Theory Of Machine - Study Mode

[#161] The lower pairs are _________ pairs.
Correct Answer

(A) Self-closed

Explanation

Solution: Definition: A lower pair is a type of kinematic pair where two links have surface or area contact with each other during relative motion. This type of contact is more stable and allows motion such as sliding, turning, or screw motion. Examples include revolute pairs (hinges), prismatic pairs (sliders), and screw pairs. Correct Answer: Option A – Self-closed Explanation: In mechanical systems, pairs are classified based on how the contact between the elements is maintained. Self-closed pairs are those in which the elements are kept in contact by the geometry and arrangement of the system itself, without the need for any external force. This is characteristic of lower pairs , where the connection between the links is inherently maintained by their design — such as a shaft rotating in a bearing or a slider moving in a guide. Because lower pairs have surface contact and are physically constrained by their shapes (e.g., cylindrical or prismatic), they remain connected throughout the motion without needing extra forces. This is what makes them self-closed . Why other options are incorrect: Option B: Force-closed – Force-closed pairs require an external force (like a spring or gravity) to keep the elements in contact. This applies to certain higher pairs, not lower pairs. Option C: Friction closed – This refers to systems where motion is sustained by frictional forces, such as belts or clutches. This is not a defining feature of lower pairs. Option D: None of these – This is incorrect because Option A correctly defines the nature of lower pairs. Conclusion: Lower pairs are self-closed because their elements maintain contact through their geometric configuration without requiring external forces.

[#162] In a coupling rod of a locomotive, each of the four pairs is a ________ pair.
Correct Answer

(B) Turning

Explanation

Solution: The correct answer is (B) Turning . Let's break down why: What is a Kinematic Pair (or just Pair)? A kinematic pair is a connection between two links (or elements) that allows them to move relative to each other in a specific way. Understanding the Options: * Sliding Pair: This pair allows one link to slide along another (like a piston in a cylinder). * Turning Pair: This pair allows one link to turn or rotate about a fixed axis on another link (like a hinge). * Rolling Pair: This pair allows one link to roll over another (like a wheel on a road). * Screw Pair: This pair combines turning and sliding motion (like a screw in a nut). Why Turning Pair is the Answer for a Coupling Rod: A coupling rod connects the wheels of a locomotive. At each end of the coupling rod, there's a connection point (usually a pin) that allows the rod to rotate relative to the wheel or another connecting rod. The wheels rotate, and the coupling rod rotates along with the wheel in a circular motion around the wheel's center. This rotational motion is best described by a turning pair . Therefore, each of the four pairs in a coupling rod of a locomotive is a turning pair .

[#163] A kinematic chain is known as a mechanism when
Correct Answer

(B) One of the links is fixed

Explanation

Solution: A kinematic chain is a combination of links connected in a specific order, allowing relative motion between them. When one of the links in a kinematic chain is fixed or stationary, it is termed a mechanism . This fixed link provides a frame of reference against which the motions of other links are observed. The fixed link is often referred to as the "ground" or "frame" link, and it serves as a foundation for the movement and analysis of the remaining links in the kinematic chain. By fixing a single link, the entire kinematic chain becomes a functional system with controlled or constrained motion. This is a fundamental concept in the study of mechanisms, which are essential components in various mechanical devices and machines used in engineering applications. Note: Options A and C are not accurate because the presence of fixed links is essential to define a mechanism. Option D is also not correct as one of the options (Option B) is indeed the correct condition for a kinematic chain to be termed a mechanism.

[#164] A pantograph is a mechanism with
Correct Answer

(A) Lower pairs

Explanation

Solution: Definition: A pantograph is a mechanical linkage connected in a specific manner based on parallelogram geometry. It is used to copy, scale, or reproduce motion and drawings. When one point of the pantograph is moved, the other point replicates the motion in a scaled form, either enlarged or reduced. Correct Answer: Option A – Lower pairs Explanation: In a pantograph mechanism, all the joints are of the revolute type (turning pairs), where the links are connected by pins. These connections are examples of lower pairs , because they involve surface contact and allow rotational motion about fixed axes. Lower pairs are characterized by surface contact between the connected links, such as in turning (revolute) or sliding (prismatic) joints. Since a pantograph only uses such revolute joints, it qualifies as a mechanism made entirely of lower pairs . Why other options are incorrect: Option B: Higher pairs – Higher pairs involve line or point contact, such as in cam-follower or gear mechanisms. These are not present in a pantograph. Option C: Rolling pairs – These involve rolling contact, like in a wheel on a surface. Pantographs do not involve rolling motion. Option D: Turning pairs – While it is true that pantographs consist of turning pairs, this is a subset of lower pairs . Therefore, the more accurate and inclusive answer is Option A . Conclusion: A pantograph is composed entirely of lower pairs , specifically turning (revolute) pairs, making Option A the correct answer.

[#165] A ball and a socket forms a
Correct Answer

(D) Spherical pair

Explanation

Solution: Definition: A ball and socket joint is a type of mechanical connection in which a spherical ball fits into a hollow socket, allowing rotational movement in multiple directions. This joint mimics the movement seen in the human shoulder or hip joint. Correct Answer: Option D – Spherical pair Explanation: A spherical pair is a type of kinematic pair in which one link (the ball) is enclosed within another link (the socket), allowing rotational motion in three degrees of freedom : pitch, yaw, and roll. This means the ball can rotate freely in all directions inside the socket, but it cannot translate. This type of joint is often used in mechanisms that require multi-directional motion and flexibility, such as robotic arms, automotive suspensions, and anatomical models. The ball and socket joint is classified as a lower pair because there is surface contact between the ball and the socket throughout their motion. Why other options are incorrect: Option A: Turning pair – A turning pair allows rotation only about one fixed axis. The ball and socket allows rotation about multiple axes, so it is more complex than a turning pair. Option B: Rolling pair – Rolling pairs involve rolling contact between two bodies, such as a wheel on a surface. The ball and socket does not involve rolling but rather rotational motion with surface contact. Option C: Screw pair – A screw pair combines rotational and translational motion with a helical constraint, which is not the case in a ball and socket joint. Conclusion: A ball and socket joint provides multi-directional rotational motion and fits the definition of a spherical pair . Hence, the correct answer is Option D .