# Grashof’s Law – Condition And Different Mechanism

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

In a four bar chain there are four turning pairs and no sliding pairs.

Let denote the smallest link of four bar linkage with S and the longest link by L and the other two links by P and Q.

The necessary condition to satisfy Grashof’s Law is :
S + L ≤ P + Q

This condition is divided into two cases :-
1) S + L < P + Q
2) S + L = P + Q

### 1) Now lets see the first case i.e S + L < P + Q

By fixing different links one at a time this case produces three mechanisms . These mechanisms are :-
i) Double Crank Mechanism
ii) Double Rocker Mechanism
iii) Crank and Rocker Mechanism

i) Double Crank Mechanism :-
It is also known as Crank Crank Mechanism or Drag Link Mechanism.
In double crank mechanism, the shortest link which is S is fixed or grounded. In this mechanism, both the links pivoted to the fixed link can rotate 360 degrees.

ii) Double Rocker Mechanism :-
In double rocker mechanism, the link opposite to shortest link is fixed or grounded. In this mechanism the shortest link can rotate 360 degrees. Shortest link is called coupler. Both the links pivoted to the fixed links can oscillate. These two links are called rockers.

iii) Crank and Rocker Mechanism :-
In Crank and Rocker Mechanism , the link adjacent to shortest link is fixed or grounded.In this mechanism, shortest link rotates and the other link pivoted to the the fixed link oscillates.

### 2) S + L = P + Q :-

In such kinematic chain , the links become collinear atleast once per revolution of input crank.
This case is further divided into two cases :-
Case 1 :- The length of all links are distinct
In this case, the inversions obtained are same as in the case S + L < P + Q. which are :- double crank, double rocker and crank rocker.

Case 2 :- The length of any two link are same
If the length of any two links are same, then the length of remaining two links will also be same due to equation S + L < P + Q.

In such case, two linkages are possible base on placement of links:-

a) Parallelogram Linkage :- In this linkage, links of equal lengths are placed opposite to each other.

b) Deltoid Linkage :- In this linkage, links of equal lengths are placed adjacent to each other.

In both the cases , the inversions obtained are either crank rocker or double crank mechanism.

Both these linkage suffer change point condition at the time when the links become collinear.
In change point condition , the motion of output crank become unpredictable. It can go any of the two ways. Based on the motion of the output crank at change point condition, the inversion is crank rocker or double crank .

Now lets see the case when the sum of lengths of shortest and longest link is greater than the sum of lengths of remaining two links.
i.e S + L > P + Q
In this case, no link can make a complete revolution no matter which of the four link is fixed. So this case has only one inversion and that is
Triple Rocker Mechanism :- In this mechanism no link will be able to make a complete revolution . All the three links other than the fixed link will oscillate. These three links are called rockers and hence the mechanism is called triple rocker mechanism.