Understanding Kinematic Pairs

In the study of mechanisms and machines, components are connected to transmit motion. When two links or elements are joined together in such a way that their relative motion is constrained, they form a kinematic pair.

Classification of Kinematic Pairs

Kinematic pairs can be classified in various ways, including based on the type of contact between the paired elements. Two primary types based on contact are:

• Lower Pair
• Higher Pair

What is a Lower Kinematic Pair?

A kinematic pair is classified as a lower pair when the two elements have surface contact (area contact) between them. This surface contact is maintained throughout the entire range of relative motion. Examples often involve sliding or turning action where surfaces are in full contact.

What is a Higher Kinematic Pair?

A kinematic pair is classified as a higher pair when the two elements have line contact or point contact between them. As they move relative to each other, this line or point contact is maintained. Examples often involve rolling or a combination of rolling and sliding action.

Analyzing the Given Options

Let's examine each option to determine the type of contact involved:

1. Shaft rotating in a bearing: In this pair, the outer surface of the shaft is in contact with the inner surface of the bearing. This involves contact over an area or surface. This fits the definition of a lower kinematic pair.
2. Wheel rolling on a surface: When a wheel rolls on a surface, the contact between the wheel and the surface is ideally considered to be a line contact (in 2D) or point contact (in 3D, considering a perfect sphere). Although there might be slight deformation causing a small area of contact, it is primarily treated as line or point contact for classification purposes. This is an example of a higher kinematic pair.
3. Cam and follower: In a cam and follower mechanism, the follower typically makes point or line contact with the surface of the cam (depending on the shape of the follower, e.g., knife-edge follower has point contact, roller follower has line contact). As the cam rotates, this contact point or line traces the cam profile. This is a classic example of a higher kinematic pair.
4. Gears: When gear teeth mesh, the contact between mating teeth is ideally considered line contact along the face width. Although there is a combination of rolling and sliding action, the nature of contact between the profiles is essentially line contact. Therefore, gear teeth in mesh form a higher kinematic pair.

Based on this analysis, the pair involving surface contact is the shaft rotating in a bearing.