# Grashof’s Law

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°.

Grashof’s condition for double crank mechanism: s+l > p+ q

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

Grashof’s condition for double crank mechanism: s+l > p+ q

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°.

Grashof’s condition for double crank mechanism: s+l < p+ q

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’.

Grashof’s condition for parallel linkage mechanism: s+l = p+ q

Image source: Wikimedia (Salix alba)

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

Manish Aggarwal Mar 13, 2017 8:39 am Reply
• The video has been updated for better voice quality. Here is the link to the updated video:
https://youtu.be/38vIDigJo48

Manish Aggarwal Jan 5, 2018 10:18 pm Reply
• 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.

RK Feb 5, 2018 11:18 am Reply
• Check the notation, for every mechanism different figure is considered.

Vinodh Reddy Chennu Mar 13, 2018 11:12 am Reply
• Yes, it’s a mistake.

T Jan 12, 2020 1:44 am Reply

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