which detunes the velocity ratio. The sweet spot sits firmly at the nominal 120 RPM design point.
Result
Nominal velocity ratio swings from 0. 58 to 1.46 at 120 RPM input, giving blade speeds of 70 to 175 RPM per revolution. That ratio swing produces the snap-through slicing action the vine pruner needs — slow approach, fast cut, slow reversal. At 60 RPM input the blade crushes rather than slices; at 180 RPM coupler flex distorts the velocity profile and you lose the dwell. If your prototype measures a peak-to-trough ratio narrower than predicted — say 0.75 to 1.25 instead of 0.58 to 1.46 — the most common causes are: (1) link lengths drifted from spec because the coupler eyes were drilled to nominal centres without accounting for bushing wear, (2) the ground-link pivot spacing is off, pushing you closer to the Grashof boundary and flattening the velocity curve, or (3) the coupler is flexing under load because its section modulus is undersized for the inertial peak at top speed.
Double-crank Mechanism vs Alternatives
A double-crank is one of several ways to convert constant rotation into a useful non-uniform output. The alternatives — a crank-rocker four-bar and a Geneva drive — solve overlapping but distinct problems. Pick based on whether you need full continuous output rotation, intermittent indexing, or simple oscillation.
| Property | Double-crank | Crank-rocker | Geneva drive |
|---|---|---|---|
| Output motion type | Continuous 360° non-uniform rotation | Oscillating swing, no full rotation | Intermittent indexed rotation with dwell |
| Typical input speed | 50-500 RPM | 30-300 RPM | 10-200 RPM (limited by impact at lock-up) |
| Velocity ratio range | 0.5× to 2× per revolution typical | Output reverses, no continuous ratio | Infinite (zero during dwell, finite during index) |
| Load capacity | High — all four pin joints share load | High — same joint count as double-crank | Lower — locking pin sees impact loads |
| Maintenance interval | 1000-3000 hr bushing inspection | 1000-3000 hr bushing inspection | 500-1500 hr — cam and pin wear faster |
| Cost (relative) | 1.0× baseline | 0.9× (one fewer rotating bearing) | 1.5-2× (precision cam + locking) |
| Best fit application | Baler plunger, pruning oscillator, locomotive coupling | Wiper drive, sewing machine needle bar | Indexing turret, film advance, packaging dial |
Frequently Asked Questions About Double-crank Mechanism
You're almost certainly on the boundary of the Grashof condition rather than safely inside it. If s + l equals p + q exactly, the linkage passes through a momentary collinear configuration where all four links align — this is called a change point, and the mechanism can flip into either the double-crank or non-Grashof branch unpredictably.
Rebuild with at least 5-10% margin: s + l should be no more than 0.92 × (p + q). Also verify your shortest link really is the ground — if manufacturing tolerances stacked the wrong way, your shortest link might actually be the input crank, in which case you've built a crank-rocker that hits dead points.
The velocity ratio extrema are governed by the angle the coupler makes with the output crank at the two collinear positions of the input crank and coupler. As a working rule, increasing the coupler length relative to the cranks flattens the ratio swing; making the input crank longer than the output crank biases the swing toward output speed-up.
Start with a target ratio (e.g. 2.5:1 fast-to-slow), pick the ground link length from your packaging constraint, then iterate input and output crank lengths in CAD with a parametric sketch. Modern tools like SolidWorks Motion or Linkage software let you sweep parameters in minutes — far faster than analytical solving for a non-symmetric configuration.
Pick the double-crank when you want a smooth sinusoidal-ish velocity profile, low cost, and high load capacity. Pick a cam when you need a specific arbitrary motion profile — dwells, ramps, or piecewise velocity curves that a four-bar geometry simply cannot produce.
Rule of thumb: if you can describe your required output motion with a single sentence ('faster on the cut stroke, slower on the return'), a double-crank is fine. If you need 'constant velocity for 30°, then accelerate over 60°, then dwell for 90°', you need a cam. Cams cost 3-5× more, wear faster, and need precision grinding — so don't reach for them unless the motion profile demands it.
Two usual suspects beyond the ones already covered: pin-joint clearance and ground-frame compliance. Total pin-joint clearance across all four joints accumulates — 0.05 mm at each joint becomes 0.2 mm of total play, and the linkage chooses the lowest-energy path through that play, which tends to flatten the velocity peaks.
Frame compliance is sneakier. If your ground link is a welded steel bracket rather than a machined block, it will deflect microns under load — enough to shift effective ground-link length and change the velocity profile. Measure ground pivot-to-pivot spacing with the linkage under load using a dial indicator. If it changes by more than 0.1 mm at peak torque, stiffen the frame before chasing other causes.
Yes, kinematically the linkage is symmetric and either crank can drive. But the velocity ratio inverts: if the original input-to-output ratio swung 0.58 to 1.46, driving from the other end gives you a swing of 1/1.46 to 1/0.58, i.e. 0.68 to 1.72.
Practically, watch the bearing loads. The coupler tension/compression cycle reverses sign on each end depending on which crank is driving, so the bearing on what was previously the unloaded side now sees the higher peak. Resize bearings accordingly — don't assume symmetry of load just because the kinematics are symmetric.
The coupler sees alternating tension and compression every revolution, with peak compression near the input crank's collinear positions. Buckling becomes a real risk when the coupler's slenderness ratio (length / radius of gyration) exceeds about 100 for steel.
For a 180 mm coupler in a moderately loaded ag drive, use a hollow rectangular section at least 25 × 15 × 3 mm wall, or a forged H-section like you'd see on a connecting rod. Don't use round bar unless the load is genuinely small — round bar has the worst section modulus for the cross-sectional area you're paying for. Also, machine the coupler ends concentric to within 0.05 mm to avoid eccentric loading that drops effective buckling strength dramatically.
References & Further Reading
- Wikipedia contributors. Four-bar linkage. Wikipedia
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