A crank is a rigid arm fixed to a rotating shaft, with a pin offset from the shaft axis that converts rotary motion into reciprocating or oscillating motion when coupled to a connecting rod. Unlike a cam — which uses a profiled surface for non-uniform output — a crank produces sinusoidal motion governed purely by its throw radius. The purpose is to transfer torque from a rotating prime mover into linear force at a piston, ram, or pedal. You see it everywhere from a 50 mm Bicycle Crank arm to the 600 mm crank throw on a marine diesel.
Crank General Interactive Calculator
Vary crank throw, rod length, angle, and speed to see stroke and slider-crank motion update.
Equation Used
The core crank relationship is that total reciprocating stroke equals twice the throw radius. The slider displacement shown also includes the connecting rod length, so shorter rods show more obliquity effect at the same crank angle.
- Rigid crank arm and connecting rod.
- Slider moves on the crank centerline.
- No bearing clearance, elasticity, or friction included.
- Rod length is treated as valid when L is greater than r.
How the Crank (general) Works
A crank is the simplest way to turn a spinning shaft into useful linear push or pull. The Crank (general), also called Crank Motion in older mechanical engineering texts and Ordinary crank motion in 19th-century steam-engine literature, works by offsetting a pin from the rotation axis by a fixed distance — the throw radius, r. As the shaft spins, that pin traces a circle of radius r. Couple a connecting rod to the pin and constrain the far end of the rod to a straight line, and you get a slider-crank linkage: rotary input, reciprocating output, with a stroke equal to 2r.
The motion is sinusoidal — but only approximately. The connecting rod's finite length introduces a second-order term, so the slider spends slightly more time on the side of the cylinder away from the crank than near it. Engineers call this asymmetry the obliquity effect, and it matters when the connecting-rod-to-crank ratio (L/r) drops below about 3.5. Below that ratio, you'll see noticeable side loads on the slider and accelerated wear on the cylinder wall — the classic failure pattern in undersized engine designs.
The crank pin and main bearing tolerances are where most failures originate. A typical automotive crankshaft journal runs at H7/g6 fit with diametral clearance of 0.025 to 0.060 mm. Drop below 0.020 mm and you starve the oil film; go above 0.080 mm and you get hammering, then spalling within a few hundred hours. If you notice oil pressure dropping at idle on a rebuilt engine, check journal clearance first — it's almost always the cause.
Key Components
- Crank Arm: The rigid lever that fixes the crank pin at a known offset from the rotation axis. Length sets the throw radius r and therefore the stroke (2r). On a Bicycle Crank, this is the visible arm between the pedal and the bottom-bracket spindle, typically 165 to 175 mm.
- Crank Pin (Crankpin): The hardened pin offset from the shaft axis where the connecting rod attaches. Surface finish must hit Ra 0.2 µm or better and hardness around 55-60 HRC, otherwise the rod bearing wears out fast under combustion or hydraulic loading.
- Main Journal: The cylindrical section of the shaft that rotates in the main bearings. Diameter and surface finish (typically Ra 0.4 µm) determine bearing life. Must be ground concentric to the crank pin within 0.01 mm to keep the assembly balanced.
- Connecting Rod (when used as slider-crank): Couples the crank pin to the slider or piston. Rod length L sets the obliquity ratio L/r — keep this above 3.5 to limit slider side load. Below 3.0, expect noticeable cylinder-wall scoring.
- Counterweight: Mass added opposite the crank pin to balance the rotating and reciprocating inertia. Without counterweights, a single-cylinder engine at 3,000 RPM produces shaking forces that crack the engine mounts within hours.
Real-World Applications of the Crank (general)
The crank shows up anywhere a rotating motor must drive something back and forth, or a person must spin something with their legs or arm. Some applications use the crank as a pure rotary input device (a hand crank, a Bicycle Crank). Others embed it in a slider-crank linkage to drive a piston, ram, or shuttle. The throw radius is what sets the stroke — pick the wrong throw and you either undershoot the work envelope or you overstress the linkage. Each industry tends to use its own name for the same geometry.
