Grubler’s criterion

Grubler’s criterion

If we apply the Kutzbach criterion to planer mechanism, then equation of Kutzbach criterion will be modified and that modified equation is known as Grubler‟s Criterion for planer mechanism.

Therefore in planer mechanism if we consider the links having 1 to 3 DOF, the total number of degree of freedom of the mechanism considering all restraints will becomes,

The above equation is known as Grubler’s criterion for planer mechanism.

Sometimes all the above empirical relations can give incorrect results, e.g. fig (a) has 5 links, 6 turning pairs and 2 loops. Thus, it is a structure with zero degree of freedom.

However, if the links are arranged in such a way as shown in fog. (b), a double parallelogram linkage with one degree of freedom is obtained. 

This is due to the reason that the lengths of links or other dimensional properties are not considered in these empirical relations.

Sometimes a system may have one or more link which does not introduce any extra constraint. Such links are known as redundant links and should not be counted to find the degree of freedom. For example fig. (B) has 5 links, but the function of the mechanism is not affected even if any one of the links 2, 4 and 5 are removed. 

Thus, the effective number of links in this case is 4 with 4 turning pairs, and thus 1 degree of freedom.

In case of a mechanism possessing some redundant degree of freedom, the effective degree of freedom is given by,

F = 3 (N – 1) – 2 P1 – 1P2 – Fr

Where Fr = no. of redundant degrees of freedom

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