Grublers Criterion:

Assume 'n' be the number of links in a mechanism out of which one link is set. If these (n - 1) links execute plane motion without a connection, they shall have 3 (n - 1) degrees of freedom since each moving link contain three degrees of freedom as described in Section. If these links are linked through hinges, each of links loses two degrees of freedom. If these links are links through 'j' number of hinges, the number of degrees of freedom of the mechanism may be described as follows because each of hinge results in loss of two degrees of freedom:

                                           F = 3 (n - 1) - 2 j  . . . (2.1)

The joints or hinges 'j' are simple hinges in Eq. (2.1) because each one of them connects just two links. If mechanism involves higher order hinges that connect more than two links the equivalent number of simple hinges 'j' may be resolved by the following equation :

                  j =  j₁  + 2 j₂ + 3 j₃  + 4 j₄  + ... + ij_i                    . . . (2.2)

   Here number of hinges j_i connect (i + 1) links.

It means that each hinge connecting 3 links is equal to 2 simple hinges. If the mechanism contains 'h' number of higher pairs also, the Equation (2.1) may be modified as follows:

                  F = 3 (n - 1) - 2 j - h         . . . (2.3)

If F = 0 in Equation (2.3), the mechanism contain no movability and this is a structure. If F = 1, the mechanism has completely constrained motion and this represents a functioning mechanism which contain practical utility. All the working mechanisms contain single degree of freedom.