What is a slider-crank mechanism?

A slider-crank mechanism converts rotary motion into reciprocating linear motion (or vice versa). It consists of a rotating crank, a connecting rod, and a sliding piston. It is the fundamental mechanism in internal combustion engines, compressors, and pumps.

How is piston position calculated?

The exact formula is x = r·cos(θ) + √(l² − r²·sin²(θ)), where r is crank radius, l is connecting rod length, and θ is crank angle. The result gives the distance from crank center to piston pin.

What is the lambda (λ) ratio?

Lambda (λ = r/l) is the crank-to-rod ratio. Typical values range from 0.25 to 0.35 for automotive engines. A higher λ increases the deviation from simple harmonic motion and raises peak acceleration.

How is piston velocity computed?

Piston velocity is v = r·ω·(sin(θ) + λ·sin(2θ)/2), using the approximate binomial expansion. The exact form requires differentiating the position formula, which this tool also computes.

What are TDC and BDC?

Top Dead Center (TDC) is at θ = 0° where the piston is furthest from the crank center. Bottom Dead Center (BDC) is at θ = 180° where the piston is closest. Velocity is zero at both dead centers.

Crank Mechanism Calculator

Name: Crank Mechanism Calculator
Availability: InStock
Author: Nham Vu

Enter crank radius, connecting rod length, and crank angle to instantly compute piston position, velocity, and acceleration.

Mechanism Parameters

Crank Radius (r)

Connecting Rod Length (l)

λ = r/l = 0.333

Crank Speed

RPM

= 104.72 rad/s

Crank Angle (θ)

Mechanism Diagram

Piston Position

—

mm from crank center

Piston Velocity

—

m/s

Piston Acceleration

—

m/s²

Parameter	Value	Unit
Enter parameters above

Summary

Enter crank radius, connecting rod length, and crank angle to instantly compute piston position, velocity, and acceleration.

How it works

Enter the crank radius (r) — the distance from crank center to crank pin.
Enter the connecting rod length (l) — the distance from crank pin to piston pin.
Set the crank angular velocity (omega) in RPM or rad/s.
Drag the angle slider or type a value to set the current crank angle.
Results for piston position, velocity, and acceleration update instantly.
Use the animated diagram to visualize the mechanism at any angle.

Use cases

Analyze reciprocating engine piston kinematics during design.
Validate textbook slider-crank problems in mechanical engineering courses.
Determine peak piston velocity and acceleration for stress analysis.
Visualize how rod-to-crank ratio affects motion characteristics.
Compare approximate (first-order) vs. exact piston position formulas.
Check dead-center positions (TDC and BDC) for a given geometry.

Frequently Asked Questions

Last updated: 2026-06-10 · Reviewed by Nham Vu