Mechanical & Aerospace

Four-Bar Linkage Lab

The four-bar is the building block of mechanisms — wiper arms, oil pumps, suspension. Drag the ground, crank, coupler and rocker lengths and the mechanism animates, solved by loop closure at every crank angle. Grashof's law (shortest + longest ≤ the other two) decides whether the crank can rotate a full 360° (a crank-rocker) or only rock back and forth, and the dashed line is the coupler curve traced by a point on the floating link.

Crank-rocker

Mechanism

Full 360°

Crank rotates?

Yes

Grashof S+L≤P+Q

The method, with your numbers

Grashof's law

  1. 1

    Rank the four links

    S = shortest, L = longest, P and Q = the middle pair

    S = 1 (crank), P = 2.5 (rocker), Q = 3 (ground), L = 3 (coupler)

    Grashof's law only cares about the extremes versus the middle pair — and only the ratios matter, so the units are irrelevant.

  2. 2

    Apply Grashof's law

    S + L ≤ P + Q ?

    S + L = 1 + 3 = 4 vs P + Q = 2.5 + 3 = 5.5 → satisfied (Grashof)

    If the inequality holds, at least one link can revolve fully relative to the others; if not, everything can only rock.

  3. 3

    Classify by the shortest link

    shortest = crank or rocker → crank-rocker · ground → double-crank · coupler → double-rocker

    shortest = crank (1) → Crank-rocker — crank: Full 360°

    The crank is the shortest link, so it spins full circle while the rocker oscillates — the windscreen-wiper layout.

  4. 4

    Close the loop (what the canvas solves each frame)

    P = (crank·cos θ₂, crank·sin θ₂); rocker pin = circle(P, coupler) ∩ circle(O₄, rocker)

    intersect circle(P, 3) with circle(O₄, 2.5) — O₂O₄ = 3, crank = 1

    Two circles meet at two points; the sim always keeps the same branch so the linkage never flips. No intersection means the loop can't close at that crank angle.

Drag any control above — every number here recalculates. Want this method for any problem? Step Sheets →

Ground3
Crank1
Coupler3
Rocker2.5

Grashof's law (S + L ≤ P + Q) decides whether the crank can spin all the way round. Make the crank the shortest link and you get a crank-rocker — the basis of windscreen wipers and oil pumps; the dashed trail is the coupler curve.

How to use this simulation

The four-bar is the building block of mechanisms — wiper arms, oil pumps, suspension. Drag the ground, crank, coupler and rocker lengths and the mechanism animates, solved by loop closure at every crank angle. Grashof's law (shortest + longest ≤ the other two) decides whether the crank can rotate a full 360° (a crank-rocker) or only rock back and forth, and the dashed line is the coupler curve traced by a point on the floating link.

Everything runs in your browser — no sign-up, no download. Change a value and the result updates instantly, so you can build a feel for how each input shapes the outcome. It pairs with Crameleon's practice exams and step sheets when you want to go from intuition to working the problems.