The following animation illustrates the crank mechanism – the fundamental linkage for converting rotational motion into linear motion. Crank angle, connecting rod inclination, and piston position are visualized in real time.
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Animation Description
The animation shows a crank mechanism consisting of a crank, connecting rod, and piston. The play button starts continuous rotation, causing the crank to rotate while the piston reciprocates within the cylinder.
The piston position results from the superposition of the crank radius and connecting rod geometry:
\[ x = r \cdot \cos(\varphi) + \sqrt{l^2 – r^2 \cdot \sin^2(\varphi)} \]
Where:
- \( r \) – crank radius
- \( l \) – connecting rod length
- \( \varphi \) – crank angle
The piston stroke equals twice the crank radius: \( H = 2r \).
Interactive Controls
The following parameters can be adjusted using the sliders:
- Angle (0–360°): Crank angle for manual positioning
- Radius (0–300): Crank radius, determines the piston stroke
- Connecting Rod Length (100–500): Length of the connecting rod
The play/pause button starts or stops the continuous rotation of the crank.
Physical Background
The crank mechanism converts uniform rotational motion into oscillating linear motion – or vice versa. The piston does not move sinusoidally but with a characteristic deviation that depends on the rod ratio \( \lambda = r/l \). The shorter the connecting rod relative to the crank radius, the more the piston motion deviates from a pure sinusoidal form.
The connecting rod angle changes continuously during one revolution, resulting in non-uniform piston velocity. At crank angles of 90° and 270°, the connecting rod angle reaches its maximum values.
Practical Applications
- Internal combustion engines: Converting piston motion into rotational motion of the crankshaft
- Reciprocating pumps: Driving pump pistons for liquids and gases
- Compressors: Compressing gases through oscillating piston motion
- Steam engines: Historical application for converting steam pressure into mechanical work