Engineering lab · Interactive tool
Four-Bar Linkage Explorer
Explore link proportions, open and crossed assembly branches, position closure, and output geometry for a planar four-bar mechanism.
Planar mechanism position closure
Live calculationr₂ + r₃ = r₁ + r₄Four-bar results updated. The open branch closes. Output angle 75.52 degrees. Transmission angle 51.25 degrees.
Model, assumptions, and a reproducible reference case
|B − A| = coupler length; |B − O₄| = output length
Reference inputs
Ground 100 mm; input 50 mm; coupler 100 mm; output 50 mm; input angle 90°; open branch.
- Expected output angle
- 90.000 °
- Calculated by this tool
- 90.000 °
A parallelogram reference closes at B = (100, 50) mm. Length classification alone does not guarantee full input rotation in a chosen inversion.
Check the material basis, load cases, and applicable design criteria before using a result. Warning thresholds are prompts for review, not acceptance criteria.
Position closure is the first gate
The live diagram solves the intersection of the coupler and output-link circles at the selected input angle. Grashof classification describes the link-length set; it does not guarantee unrestricted rotation for every grounded-link choice or a useful mechanism.
A complete mechanism design must also control branch and circuit behavior, transmission angle, singularities, packaging, joint reactions, bearing life, tolerance sensitivity, stiffness, inertia, and interference through the intended motion.
Before committing a linkage
- Sweep the entire required input range on the intended assembly branch
- Confirm no order, branch, or circuit defect enters the operating range
- Check minimum transmission angle and mechanical advantage
- Model joint clearance and dimensional variation
- Evaluate collisions, hard stops, and actuator packaging
- Resolve dynamic loads, balance, fatigue, wear, and lubrication
Direct conversation
Let’s work through the engineering.
Tell me what you are building, the challenge, and the timing. I will respond directly.
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