Theory Of Machine — Part 1 MCQs with Explanations

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 .

In a clock mechanism , both the hour hand and the minute hand rotate about the same central axis , but they rotate at different angular speeds (the minute hand completes one revolution per hour, while the hour hand completes one revolution in twelve hours). A reverted gear train is specifically designed so that the input shaft and output shaft are coaxial , which is an essential requirement in clocks where both hands must be mounted on the same axis. Although a simple gear train can transmit motion between gears, it generally does not satisfy the coaxial shaft requirement when multiple gears are needed to obtain the 12:1 speed reduction within a compact space. A compound gear train can provide large speed ratios but the input and output shafts are not coaxial , making it unsuitable for clock hands. An epicyclic gear train is used in applications like automatic transmissions and is unnecessarily complex for clock mechanisms. Hence, the correct and standard answer in Theory of Machines is Reverted gear train .

Imagine a cam , that rotating part that makes other parts move up and down or back and forth. It has a circular shape , but only a part of it is important for the actual movement. This important part is called the pitch circle . Now, imagine drawing a circle that goes through the pitch point (the point where the cam and the follower first touch). And imagine that the center of this circle is exactly the same as the center of the cam's axis of rotation . That special circle is called the prime circle . So, a circle passing through the pitch point with its center at the center of cam axis is known as a prime circle .

A cylindrical cam is a type of cam where the follower moves along the surface of a rotating cylinder. The profile controlling the follower's motion is cut on the surface or end of the cylinder. Cylindrical cams are typically used when a translating or oscillating follower motion is required, guided by the groove on the cam's cylindrical surface. Correct Answer: Option D – None of the above Explanation: Cams are mechanical elements used to convert rotary motion into linear or oscillatory motion. Based on geometry and motion, cams can be classified in different ways. Cylindrical cams specifically refer to cams where the follower moves parallel or perpendicular to the cam axis and follows a groove on the cylindrical surface. Cylindrical cams are typically classified based on the type of follower motion (translating or oscillating) or based on the profile of the groove (helical, radial, etc.), but not as "circular" or "tangent". The options given are unrelated to the standard classification of cylindrical cams: Option A: Circular – This refers more to disc cams with circular profiles, not cylindrical cams. Option B: Tangent – This is a term used for tangent or radial cam profiles, not for cylindrical cams. Option C: Reciprocating – This refers to follower motion, not a classification of cams themselves. Since none of the given options correctly represent types of cylindrical cams , Conclusion: The correct answer is Option D – None of the above .

When a rigid body is suspended vertically and it oscillates with a small amplitude under the action of the force of gravity, the body is known as Option A: Simple pendulum This option is not correct . A simple pendulum consists of a mass (called the pendulum bob) attached to a string or rod and swings back and forth under gravity. It is not a rigid body. Option B: Compound pendulum This is the correct answer . When a rigid body, such as a physical rod or a physical object, is suspended vertically and allowed to oscillate under gravity, it is referred to as a compound pendulum. The oscillation of the rigid body is similar in nature to that of a simple pendulum. Option C: Torsional pendulum A torsional pendulum is different from a compound pendulum. It consists of a rod or wire that is twisted and oscillates in torsional motion. Option D: Second's pendulum A Second's pendulum is a specific type of simple pendulum with a length such that it completes one full oscillation in exactly two seconds. It is not related to a rigid body. Therefore, the correct answer is Option B: Compound pendulum .

Option A: Offset between center lines of cam and follower The pressure angle in a cam mechanism is influenced by the offset between the center lines of the cam and follower. This offset changes the geometry of contact, which in turn affects the pressure angle. Option B: Lift of follower The lift of the follower , or the maximum displacement of the follower, also impacts the pressure angle. A larger lift generally results in a greater pressure angle as the cam profile must be adjusted to achieve the desired lift. Option C: Angle of ascent The angle of ascent is the angle over which the cam raises the follower to its maximum position. A steeper or larger angle of ascent increases the rate of lift, which also affects the pressure angle. Conclusion: The correct answer is Option D: All of the above . The pressure angle of a cam depends on the offset between the cam and follower, the lift of the follower, and the angle of ascent, as all these factors influence the cam profile and contact geometry.

Option A: Rotating A cam mechanism can impart rotational motion to the follower when designed to produce continuous circular movement. This occurs in certain cam profiles where the follower needs to rotate along with the cam. Option B: Oscillating A cam mechanism can produce oscillating motion in the follower. This happens when the follower is designed to move back and forth over a limited angle, which is common in applications like valve actuators. Option C: Reciprocating A cam mechanism is also capable of imparting reciprocating motion to the follower, where it moves in a linear path back and forth. This is often seen in applications such as engine valves and pumps. Option D: All of the above Cams are versatile mechanisms that can impart rotating, oscillating, and reciprocating motions depending on the design and profile of the cam and follower. Therefore, the correct answer is all of the above. Conclusion: The correct answer is Option D: All of the above . Cam mechanisms can be designed to impart various types of motion, including rotating, oscillating, and reciprocating, to meet different mechanical requirements.

In a kinematic chain, a quaternary joint is equivalent to Option A: One binary joint This option is not correct . A quaternary joint is not equivalent to just one binary joint. Option B: Two binary joints This option is not correct . A quaternary joint is not equivalent to two binary joints. Option C: Three binary joints This is the correct answer . In a kinematic chain, a quaternary joint is equivalent to three binary joints. It means that the motion and constraints at a quaternary joint can be represented by three separate binary joints. Option D: Four binary joints This option is not correct . A quaternary joint is not equivalent to four binary joints. Therefore, the correct answer is Option C: Three binary joints . In a kinematic chain, a quaternary joint is equivalent to three binary joints.

