# Mobility / Grashof's Condition and Barker's Classification

## Mobility of Mechanism

Degrees of freedom for planar linkages joined with common joints can be calculated through Gruebler’s equation.

Gruebler’s equation is given by the formula:

> M = 3(L-1) - 2J<sub>1</sub> - J<sub>2</sub>

where:
- M is degree of freedom or Mobility
- L is number of links
- J<sub>1</sub> is number of full joints
- J<sub>2</sub> is number of half joints


![image.png](https://cdn.hashnode.com/res/hashnode/image/upload/v1647244176862/dSsKALnhE.png)



## Grashof Condition

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.

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.


![image.png](https://cdn.hashnode.com/res/hashnode/image/upload/v1647708655845/_Utk_bIFy.png)

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



## Barker's Classification

![image.png](https://cdn.hashnode.com/res/hashnode/image/upload/v1647703708201/V3QTFbwLt.png)


## Try Yourself

%%[mobility-grashof-barker]