An inversion is created by grounding a different link in a kinematic chain.  There are as many inversions of a given linkage as it has links.

For example, in Grashof four bar linkage, for which the sum of the lengths of the smallest link and the largest link is less than the sum of the lengths of the other two links, we have four inversions of which three are distinct inversions.

Case 1: Link adjacent to the shortest link is fixed.

Case 1 - Crank Rocker Mechanism

The shortest link is the one which is coloured green. So, either we can fix blue link or we can fix red link.  Therefore, there are two inversions and both are crank rocker mechanisms.

Case 2: Shortest link is fixed.

Case 2 - Double Crank Mechanism

This configuration is double crank mechanism.

Case 3: Link opposite to the shortest link is fixed.

Case 3 - Double Rocker Mechanism

This configuration is double rocker mechanism.

It is not necessary that everytime you ground a different link in a kinematic chain, you will obtain a different mechanism. We saw this in case 1 of the grashof four bar linkage where we grounded the link adjacent to the shortest link. There were two ways of doing that and both ways we obtained a crank rocker mechanism.

Another example is a Triple Rocker Mechanism. All the inversions of a triple rocker mechanism are triple rocker only. Watch the video below to see the triple rocker mechanism inversions:

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Kinematic Inversion

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