Kinematics & Dynamics
4-Bar Linkage Synthesizer
Synthesize and analyze four-bar linkages. Model planar mechanisms, compute coupler curves, map input/output transmission curves, and check Grashof boundary conditions.
Type
Crank-Rocker
Grashof classification
Status
Active
Valid geometry
Output
CSV
Export ready
Parameters
Mechanism Preset
Crank angle rotation
Kinematic Formulations
Grashof Condition
s + l ≤ p + q
Freudenstein Equation
K₁ cos(θ₄) - K₂ cos(θ₂) + K₃ = cos(θ₂ - θ₄)
Link Constants
K₁ = d/a, K₂ = d/c, K₃ = (a² - b² + c² + d²)/(2ac)
s = shortest link, l = longest link, p, q = remaining links.
If the Grashof condition is met, at least one link can rotate fully (360°).
In Crank-Rocker, the crank (L2) rotates fully, making it ideal for motor inputs.
Linkage Kinematics Diagram
Crank Angle (θ₂)
0.0°
Rocker Angle (θ₄)
248.0°
Rocker Amplitude
60.5°
Linkage Type
Grashof
Transmission Curve (θ₄ vs θ₂)
Kinematic Data Samples
| Crank Angle θ₂ (°) | Rocker Angle θ₄ (°) | Coupler Cx (mm) | Coupler Cy (mm) |
|---|---|---|---|
| 0° | 248° | 183.8 | -74.0 |
| 20° | 234.1° | 162.4 | -54.2 |
| 40° | 222.1° | 138.7 | -28.7 |
| 60° | 213.6° | 116.0 | -3.7 |
| 80° | 207.9° | 93.3 | 16.4 |
| 100° | 204.4° | 70.5 | 29.3 |
| 120° | 202.6° | 48.5 | 33.7 |
| 140° | 202.5° | 29.6 | 29.3 |
| 160° | 204.5° | 16.4 | 16.1 |
| 180° | 209° | 11.7 | -4.7 |
| 200° | 215.9° | 17.8 | -30.2 |
| 220° | 224.8° | 34.9 | -56.4 |
| 240° | 234.8° | 61.5 | -78.8 |
| 260° | 244.8° | 94.4 | -94.2 |
| 280° | 253.8° | 129.1 | -101.1 |
| 300° | 260.4° | 161.0 | -100.2 |
| 320° | 262.8° | 184.3 | -94.3 |
| 340° | 258.8° | 193.1 | -85.9 |
| 360° | 248° | 183.8 | -74.0 |