# Grashof’s Law

The Grashof’s law states that for a four-bar linkage system, 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 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 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