Slider-crank mechanism
Displacement and velocity, plus crank torque, connecting rod force and side thrust on the guide.
From the crank radius, connecting rod length and crank angle, the tool gives the displacement and velocity of the slider, and — for a given slider force — the crank torque, the connecting rod force and the side thrust on the guide.
Press "Rotate" and the crank angle sweeps continuously through 0 to 360 degrees, so you can see how velocity and torque change around top and bottom dead centre. Useful for first-pass work on reciprocating and press mechanisms.
| Slider position (from the crank centre) | –mm |
|---|---|
| Displacement from top dead centre | –mm |
| Full stroke 2r | –mm |
| Connecting rod swing angle φ | –deg |
| Side thrust (lateral force on the guide) | –N |
| Angular velocity ω | –rad/s |
Why the l/r ratio matters
The ratio of the connecting rod length l to the crank radius r largely decides the character of this mechanism. The larger l/r is, the closer the rod stays to horizontal and the closer the slider motion comes to simple harmonic. The smaller it is, the more the rod swings, and the more asymmetric the velocity becomes between the forward and return strokes.
Where this actually bites is side thrust. When the rod is inclined by an angle φ, a lateral force of F·tanφ presses the slider against its guide, for a slider force F. The maximum swing is asin(r/l), so at l/r = 2 that is about 30 degrees, and tan30° ≈ 0.58 — a lateral force close to 60 per cent of the slider force on the guide. Wear and seizure of the sliding surface come from here.
As a guide, keep l/r between 3 and 5. Longer is better if you have the room, but you need r + l of installation space. This tool warns below 2.5.
Why crank torque goes to zero at dead centre
The torque transmitted to the crank from a slider force F is T = F·r·sin(θ+φ)/cosφ. At top dead centre (θ = 0°) and bottom dead centre (θ = 180°), φ is also zero, so sin(θ+φ) vanishes and no amount of slider force will turn the crank. That is the dead point.
Driving from the crank side instead, the slider velocity is zero at dead centre. For applications such as a press, where you want a large force at bottom dead centre, that property works in your favour. Torque peaks near θ ≈ 90°, though the influence of φ means it is not exactly symmetric.
Press "Rotate" to turn the crank continuously and follow how torque and velocity vary with θ. The difference between the forward and return strokes shows up directly.
How this is calculated
The slider position uses the closed-form solution x = r·cosθ + √(l² − r²sin²θ). It is not an approximation, so accuracy does not fall away at small l/r. The velocity comes from differentiating that analytically as v = ω·dx/dθ.
What is treated here is statics (equilibrium) only. The inertia of the reciprocating parts, the moment of inertia of the connecting rod and bearing friction are not included. In a high-speed mechanism the inertia forces can exceed the slider force, and a separate dynamic study is then needed.
This is a simplified calculation intended for first-pass sizing. Stress concentration, buckling, fatigue, welds, dynamic loading and temperature effects are not included. Yield, proof and allowable stress figures are representative guide values and are not guaranteed to match the standards themselves. Always carry out your own verification before building and manufacturing real hardware. We accept no liability for loss arising from the results of this tool.
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