In Mechanisms and Machines Theory we were introduced to Assur groups and structural analysis where a mechanism is subdivised into elementary Assur groups of different classes. But what is really the practical use of it?
Things have to be assembled. Assur group gives you a catalog of possible ways to make a rigid assembly out of joints. Each joint in this case represents a connection that will be assembled later, or locked down in case of foldable structures meant for reuse.
Being 0 degrees of freedom means that analysis of these is straight forward. Recognizing them will also make kinematic and dynamic analysis easier since you can replace them with a single rigid body.
Since assur groups can be predicted in a organized manner nothing stops you from generating a very big catalogue of these. Allowing you to systematically search for new solutions for the task at hand.