The Grubler’s criterion applies to mechanisms with only single degree of freedom joints where the overall movability of the mechanism is unity.

When the kinematic pairs are coupled in such a way that the last link is joined to the first link to transmit definite motion (i.e. completely or successfully constrained motion), it is called a kinematic chain. In other words, a kinematic chain may be defined as a combination of kinematic pairs, joined in such a way that each link forms a part of two pairs and the relative motion between the links or elements is completely or successfully constrained.

When the two elements of a pair are connected in such a way that one element (with spherical shape) turns or swivels about the other fixed element, the pair formed is called a spherical pair, and ball and socket joint are such pairs.

When the two elements of a pair are connected in such a way that one element can turn about the other by screw threads, the pair is known as screw pair. The lead screw of a lathe with nut, and bolt with a nut are examples of a screw pair.

in a reciprocating steam engine, piston, piston rod and crosshead constitute one link ; connecting rod with big and small end bearings constitute a second link ; crank, crank shaft and flywheel a third link and the cylinder, engine frame and main bearings a fourth link.

When the two elements of a pair are connected together mechanically in such a way that only required kind of relative motion occurs, it is then known as self closed pair. The lower pairs are self closed pair and the motion of cam and follower is relative to each other.

In general, when n number of links are joined at the same connection, the joint is equivalent to (n – 1) binary joints.

A kinematic chain which consists of two turning pairs and two sliding pairs is known as double slider crank chain and elliptical trammels are such pairs.

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