Crank Mechanism

Part of Machine Tools

Converting rotary motion to reciprocating motion (and vice versa) — the fundamental mechanism driving pumps, presses, saws, engines, and lathes.

Why This Matters

The crank is one of the most important mechanical inventions in history. It converts continuous rotary motion (from a wheel, motor, or engine) into back-and-forth linear motion — or converts human push-pull motion into rotation. Without the crank, you cannot build a reciprocating pump, a piston engine, a crank-driven saw, a trip hammer, or a pedal-powered vehicle.

Understanding how cranks work — the geometry, the forces, the critical design dimensions — lets you design reliable mechanisms for pumps, compressors, steam engines, and any other reciprocating machinery. It also lets you identify and fix the most common failures: excessive stress at the crank pin, vibration from imbalance, and wear in the connecting rod bearings.

Every time you turn a bicycle pedal, operate a hand drill, or use a hand pump for water, you’re using a crank mechanism. Bringing this knowledge to intentional machine design moves you from user to builder.

Crank Geometry and Kinematics

A basic slider-crank mechanism consists of:

• Crankshaft: The main rotating shaft with an offset pin (crank pin) at a radius (crank radius) from the center
• Connecting rod: Links the crank pin to the piston/slider, allowing the rotary motion to be converted to linear
• Slider (piston or crosshead): Moves linearly back and forth

Stroke: The total linear travel of the piston = 2 × crank radius. A 3-inch crank radius gives a 6-inch stroke.

Instantaneous piston position: At angle θ from top dead center (TDC): x = r(1 - cos θ) + r²/(2L) × sin²θ

Where r = crank radius, L = connecting rod length, θ = crank angle. The second term is the “obliquity correction” and is often small (about 10-15% of r²/L).

Connecting rod ratio: L/r (connecting rod length divided by crank radius). A ratio of 3-5 is typical for engines and pumps. Shorter rods (lower ratio) cause more side thrust on the cylinder walls but allow more compact design. Longer rods (higher ratio) reduce side thrust and approach true sinusoidal motion.

Piston velocity: Not constant through the stroke. Maximum velocity occurs slightly past mid-stroke; velocity is zero at both TDC (top dead center) and BDC (bottom dead center). This non-uniform motion creates inertia forces that must be considered in design.

Types of Cranks

Single-throw crank: One offset pin. Simple to make; one stroke per revolution. Forces are unbalanced at each stroke — requires a flywheel to smooth out the torque pulses.

Double-throw crank (180° apart): Two pistons at opposite ends of the stroke at the same time. More balanced than single-throw; smoother power delivery. Used in two-cylinder engines and double-acting pumps.

Bent axle (single piece): The simplest crank for hand tools — a solid steel rod bent at 90°, like a bicycle crank arm. Strong, simple, no separate crank pin needed. Limited to designs where the connecting rod can be attached from the side.

Disc crank: A round disc with a hole offset from center, used as the crank pin mount. Larger contact area than a pin crank, stronger, better for heavy loads. Standard in large slow-speed machinery.

Eccentric: Not a true crank but achieves the same result — a disc mounted off-center on a shaft. A strap (eccentric strap) encircles the disc and connects to the connecting rod. Very simple to make; no offset in the shaft itself required. Used historically in steam engine valve gear, pumps, and small presses.

Fabricating a Crank

Forged steel crank: The traditional and strongest method. Heat steel bar to bright yellow-orange. Forge the crank pin location with an offset using swage blocks and top/bottom tooling. The grain of the steel flows with the crank shape, giving excellent fatigue resistance. Requires skilled blacksmithing.

Machined crank from solid: Turn the main journals on a lathe, then offset-turn the crank pin (mount the blank off-center in the lathe using an offset fixture). Machine the crank cheeks (the sides of the crank). This requires planning — you can’t mount and machine everything without multiple setups. Used for one-off or small quantity production.

Built-up crank: Separate main shaft + press-fit or keyed crank pins + crank cheeks. Allows each component to be made separately, then assembled. The interfaces (press fits and keyways) must be tight and strong — built-up cranks fail at the joints if underdesigned. Used in large slow-speed machinery where a one-piece forged crank would be impossibly large and heavy to manufacture.

Key dimensions:

• Crank pin diameter: approximately 0.6-0.8 × main journal diameter
• Crank pin length: sized for bearing pressure = Force / (diameter × length) < allowable pressure for the bearing material
• Crank cheek thickness: approximately equal to crank pin diameter
• Fillet radius at all stress risers (where pin meets cheek): minimum 10% of pin diameter — stress concentrations at sharp corners cause fatigue cracking

Connecting Rod Design

The connecting rod must handle both tensile (pulling) and compressive (pushing) loads. It must also be light enough that its own inertia doesn’t create excessive unbalanced forces at high speed.

Big end bearing: The end connecting to the crank pin. Must be split (two-piece) to allow assembly around the crank. The bearing surface is babbitt-lined or bronze-bushed (see Plain Bearings article). Sized for bearing pressure under maximum force.

Small end bearing: The end connecting to the piston pin. Usually a solid bronze bush pressed into the connecting rod eye — the piston pin slides or rotates in this bush.

Rod material: Forged medium-carbon steel is standard. Cast iron is used for low-speed, low-duty applications (hand pumps, slow agricultural machinery) where the compressive strength of cast iron is adequate and the lower tensile strength is acceptable.

Buckling check: A long connecting rod under compressive load can buckle (like a column under compression). The critical buckling load (Euler’s formula): P_critical = π²EI / L². Ensure maximum compressive force is less than P_critical with a safety factor of 5-10.

Flywheel Sizing

A single-throw crank delivers power in pulses — power stroke, then return stroke, with varying torque throughout each revolution. A flywheel stores kinetic energy during the power stroke and releases it during the return, smoothing the rotation.

Flywheel sizing: The required moment of inertia (I) depends on the energy variation per cycle (ΔE) and the allowable speed variation (coefficient of fluctuation, Cs):

I = ΔE / (Cs × ω²)

For a single-cylinder pump with 1 HP at 60 rpm and Cs = 0.1 (10% speed variation): ω = 2π × 60/60 = 6.28 rad/s ΔE ≈ Power × (1/2N) = 1 × 33,000/60 ÷ 2 = 275 ft-lbs (energy per half cycle) I = 275 / (0.1 × 6.28²) = 275 / 3.95 = 69.6 slug-ft² — this is a very heavy flywheel!

In practice, accept higher speed variation (Cs = 0.3-0.5) and correspondingly smaller flywheels. For intermittent loads (pumps, presses), the load itself provides some energy storage, reducing flywheel requirements.

Cast iron flywheels are traditional — dense, strong in compression, and easily cast. Mount securely on the shaft with key and setscrew. At maximum operating speed, the rim stress should not exceed 10-15% of cast iron’s tensile strength.