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

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.

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.

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.

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 :

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.

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When the two elements of a pair are not connected mechanically but are kept in contact by the action of external forces, the pair is said to be a force-closed pair. The cam and follower is an example of force closed pair, as it is kept in contact by the forces exerted by spring and gravity.

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.