Mechanical
Crank-Slider Mechanism
Converts rotation into reciprocating linear motion (and vice versa)
A crank-slider mechanism transforms rotational motion of a crank into reciprocating translation of a slider via a connecting rod. Found in every internal combustion engine: piston (slider) ↔ crankshaft (crank) ↔ connecting rod. Geometry: crank rotates at constant angular velocity, slider position oscillates approximately sinusoidally with second-harmonic distortion. Stroke = 2 × crank radius. Compression-stroke and expansion-stroke kinematics drive engine timing. Inverse mechanism (slider-crank) drives compressors, pumps, sewing machines. Inertia forces require careful balancing.
- InputsRotation OR translation
- ComponentsCrank, connecting rod, slider
- Stroke2 × crank radius
- Engine ratioRod length / crank radius (3:1 to 4:1)
- Positionx ≈ r·cos(θ) + r²/(4l)·cos(2θ)
- UseEngines, pumps, compressors
Interactive visualization
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Why crank-sliders matter
- Internal combustion engines. Universal piston-crank arrangement.
- Compressors. Reciprocating air, refrigeration.
- Steam engines. Historical foundation of industrial revolution.
- Pumps. Reciprocating piston pumps for high pressure.
- Sewing machines. Needle drive.
- Punch presses. Convert flywheel inertia to stamping force.
- Pneumatic tools. Hammer drills, jackhammers.
Common misconceptions
- Piston motion is sinusoidal. Second-harmonic distortion always present.
- Long rod is always better. Tradeoffs with engine height and weight.
- Inertia self-balances. Most arrangements need explicit counterweights.
- Stroke = crank length. Stroke = 2 × crank radius.
- Side load is negligible. Causes major piston/cylinder wear.
- Power = piston × pressure only. Friction losses substantial at high RPM.
Frequently asked questions
How does a crank-slider work?
A crank arm (length r) rotates about a fixed pivot. The end of the crank connects to a connecting rod (length l) whose other end joins a slider constrained to move in a straight line. As the crank rotates, the slider moves back and forth. The instantaneous geometry — angle, position, velocity — is fully determined by crank angle.
What's the position equation?
For crank angle θ measured from the slider's away position, slider position x = r·cos(θ) + sqrt(l² − r²·sin²(θ)). For small r/l ratios, this approximates x ≈ r·cos(θ) + r²/(4l)·cos(2θ). The first term is the fundamental sinusoid; the second is the second-harmonic distortion that creates uneven motion characteristic of pistons.
Why isn't piston motion sinusoidal?
Because the connecting rod has finite length. If the rod were infinitely long, slider motion would be pure sinusoid (simple harmonic motion). Real rods (l/r ≈ 3 to 4) introduce the second-harmonic term — the piston spends slightly more time near top dead center than bottom dead center. This affects valve timing and combustion design.
What's TDC and BDC?
Top Dead Center: piston at the highest point, crank at 0°. Bottom Dead Center: piston at the lowest point, crank at 180°. Both positions have zero piston velocity but maximum acceleration. Valve timing references these positions — intake valve opens before TDC, exhaust valve closes after TDC for overlap. Critical reference points in engine design.
How are inertia forces balanced?
Reciprocating mass creates an inertia force F = mω²r·cos(θ) − mω²r²/l·cos(2θ). The first-order force can be balanced by counterweights on the crankshaft. The second-order (second-harmonic) force is harder — it requires balance shafts spinning at twice crank speed. Inline-4 engines have inherent second-order imbalance; flat-six and inline-6 engines balance naturally.
Slider-crank vs crank-slider?
Same mechanism, different actuator. Crank-slider: crank drives slider (engine driving piston pump). Slider-crank: slider drives crank (piston driving crankshaft). Engines do both in sequence — combustion pushes piston, piston turns crank during expansion stroke; crank pushes piston during compression. Both names describe the same four-bar topology.
What about side load on the piston?
The connecting rod transmits force at an angle to the cylinder axis, producing a transverse force on the piston that pushes it against one side of the cylinder. This causes wear, friction, and noise. Piston design (offset wrist pin, shaped skirt) and cylinder honing manage these effects. Some engines use crosshead designs to eliminate piston side loads entirely.