Inversions of four bar mechanism

Prerequisite : Classification of Four bar mechanism and Harding's notation

Inversions of the mechanism is obtained when the the fixed link is changed to a free link and another link is fixed. A single four bar mechanism can give different type of motion based on the link which is fixed.

Harding's notation for four bar mechanism

Inversions of class 1 four bar mechanism

1. When link 'b' is fixed : Crank Rocker or Crank Lever mechanism, in the the shortest link rotates 360 deg where as the other link oscillates
2. When link 'a' is fixed : Crank Rocker or Crank Lever mechanism, in the the shortest link rotates 360 deg where as the other link oscillates
3. When link 'd' is fixed : Drag link or Double crank mechanism in which the links 'a' and 'b' undergoes complete 360 deg motion
4. When link 'c' is fixed : Double rocker or Double lever mechanism in which no link makes a complete rotation about its joints. In such case it is similar to class 2 four bar mechanisms

Inversions of class 2 four bar mechanism

Since in class 2 mechanisms, no link can complete complete complete rotation, all the mechanism are double rocker or double lever mechanisms.

Please apologize for not adding the pictures of these inversions. you can find these pictures on "Kinematics and Linkage Design" by Allen S Hall (Fig 3.4)

Classification of four bar mechanism

Four bar mechanism, can be classified into two types.

• Class 1 four bar mechanism and
• Class 2 four bar mechanism

Lets the dimensions and name of the four links of the mechanism be as shown in the figure below.

Notation used in the discussion of classification of 4-bar mechanism

Here,
'a' denotes the largest link and its dimension;
'b' denotes the link opposite to 'a';
'c' is the largest among the two remaining links;
'd' denotes the link opposite to 'c'

Now, we can write,
a > b and c > d
Also (a+b) > (c+d)

The above established notation was done by Harding. Once we have understood this notation, we can classify any four bar mechanism as follows;

• Class 1 Mechanism : If the shortest of the four link can makes a complete 360 deg rotation, and all other links just oscillates, then that type of mechanism is called class 1 mechanism. Criteria for a mechanism to be class 1 is (a-b) < (c-d).
• Class 2 Mechanism : In this class, link dimensions are such that not any of the four links can makes a complete  360 deg rotation, criteria of mechanism to be class 2 is (a-b) > (c-d).

Various inversion of class 1 and class 2 mechanism can obtained which is discussed here