Theory Of Machine MCQ Questions & Answers | Mechanical Engineering

The virtual coefficient of friction in a V-thread is derived from the normal reaction forces and frictional forces acting on the inclined plane of the thread.

In a V-thread, the friction force is influenced by the helix angle and the thread angle (\(\beta\)). The relationship between the actual coefficient of friction (\(\mu\)) and the virtual coefficient of friction (\(\mu_1\)) is determined by resolving forces along and perpendicular to the inclined thread surface.

For a V-thread, the normal force component acts at an angle, leading to the effective coefficient of friction being altered by a factor of \( \cos \beta \).

Thus, the virtual coefficient of friction is given by:

\[ \mu_1 = \frac{\mu}{\cos \beta} \]

This indicates that the effective friction increases as the thread angle (\(\beta\)) increases because the normal force component decreases, requiring a larger effective friction to compensate.

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.

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.

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.

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.

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.

An involute gear tooth profile is the most commonly used tooth shape in gear design. It is generated by tracing the end of a taut string unwinding from a circle. The resulting curve is known as the involute of a circle.

The base circle is the circle from which the involute profile is generated. It plays a crucial role in defining the geometry of involute gear teeth.

Correct Answer: Option B – Base circle

Explanation:
In gears with involute teeth, the normal to the involute profile at any point is always tangent to the base circle from which the involute is generated. This is a fundamental property of the involute curve.

As the involute curve is traced by unwinding a string from the base circle, the direction of the tension (which is always tangential to the base circle) becomes the normal to the involute curve at the point of contact. This ensures constant velocity ratio and smooth power transmission in gear systems.

Therefore, the line normal to the tooth profile at the point of contact always touches the base circle tangentially, confirming that the base circle is essential in defining the involute geometry.

Why other options are incorrect:
Option A: Pitch circle – The pitch circle is an imaginary circle where the gear teeth theoretically engage. It is not the reference circle for generating the involute profile.
Option C: Addendum circle – This is the outermost circle of the gear, representing the tips of the teeth. It is not involved in generating the involute.
Option D: Dedendum circle – This is the root circle of the gear, below the pitch circle. It also has no role in defining the involute shape.

Conclusion:
In a gear with involute teeth, the normal to the involute curve is always tangent to the base circle. Hence, the correct answer is Option B.

Definition:
A mechanism is a combination of rigid bodies, known as links, connected by joints in such a way that they produce a desired motion when one of the links is given an input motion. The purpose of a mechanism is to convert input motion into a specific output motion.

Correct Answer: Option C – Four or more than four links

Explanation:
In the theory of machines, a mechanism must be able to produce definite relative motion between its parts. For this to be possible, at least one link must be fixed, and the remaining links must be capable of moving in a controlled manner.

According to Gruebler’s criterion for planar mechanisms, a mechanism generally requires a minimum of four links. When four or more links are connected in such a way that one is fixed and others can move, they form a kinematic chain, and if that chain is closed and at least one link is fixed, it becomes a mechanism.

Therefore, a mechanism is typically defined as an assemblage of four or more links that transforms input motion into a controlled output motion.

Why other options are incorrect:
Option A: Two links – Two links connected by a joint form a single pair, not a mechanism. It cannot produce a constrained output motion by itself.
Option B: Three links – Three links connected together form an incomplete kinematic chain and are generally not capable of producing definite motion without adding a fourth link.
Option D: All of these – This is incorrect because only Option C meets the proper condition for forming a mechanism.

Conclusion:
A mechanism requires at least four links to produce constrained and useful motion. Hence, the correct answer is Option C.

Definition:
A machine is a device that consists of a combination of moving parts (links and pairs) designed to transmit force and motion to perform work. A structure, on the other hand, is a stationary system of connected elements that supports loads without transmitting motion.

Correct Answer: Option D – All of the above

Explanation:
The distinction between a machine and a structure can be understood by analyzing several fundamental differences:

1. Relative Motion:
In a machine, the parts move relative to one another to perform a function. These relative motions are essential for the machine's operation.
In a structure, there is no relative motion between the connected members; they remain in fixed positions relative to each other to bear loads.
This supports Option A.

2. Transmission of Power and Motion:
In a machine, links are used to transmit both power and motion between components to produce mechanical work.
In contrast, a structure’s members only transmit forces (tensile or compressive) to maintain equilibrium without generating motion.
This validates Option B.

3. Energy Transformation:
A machine is specifically designed to transform energy into useful work by means of mechanical processes (e.g., engines, pumps).
In a structure, there is no transformation of energy into work; instead, the goal is to remain stable under applied loads.
This confirms Option C.

Since all three statements are accurate descriptions of the difference between a machine and a structure,

Conclusion:
The correct answer is Option D – All of the above.