When four links are joined at the same connection, the joint is called a quaternary joint. It is equivalent to three binary joints.

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When n = 0, then the mechanism forms a structure and no relative motion between the links is possible.

If the left hand side is greater than the right hand side, therefore it is not a kinematic chain and hence no relative motion is possible. Such type of chain is called locked chain and forms a rigid frame or structure which is used in bridges and trusses.

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 one of the links of a kinematic chain is fixed, the chain is known as mechanism. It may be used for transmitting or transforming motion e.g. engine indicators, typewriter etc.

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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When the two elements of a pair have a line or point contact when relative motion takes place and the motion between the two elements is partly turning and partly sliding, and in mesh the gears have a point contact.