Understanding Kinematic Pairs and Higher Pairs

In the study of mechanisms, we analyze how different machine parts move relative to each other. These relative motions occur at connections between components, known as kinematic pairs. Kinematic pairs are broadly classified into two types based on the nature of contact between the elements:

• Lower Pairs: These pairs have surface or area contact between the two elements. Examples include revolute joints (pin joints), prismatic joints (sliding joints), screw pairs, cylindrical pairs, and spherical pairs.
• Higher Pairs: These pairs have line or point contact between the two elements when relative motion takes place. The contact area is theoretically a line or a point, although in reality, there is always some deformation leading to a small area of contact.

Identifying higher pairs is crucial for analyzing the motion and forces in a mechanism. Let's examine the pairs given in the question to determine which ones fit the definition of higher pairs.

Analyzing Potential Higher Pairs

Pairs of Gear in Mesh

When two gears mesh, the contact between the teeth occurs along a line (the line of contact shifts as the gears rotate). The relative motion between the gear teeth involves both rolling and sliding along this line of contact. Since the contact is along a line rather than a surface, pairs of gear in mesh are considered higher pairs.

Belt and Pulley

In a belt and pulley system, the belt wraps around the pulley. The contact between the belt and the pulley surface is distributed over an arc. However, the nature of contact during relative motion involves flexible elements (the belt) and can be viewed as a series of line contacts or point contacts as the belt engages and disengages with the pulley surface curvature. Due to the flexible nature of the belt and the resulting contact conditions, the belt and pulley pair is typically classified as a higher pair in mechanism analysis.

Cam and Follower

A cam and follower mechanism involves a cam rotating and a follower moving in response to the cam's profile. The contact between the cam and the follower is typically at a point (e.g., a roller follower against a plate cam) or along a line (e.g., a flat-faced follower against a plate cam, or a roller follower against a cylindrical cam). Since the contact is theoretically a point or a line, a cam and follower pair is a classic example of a higher pair.

Conclusion

Based on the analysis of each pair:

• Pairs of gear in mesh involve line contact, fitting the definition of a higher pair.
• Belt and pulley involves flexible elements and contact that is considered line-like during relative motion, also fitting the definition of a higher pair.
• Cam and follower involves point or line contact, clearly fitting the definition of a higher pair.

Therefore, all three listed pairs - Pairs of gear in mesh, Belt and Pulley, and Cam and follower - can be considered as higher pairs.

This corresponds to the option listing 1, 2, and 3.