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 calculation

01Link lengths

02Assembly position

Length criterionGrashof
Live four-bar position solutionGround, input, coupler, and output links shown at the selected input angle and assembly branch.O₂AO₄BPOSITION CLOSURE: VALID
Vector-loop closurer₂ + r₃ = r₁ + r₄

Four-bar results updated. The open branch closes. Output angle 75.52 degrees. Transmission angle 51.25 degrees.

Assembly statusClosedopen branch
Coupler angle24.27°global orientation
Output angle75.52°global orientation
Transmission angle51.25°coupler-to-output angle
Revision1.2
AuthorJared Maffucci
Last technical review23 July 2026
Input guardrailsFinite values; nonnegative magnitudes; physical geometry and material domains enforced
UsePreliminary engineering judgment only
Variable definitions
  • a: input link
  • b: coupler
  • c: output link
  • d: ground link
  • θ₂: input angle
Hand-verified examples
  • Reference length set: Grashof classification
  • Open and crossed assembly branches both close
Change log · revision 1.2

Added visible variables, two verification examples, and an experience connection. Calculation method is unchanged.

Related engineering capability

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

Review the product, the available evidence, and the decision blocking progress.

Send a concise, non-confidential brief. You will work directly with Jared from the first review through final handoff.

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