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Types of Kinematic pairs

Tania Alam


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.
In simple words, a kinematic pair or simply a pair is a joint of two links having relative motion between them. 

Material Science and Engineering (1).jpg

Kinematic pairs can be classified on the basis of:


1) Nature of contact between the pairing elements 

(a) Lower pair – surface or area contact between the members of the pair

There are 6 types of lower pairs

I. Revolute pair (R)
II. Prismatic pair (P)
III. Screw or helix pair (H)
IV. Cylindrical pair (C)
V. Spherical or globular pair (G)
VI. Planar pair or Ebony (E)  


Types of Lower pair


(b) Higher pair – point or line contact between the members of the pair 
Examples of line contact  
I. Tooth gears 
II. Ball and roller bearings 
III. Wheel rolling on a surface    

 gear-a04.jpg   spherical_roller_bearing.jpg   wheel-contact-with-road-rolling-friction


Examples of point contact  
I. Cam and follower pair      



(c) Wrapping pair – similar to higher pair, but there are multiple point contacts, one body wraps over the other, comprises of belts, chains, etc.

Examples – A belt driven pulley      



2) Nature of mechanical constraint 

(a) Form or Self closed pair – the contact between the two bodies is maintained by geometric form
Examples – Screw pair (lower pair)    



(b) Forced closed pair – the contact between the two bodies is maintained by application of external force
Examples – Ball and roller bearings       


(c) Open pair – links are not help together mechanically, contact due to the force gravity or some spring action.
Examples – Cam and follower pair

3) Nature of relative motion of one link to the other in the pair 

(a) Sliding pair – sliding motion
Examples – Rectangular rod in a rectangular hole in a prism  


(b) Turning pair – turning or revolving motion
Examples – Circular shaft revolving inside a bearing  

(c) Rolling pair – rolling motion
Examples – Ball and roller bearings    


(d) Screw or Helical pair – both turning and sliding motion
Examples – Lead screw and nut of a lathe  


(e) Spherical pair – one link is in the form of a sphere and can turn inside a fixed link
Examples – Ball and socket joint


P.S. ~ Suggestions are always welcomed.


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Tania, I am very pleased to see someone else writing in this area. Welcome to the club! You have some very nicely done figures, and are to be congratulated for them.

In your presentation of "Lower Pairs," you seem to be following the classical approach used by Releaux (I'm not at all sure about that spelling!). After teaching Theory of Machines for many years, I can honestly say I have never found these classifications to be useful at all. The problem, as I see it, is that you associate "degrees of freedom" with a pair, where as I would associate "degrees of freedom" with the number of independent coordinates required to locate a body.

By the way, your cam with the pointed follower is absolutely worthless. A pointed follower will rapidly wear and soon no longer be a pointed follower. Real cams almost always use either flat-faced followers or roller followers (as per your man seated at the table with the cam below).

I look forward to your future contributions.


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Thanks for an awesome representation of things. 

Can I get this at my email tuli.aashish1989@gmail.com

Mam if you have something on inversion of mechanism and degree of freedom calculations then please please please post.


Also, mam shouldn't the revolute pair be represented with collars. It seems only a cylindrical bar in a cylindrical hole and then it may have two degrees of freedom.

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