Apr 032013

A kinematic pair is a combination of two kinematic links that have relative motion with respect to each other.

When two links (or elements) in a machine are in contact with each other, they form a pair. When the relative motion between these two links is completely or partially constrained, then the links are said to form a kinematic pair.

Types of Kinematic Pairs:

Kinematic Pairs can be broadly classified into many types based on three main criteria. The classification of kinematic pairs is listed and described below:

  1. Based on the nature of contact between the pairing elements
    1. Lower Pair
    2. Higher Pair
  2. Based on the type of mechanical constraint (or mechanical contact)
    1. Self Closed Pair
    2. Force Closed Pair
  3. Based on the type of relative motion between the elements of the pair
    1. Sliding Pair
    2. Rolling Pair
    3. Turning Pair
    4. Screw Pair (or Helical Pair)
    5. Cylindrical Pair
    6. Spherical Pair

I. Based on the nature of contact between the pairing elements:

1. Lower Pair:

A kinematic pair is said to be a lower pair if the links in the pair have surface or area contact between them.

Along with a cylinder, a piston forms a lower pair


2. Higher Pair:

A higher pair is a kinematic pair in which the links have point or line contact. Ball bearings, cam and follower are examples of higher pair.

Ball Bearings

Ball Bearings

II. Based on the type of mechanical constraint:

1. Self Closed Pair:

A pair is said to be self closed if the links in the pair have direct mechanical contact, even without the application of external force.

2. Force Closed Pair

A kinematic pair is said to be force closed if the links in the pair are kept in contact by the application of external forces. A good example of this type of pair is ball and roller bearings.

III. Based on the type of relative motion between the elements of the pair

1. Sliding Pair:

As the name suggests, a sliding pair is a kinematic pair in which each element has sliding contact with respect to the other element. Some good examples of sliding pairs are piston inside a cylinder, spur gear drive and square bar in a square hole.

Square Bar in a Square Hole – An example of Sliding Pair

Square bar in a square hole

2. Rolling Pair:

In a rolling pair, one element undergoes rolling motion with respect to the other.

Wheel rolling on a flat surface – An example of Rolling Pair

Wheel Rolling on a Flat Surface

3. Turning Pair:

In a turning pair, one link undergoes turning motion relative to the other link. Example is a shaft with collars in a circular hole.

4. Screw pair:

A screw pair consists of links that have both turning and sliding motion relative to each other.

Bolt and Nut – An Example of Screw Pair

Bolt and Nut

5. Cylindrical Pair:

A cylindrical pair is a kinematic pair in which the links undergo both rotational and translational motion relative to one another.

Example: A solid cylindrical bar inside a hollow shaft.

6. Spherical Pair:

In a spherical pair, a spherical link turns inside a fixed link.

A spherical pair has three degrees of freedom.

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Written by

I am a mechanical engineer with a passion for technical stuff. I am the founder and former editor-in-chief of Mechteacher.com.

  • khalid

    great job….

    • shubham

      Dif. B/w turning and rolling
      Turning – eh car wheel on road
      Rolling – shaft rotating with a gear(other link) fixed on it

  • Ashley Lionell

    hey Surjeet…nice job…however, I would like to ask you what type of a pair would a gear-chain or a rope-pulley be. The chain in the gear-chain ex that I mentioned is stright

    • http://mechteacher.com/ Surjeet S

      Chain-sprocket and rope-pulley are wrapping pairs. Wrapping pair is formed whenever there is a flexible link involved.

  • Sandy

    Hi surjeet, what do you mean by “direct mechanical contact” in self closed pair??

    • http://mechteacher.com/ Surjeet Sankararaj

      If two links in a pair directly touch each other, then they are said to have direct mechanical contact. In self closed pair, such a contact can be achieved without the application of an external force.

  • Renuka

    In some times, the angular contact is occurred due to the application requirement that time angular contact pair is used.

  • rahavan

    hai im a mechanical engineering student ,,,,,i want this pdf file ……this is my mail [email protected],com

  • http://www.fb.com/toshendra.rajwade Toshendra Rajwade

    awsm blog for MECH guys…..!!!

  • siddhardha

    what is the difference between rolling pair and turning pair

    • K.Re’1′Th

      Rolling includes linear motion …but turning doesnot..

  • Aravind Amuthuraj

    can ball-socket joint come under higher pair?

    • http://mechteacher.com/ Surjeet Sankararaj

      Ball and socket joint is a lower pair because its links have area contact.

  • akshay malviya

    difference b/w rolling & turning pair//

    • http://mechteacher.com/ Surjeet Sankararaj

      The difference is explained in the article.

  • http://www.hrbearings.net/ball-bearings.html hrbearingscom

    Based on your blog content, are all the bearings having the kinematic pair?

  • Sasi Kiran

    Does foot step bearing comes under force closed pair?


    Degree of freedom?

    • arslan ahmed

      number of coordinates that are needed to describe the relative movement permitted in kinematic pair or no: of independant pair variables needed to define moment b/w all links

      • ROHIT PAL

        Advantages of using involute as gear tooth profile?


    What is kinematic chain

    • Prakash Babu

      the links haveing more then 2 and 1 st link is conneted to the last one

  • JBS

    Hey, I am not able to understand how come a piston rod and a piston have an area contact.
    I mean they are connected by a pin so how do they have an area contact. Is it because they are in contact with the curved surface of the pin?

  • sai charan

    A universal joint is an example of…?

  • ranjan

    cylinderical pair and spherical pair has more then one degree of freedom and kinematic pair are define as pair which has completely or partially constrained motion

  • Pradeep Tangudu

    what is the definition of open pair???

  • shivanand arwat

    Dof of rolling pair?

  • shivanand arwat

    Dof of screw pair

  • shivanand arwat

    Dof of rolling pair and screw pair?

  • Dev Shukla

    car mirror attachment eg of??
    spherical pair . is it right?

  • swap

    is screw pair a self cloased pair???

  • Jatin

    Can u explain about closed pair and open pair? This is the classsification according to mechanical arrangement.