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
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
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
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
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 →
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.