How to classifed the kinematic pairs ?

When the two links or elements of machines which in contact between each other, if the relative motion between them with constrained then is known as kinematic pair.

Types of kinematic pairs :

Kinematic pair may be classified according to following consideration :

According to the type of relative motion between the elements :

Sliding pair : When the two elements of pair connected in such a way that one can only slide relative to the other , the pair is known as a sliding pair.The piston and cylinder cross head and guide of reciprocating steam engine, ram and guide in shaper, tail stock on the bed etc. are the example of sliding pair.The sliding pair has a constrained pair.

Piston and cylinder cross head and guide of reciprocating steam engine

Ram and guide in shaper

Turning pair : When the two elements of pair 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 collar both ends fitted into a circular hole,crank shaft in journal bearing in engine,lathe spindle supported in head stock ,cycle wheels turning over their axles etc. are examples of turning pair.A turning pair also has a constrained motion.

shaft with collar both ends fitted into a circular hole

cycle wheels turning over their axles

Rolling pair : When the two elements of pair connected in such a way that one can rolls over another fixed link, their the pair is known as rolling pair.

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

lead screw of a lathe with nut and bolt

Spherical pair : When the two elements of pair connected in such a way that one element turns or swivels about the other fixed element , the pair formed is known as spherical pair.The ball and socket joint , attachment of a car mirror, pen stand, are example of spherical pair.

ball and socket joint

According to the type of contact between the elements :

Lower pair : When the two elements of pair have a surface contact when relative motion takes place and the surface of one elements slides over the surface of the other , the pair formed is known as as lower pair. It will be seen that sliding pairs and screw pairs form lower pairs.

Higher pair : When the two elements of 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, then the pair is known as higher pair. A pair of friction discs, toothed gearing , belts and rope drives , ball and roller bearing and cam and follower are the examples of higher pair.

According to the type of closure between the element :

Self closed pair : When the two elements of 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 pair are self closed pair.

Forced closed pair : When the two elements of pair are not connected together mechanically. But are kept in contact of external forces , the pair is said to be a force closed pair. the cam and follower is example of force closed pair ,as it is kept in contact by the forces exerted by spring and gravity.

What is Kinematic chain ?

A kinematic chain 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 elements or links is completely constrained or successfully constrained . for example the crank shaft of an engine forms a kinematic pair with the bearing which are fixed in a pair , the connecting rod with the crank a second kinematic pair, the piston with the connecting rod forms a third pair and the crank forms a third pair and piston with the cylinder forms a fourth pair .The total combination of these links is kinematic chain.

If each link is assumed to form two pairs with 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 :

L= 2 p-4

Another relation between the number of links (L) and the number of joints(j) which constitute a kinematic chain is given by the expression :

j =3/2 L-2

In constrained condition the relation between the number of links (L) and the number of joints(j) which constitute a kinematic chain is given by the expression :

j+ h/2 =3/2 L-2