How to use the Four-Bar Linkage Grashof Checker
- 1. Enter the linksFrame, input crank, coupler and output link lengths.
- 2. Set an input angleThe sketch and the coupler and rocker angles are drawn for this θ2.
- 3. Read the typeGrashof result, linkage type, transmission angle and quick-return ratio.
Grashof's law
Let s be the shortest link, l the longest, and p and q the other two. If s + l ≤ p + q, at least one link can turn a full circle (a Grashof linkage). If s + l > p + q, no link can turn fully, and it is a triple rocker.
- Shortest link is the frame: double crank (drag link).
- Shortest link is next to the frame: crank-rocker.
- Shortest link is the coupler: double rocker.
- s + l = p + q: change-point linkage, which can lock or flip at the in-line position.
The transmission angle μ is the angle between the coupler and the output link: cos μ = (b² + c² − AO4²) / (2bc). Keep it between about 40° and 140° for smooth force transfer.
Worked example and exam tips
Frame 100, crank 40, coupler 120, rocker 80. s + l = 40 + 120 = 160 and p + q = 100 + 80 = 180, so it is Grashof. The shortest link is the crank, next to the frame, so this is a crank-rocker. The rocker swings between the two toggle positions, and because the forward and return strokes take different crank angles, the time ratio is above 1.
- Fixing a different link (an inversion) changes the type but not the Grashof result.
- Check that the linkage can be built: the longest link must be shorter than the other three added together.
- Quick-return time ratio = (180° + α)/(180° − α), where α is the crank angle between the two toggle positions.
Frequently asked questions
What is the Grashof condition?
For a four-bar chain, s + l ≤ p + q. When it holds, the shortest link can rotate fully relative to the others.
What are inversions of a four-bar chain?
Different mechanisms you get by fixing different links of the same chain. A Grashof chain gives crank-rocker, double crank or double rocker depending on which link is fixed.
Why does the transmission angle matter?
When μ is close to 0° or 180°, almost none of the coupler force turns the output link, so the mechanism jams or wears quickly.
Is this calculator free?
Yes. You fill in a short form once to see your result, and the other Uncodemy tools then open without it. Every calculation runs in your browser and nothing you type is sent anywhere.