Kinematic Pairs Matching Solution

Understanding kinematic pairs is fundamental in the study of mechanisms and machines. A kinematic pair is a joint between two elements that permits a definite relative motion. These pairs are classified based on the type of relative motion they allow. Let's explore the given kinematic pairs and their corresponding examples to determine the correct matches.

Revolute Pair Analysis

A revolute pair is a type of kinematic pair where one element can only rotate relative to the other about a fixed axis. It allows for one degree of freedom, which is pure rotational motion.

• Example C: Lathe spindle in the headstock

  In a lathe machine, the spindle rotates within its bearings in the headstock. This motion is purely rotary, making it an ideal example of a revolute pair. The spindle turns, allowing for machining operations, but it does not translate along its axis or move in other directions relative to the headstock.

Therefore, Revolute pair (1) matches with Lathe spindle in the headstock (C).

Helical Pair Analysis

A helical pair, also known as a screw pair, is a kinematic pair that allows for both rotational and translational motion simultaneously. The translational motion is directly proportional to the rotational motion, following a helical path. It also has one degree of freedom.

• Example D: Motion between the bolt and fixed nut

  When a bolt is turned into a fixed nut, it undergoes both rotation about its axis and linear translation along the axis of the nut. This combined rotational and translational motion along a helical path perfectly describes a helical pair.

Therefore, Helical pair (2) matches with Motion between the bolt and fixed nut (D).

Rolling Pair Analysis

A rolling pair is a kinematic pair where the relative motion between the two elements is purely rolling motion. There is no slipping between the surfaces in contact.

• Example A: Ball-bearing

  A ball-bearing consists of an inner ring, an outer ring, and a set of balls between them. The balls roll between the two rings, allowing the shaft to rotate with minimal friction. The primary motion of the balls relative to the races is rolling, making a ball-bearing an excellent example of a rolling pair.

Therefore, Rolling pair (3) matches with Ball-bearing (A).

Globular Pair Analysis

A globular pair, also known as a spherical pair or ball-and-socket joint, allows for three degrees of freedom of rotational motion. One element has a spherical shape and fits into a corresponding spherical cavity in the other element, allowing rotation about any axis passing through the center of the sphere.

• Example B: Ball and socket

  A ball and socket joint is a classic example of a globular pair. The spherical head (ball) of one component fits into a cup-like depression (socket) of another, enabling rotation in multiple planes, such as the human shoulder or hip joint.

Therefore, Globular pair (4) matches with Ball and socket (B).

Kinematic Pairs Summary

Based on the detailed analysis, the correct matches are summarized in the table below:

This matching aligns with the principles of machine elements and their relative motions. Understanding these basic kinematic pairs is crucial for designing and analyzing mechanical systems.