- Automotive: The crankshaft in a Toyota 2GR-FE V6 uses a 41 mm throw to give an 83 mm stroke, with offset crank pins phased at 120° between cylinders.
- Cycling: Shimano Dura-Ace FC-R9200 Bicycle Crank arms come in 165, 170, 172.5, and 175 mm lengths — the rider's leg geometry sets which throw is correct.
- Industrial Machinery: Bliss mechanical stamping presses use a heavy crank with throws from 25 to 200 mm to produce calibrated stroke depth on the ram.
- Rail (Historical): Steam locomotives like the LNER Class A4 used outside cranks on the driving wheels — the very phrase 'Ordinary crank motion' came from this era of valve-gear analysis.
- Hand Tools: A bench-mounted hand drill, a coffee grinder, or a fishing reel all use a hand crank where the operator's arm provides the torque.
- Marine: A Wärtsilä RT-flex96C two-stroke marine diesel uses crank throws over 1,250 mm to deliver 2.5 m piston strokes.
The Formula Behind the Crank (general)
The fundamental crank-to-slider relationship gives you the slider position as a function of crank angle. At crank angles near 0° and 180° (top and bottom dead centre), slider velocity is zero and acceleration peaks — that's where shock loading lives. At 90°, slider velocity hits its maximum. The sweet spot for most slider-crank designs sits at L/r ≈ 4, where obliquity is small enough to ignore for first-pass sizing but the linkage stays compact. Push L/r below 3 and you get harsh side loads; push above 6 and the assembly gets unnecessarily bulky.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| x(θ) | Slider position from crank centre at crank angle θ | m | in |
| r | Crank throw radius (half the stroke) | m | in |
| L | Connecting rod length, pin centre to pin centre | m | in |
| θ | Crank angle measured from top dead centre | rad or ° | rad or ° |
Worked Example: Crank (general) in a pedal-powered water pump for an off-grid agricultural site
You are designing a pedal-powered piston water pump for a small Kenyan smallholder farm. The pedal assembly uses a 170 mm Bicycle Crank arm driving a connecting rod down to a piston pump. Target cadence is 60 RPM (typical sustained pedalling), with the operator able to push to 90 RPM short-term and slow to 30 RPM when fatigued. You need the piston velocity at mid-stroke to size the pump's check valves correctly.
Given
- r = 0.170 m
- L = 0.680 m
- Nnom = 60 RPM
- θ = 90 °
Solution
Step 1 — convert nominal cadence to angular velocity. At 60 RPM:
Step 2 — at θ = 90° (mid-stroke) the slider velocity simplifies, since the obliquity term goes to its maximum effect. Approximate piston velocity at mid-stroke:
That's the nominal mid-stroke piston speed. The L/r ratio here is 0.680 / 0.170 = 4.0, comfortably in the sweet spot, so the simplified formula is within 3% of the exact answer.
Step 3 — at the low end of the operating range (30 RPM, the fatigued-operator case):
At 0.53 m/s the check valves see gentle, predictable loading and water delivery drops to roughly half nominal — the pump still works but the operator notices less water per minute. At the high end (90 RPM, sprint cadence):
At 1.60 m/s, cheap rubber flapper check valves start slamming shut hard enough to cavitate and chatter. You'll hear a knocking sound from the pump body and pressure pulses will start fatiguing the discharge line. For sustained operation above 80 RPM, switch to spring-loaded poppet check valves rated for the higher closing velocity.
Result
Nominal mid-stroke piston velocity is 1. 07 m/s at 60 RPM cadence. That's a brisk but quiet flow you can hear as a steady pulse, not a hammer. At 30 RPM you get 0.53 m/s — the pump audibly slows but operates smoothly; at 90 RPM the 1.60 m/s peak starts to overdrive cheap check valves and you hear knocking. If your measured piston velocity is 20% below predicted, the most common causes are: (1) connecting-rod bearing slop letting the piston lag the crank pin, (2) flexing in the wooden or thin-wall steel pedal frame absorbing 10-15% of the input motion, or (3) the crank arm not being square to the bottom bracket, which shortens effective throw radius by the cosine of the misalignment angle.
