How It Works - Four-Bar Linkage Theory
What is a Four-Bar Linkage?
A four-bar linkage is the simplest closed-chain mechanism with four rigid links connected by four revolute joints. It converts rotary motion to various output motions and is fundamental to mechanical design.
- Link a (Crank): Input link - typically connected to a motor
- Link b (Coupler): Floating link connecting crank to rocker
- Link c (Rocker): Output link - provides the desired motion
- Link d (Ground): Fixed frame - the reference link
Grashof Criterion
The Grashof condition determines if any link can make a complete 360-degree rotation:
S + L <= P + Q
S = shortest, L = longest, P & Q = other two links
- S + L < P + Q: Grashof linkage - at least one link rotates fully
- S + L = P + Q: Change-point - special configurations possible
- S + L > P + Q: Non-Grashof - no link rotates fully (triple-rocker)
Linkage Classifications
- Crank-Rocker: Shortest link is crank, one full rotation possible
- Double-Crank (Drag Link): Shortest link is ground, both pivoted links rotate fully
- Double-Rocker: Shortest is coupler, neither pivoted link rotates fully (but coupler does)
- Triple-Rocker: Non-Grashof, no link can fully rotate
Transmission Angle
The angle between the coupler and output link determines force transmission efficiency:
- Optimal: 90 degrees (maximum force transfer)
- Acceptable: 40-140 degrees
- Poor: Below 30 degrees or above 150 degrees (toggle position)
Design Applications
- Windshield wipers (crank-rocker)
- Sewing machines (crank-slider variant)
- Robotic arms and manipulators
- Automotive suspensions
- Engine mechanisms (slider-crank)
Four-Bar Linkage Anatomy & Grashof Classification
Quick Select - Common Linkage Types
Four-Bar Linkage Calculator
Analyze four-bar linkage mechanisms including Grashof classification, position analysis, and transmission angle calculations.
Link naming: a = crank (input), b = coupler, c = rocker (output), d = ground (frame)
RPM (for velocity analysis)
Grashof Linkage
Calculating...
Live Linkage Position
Grashof Analysis
Linkage Type
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Classification
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Shortest Link
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Longest Link
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S + L
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P + Q
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Position Analysis
Coupler Angle (theta3)
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Rocker Angle (theta4)
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Transmission Angle (mu)
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Mechanical Advantage
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Coupler Angular Velocity
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Rocker Angular Velocity
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Design Guidelines
| Parameter | Recommendation |
|---|---|
| Transmission angle | 40 deg to 140 deg ideal |
| Min transmission angle | > 30 deg for smooth motion |
| Link ratio (max/min) | < 3:1 for compact design |
| Mechanical advantage | Maximized near 90 deg transmission |