The Grashof’s law states that for a four-bar linkage system, the sum of the shortest and longest link of a planar quadrilateral linkage is less than or equal to the sum of the remaining two links, then the shortest link can rotate fully with respect to a neighboring link.

Consider a four-bar-linkage. Denote the smallest link by S, the longest link by L and the & other two links by P and Q.

If the Grashof’s Law condition is satisfied i.e S+L ≤ P+Q,

then depending on whether shortest link ‘S’ is connected to the ground by one end, two ends, or no end there are 3 possible mechanisms. They are:

**1. Double crank mechanism**

In double crank mechanism, the shortest link ‘S’ is a ground link. Both input crank and output crank rotate at 360°.

Let:

*‘s’*= length of shortest link,

*‘l’*= length of longest link,

*‘p’*= length of one remaining link and

*‘q’*= length of other remaining link.

**2. Double-rocker mechanism**

In double-rocker mechanism, the shortest link ‘S’ is coupler link. The coupler link can rotate 360°.

**3. Crank and rocker mechanism**

In crank and rocker mechanism, the shortest link “S’ is input crank or output crank. Input crank or output crank rotates 360°.

**4. Parallel linkage mechanism**

the parallel linkage mechanism is a special case of Grashof’s criteria, where the sum of the shortest link ‘S’ and longest link ‘L’ of a planar quadrilateral linkage is less than or equal to the sum of the remaining two links ‘P+Q’.

Image source: Wikimedia (Salix alba)

## All Comments

Very Nice explanation. In addition this video can also be included within post:

The video has been updated for better voice quality. Here is the link to the updated video:

https://youtu.be/38vIDigJo48

I’m confused. In number 2, it states there “Grashof’s condition for double crank mechanism: s+l > p+q” shouldn’t it be a double-rocker and also s+l < p+q?

I would like to clarify if I understood it, thanks.

Check the notation, for every mechanism different figure is considered.

Yes, it’s a mistake.