Crank (general) vs Alternatives
A crank is one option among several for converting rotary input to reciprocating motion. The decision usually comes down to stroke profile (sinusoidal vs custom), maximum RPM, cost, and how much side load your slider can tolerate. Cranks (also called Crank Motion or Ordinary crank motion in the older literature) compete primarily with cams and Scotch yokes.
| Property | Crank (slider-crank) | Cam & Follower | Scotch Yoke |
|---|---|---|---|
| Output motion profile | Near-sinusoidal with obliquity error | Arbitrary, set by cam profile | Pure sinusoidal |
| Typical max RPM | Up to 8,000+ in automotive use | 300-3,000 depending on follower type | 200-1,500 (yoke wear-limited) |
| Side load on slider | Significant — needs L/r ≥ 3.5 | None on roller follower | None |
| Cost (small batch) | Low — standard parts | Medium-high — cam grinding | Medium — yoke fabrication |
| Lifespan (typical) | 10,000+ hours with proper bearings | 5,000-20,000 hours, follower-limited | 1,000-3,000 hours, yoke wear-limited |
| Application fit | Engines, pumps, presses, pedals | Valve trains, indexing, shaped motion | Steam pumps, special-purpose drives |
Frequently Asked Questions About Crank (general)
Yes — geometrically identical. A Bicycle Crank arm of 170 mm gives an 85 mm pedalling radius (throw), which is essentially what a car engine crankshaft does at the journal level, just driven by your leg instead of combustion gas pressure. The difference is loading direction: on a bike the human leg applies torque almost continuously, while in an engine the combustion event is concentrated near top dead centre. That's why engine cranks need counterweights and bike cranks don't.
That's the obliquity effect showing up in your build. With a connecting rod that's too short (L/r below about 3.0), the slider accelerates and decelerates asymmetrically — it dwells slightly longer near the far dead centre and snaps faster through the near one. The fix is to lengthen the connecting rod until L/r is at least 3.5, or accept the asymmetry and stiffen the slider guides to absorb the side load.
Throw radius equals exactly half the stroke. If you need a 100 mm stroke on a press ram, the crank throw is 50 mm. The harder design choice is connecting rod length — make it 4× the throw as a starting point (so 200 mm rod for a 50 mm throw), then check that your slider guide is long enough to handle the angular swing of the rod without binding.
This is a torque-angle problem, not a crank problem. Human legs produce peak force at roughly 90° and 270° crank angle (legs roughly horizontal) and almost zero force at 0° and 180° (legs vertical, top and bottom dead centre). Single-leg pedalling tests show torque varies by 4-5× across one revolution. The mechanism is fine — your biology is the limiter. Adding a flywheel or coupling two cranks 180° out of phase (which is exactly what a normal bicycle does) smooths it.
For an unbalanced single-throw crank in the 50-100 mm throw range, you start feeling shaking forces above about 1,500 RPM and they become destructive above 3,000 RPM. The reciprocating mass at the slider produces an inertial force proportional to ω² × r — double the speed, quadruple the force. If you need higher speeds, add a counterweight sized at roughly 50-60% of the reciprocating mass times the throw radius. That cancels the primary shaking force, though a residual secondary force at twice crank frequency remains.
One-sided journal wear almost always means the bearing housing is misaligned with the crankshaft centreline, or the crank itself is bent. Check shaft straightness with a dial indicator — runout above 0.02 mm at the centre journal of a 3-bearing shaft will load one side preferentially. The other common cause is belt or chain side load pulling the shaft sideways in the bearings; if the wear pattern lines up with the direction of belt pull, that's your culprit.
References & Further Reading
- Wikipedia contributors. Crank (mechanism). Wikipedia
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