KINEMATIC PAIR OR PAIR: CLASSIFICATION OF PAIRS, Lower Pairs, Higher Pair, Sliding Pair, Turning Pair, Screw Pair, Rolling Pair, Spherical pair, Closed pair, Open Pair


A kinematic pair is a connection between rigid bodies, which permits relative motion between them. When the links are supposed to be rigid in kinematics, then, there cannot be any change in the relative positions of any two chosen points on the selected link. In other words, the relative position of any two points does not change and it is treated as one link. Due to this rigidness, many complex shaped links can be replaced with simple schematic diagrams for the kinematic and synthesis analysis of mechanism.


Kinematic pairs can be classified according to

a) Type of contact between elements

b) Type of relative motion

c) Nature of constraint or Type of closure

a) Type of contact between elements

Lower Pairs: 

A pair of links having surface or area contact between the members is known as a lower pair. The surfaces in contact of the two links are similar.

Examples: Nut turning on a screw, shaft rotating in a bearing, universal joint, etc.

Nut and screw (lower pair)
Nut and screw (lower pair)

Higher Pair: 

When a pair has a point or line joint contact between the links, it is known as a higher pair. The contact surfaces of the two links are dissimilar.

Examples: Wheel rolling on a surface, cam and follower pair, tooth gears, ball and roller bearings, etc.

ball and roller bearing (higher pair)
ball and roller bearing (higher pair)

b) Type of relative motion

Sliding Pair: 

When two pairs have sliding motion relative to each other.

Examples: piston and cylinder, rectangular rod in rectangular hole.

Turning Pair: 

When one element revolves around another element it forms a turning pair.

Examples: shaft in bearing, rotating crank at crank pin.

Screw Pair: 

This is also known as helical pair. In this type of pair two mating elements have threads on it or its relative motion takes place along a helical curve.

Examples: Nut and screw pair as shown in figure, Screw jack

Rolling Pair: 

When one element is free to roll over the other one.

Examples: Ball and rolling as shown in figure, motion of wheel on flat surface

Spherical pair: 

When one element move relative to the other along a spherical surface.

Examples: Ball and socket joint


In slider crank mechanism (Fig.), crank (link 2) rotates relative to ground (link 1) and form a turning pair. Similarly, crank (link 2), connecting rod (link 3) and connecting rod (link 3), slider (link 4) also form turning pairs. Slider (link 4) reciprocates relative to ground (link 1) and form a sliding pair.

Slider crank mechanism

It should be noted here that the slider crank mechanism showed here is useful only in kinematic analysis and synthesis of the mechanism as actual physical appearance will be different and more complex than showed here. For designing the machine component the different approach will be followed.

c) Nature of Constraint or Type of closure

Closed pair: 

One element is completely surrounded by the other.

Examples: Nut and screw pair

Open Pair: 

When there is some external mean has been applied to prevent them from separation.

Examples: cam and follower pair

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