When the two elements of a pair are connected in such a way that one can only turn or revolve about a fixed axis of another link, the pair is known as turning pair. A shaft with collars at both ends fitted into a circular hole, the crankshaft in a journal bearing in an engine, lathe spindle supported in head stock, cycle wheels turning over their axles etc. are the examples of a turning pair.

If each link is assumed to form two pairs with two adjacent links, then the relation between the number of pairs ( p ) forming a kinematic chain and the number of links ( l ) may be expressed in the form of an equation :

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

The piston and cylinder in a steam engine form a pair and the motion of the piston is limited to a definite direction (i.e. it will only reciprocate) relative to the cylinder irrespective of the direction of motion of the crank.

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.

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.

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A very important consideration in designing a mechanism is to ensure that the input crank makes a complete revolution relative to the other links. The mechanism in which no link makes a complete revolution will not be useful. In a four bar chain, one of the links, in particular the shortest link, will make a complete revolution relative to the other three links, if it satisfies the Grashof ’s law. Such a link is known as crank or driver.

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

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