When two elements of a pair have a surface contact when relative motion takes place and the surface of one element slides over the surface of the other, the pair formed is known as lower pair.

For a given lift of the sleeve, the sensitiveness of the governor increases as the speed range decreases.

$$\frac{3}{2}$$ v is the correct answer to “ABCD is a four bar mechanism in which AB = 310 mm and CD = 450 mm. AB and CD are both perpendicular to the fixed link AD, as shown in the below figure. If the velocity of B at this condition is v. Then the velocity of C is”. This question is standard in competitive examination syllabi for Theory Of Machine.

Forced vibrations occur when a body is made to vibrate by the continuous action of an external periodic force . In this case, the vibration is maintained by the applied external force rather than by the body’s own natural tendency to vibrate. Option A describes damped vibrations , where amplitude decreases after each cycle due to energy loss. Option B refers to free vibrations , where no external force acts after the initial displacement. Therefore, a body is said to be under forced vibrations when it vibrates under the influence of an external force , making Option C the correct answer.

30° V-engine is the correct answer to “For a twin cylinder V-engine, the crank positions for primary reverse cranks and secondary direct cranks are shown in the below figure. The engine is a”. This question is standard in competitive examination syllabi for Theory Of Machine.

$${{\text{G}}^2} \times {I_2}$$ is the correct answer to “A torsional system with discs of moment of inertia $${I_1}$$ and $${I_2}$$ as shown in the below figure, is gear driven such that the ratio of speed of shaft B to shaft A is 'G'. Neglecting the inertia of gears, the equivalent inertia of disc on shaft B at the speed of shaft A is equal to”. This question is standard in competitive examination syllabi for Theory Of Machine.

The number of links in a pantograph mechanism is equal to 4. A pantograph mechanism typically consists of: 1. The fixed frame (link 1) 2. The driving link (link 2) 3. The follower link (link 3) 4. The coupler link (link 4) This arrangement forms a four-bar linkage system. Therefore, the correct answer is Option C: 4 .

Between $${l_1}$$ and $${l_2}$$ but nearer to $${l_2}$$ is the correct answer to “In the two rotor system as shown in the below figure $$\left( {{l_1} < {l_2}} \right),$$ a node of vibration is situated”. This question is standard in competitive examination syllabi for Theory Of Machine.

The frequency of oscillation of a compound pendulum is inversely proportional to the radius of gyration about the axis of rotation. The radius of gyration (k) is a measure of how mass is distributed relative to the axis of rotation. A larger radius of gyration means the mass is more spread out, leading to a lower frequency of oscillation. Let's analyze each option: Option A: "Less" - This is correct because a larger radius of gyration results in a longer period of oscillation, thus reducing the frequency. Option B: "More" - This is incorrect as frequency decreases with an increase in the radius of gyration. Option C: "Same" - This is incorrect because frequency and radius of gyration are inversely related. Option D: "Data are insufficient to determine same" - This is incorrect because the relationship between frequency and radius of gyration is well-established in physics. Therefore, the correct answer is Option A: Less .

Zero is the correct answer to “In the below figure, PC is the connecting rod and OC is the crank making an angle $$\theta $$ with the line of stroke PO and rotates with uniform angular velocity at $$\omega $$ rad/s. The Klien's acceleration diagram for determining the acceleration of the piston P is shown by quadrilateral CQNO, the acceleration of the piston is _________ when the crank OC and connecting rod PC are at right angles to each other.”. This question is standard in competitive examination syllabi for Theory Of Machine.

The train value of a gear train is equal to the velocity ratio of a gear train . Train Value: This is the measure of how the rotational speed changes from one gear to another in the gear train. It is defined as the product of the gear ratios of all the gears in the train. Velocity Ratio: The ratio of the angular velocities of the driving gear to the driven gear in a gear train. It is the reciprocal of the gear ratio, but when calculating the overall effect in a series of gears, it directly reflects the train value. Always greater or less than unity: The train value or velocity ratio can be greater than, less than, or equal to unity depending on the configuration of the gear train. The key point is that the train value equals the velocity ratio.

The correct answer is Option A: Bevel gear . In automobiles, the power is transmitted from the gearbox to the differential through a bevel gear . Bevel gears are specially designed gears with tapered and conical-shaped teeth that allow the transmission of power at right angles. In this context, they are commonly used in the drivetrain to transfer power from the gearbox to the differential, which further distributes power to the wheels. Option B: Universal joint is incorrect because universal joints are typically used to transmit power at variable angles, not specifically from the gearbox to the differential. Option C: Hooke's joint is incorrect as Hooke's joint is another term for a universal joint, which is not the primary component in the described power transmission. Option D: Knuckle joint is incorrect as knuckle joints are not used for transmitting power in the drivetrain of automobiles.

Slightly less than 95 mm is the correct answer to “In a four-bar chain it is required to give an oscillatory motion to the follower for a continuous rotation of the crank. For the lengths of 50 mm of crank and 70 mm of the follower, determine theoretical maximum length of coupler. The distance between fixed pivots of crank and followers is”. This question is standard in competitive examination syllabi for Theory Of Machine.

Remain same as before is the correct answer to “A rotor which is balanced statically but not dynamically is supported on two bearings L apart and at high speed of the rotor, reaction on the left bearing is R. The right side of the bearing is shifted to a new position 2L apart from the left bearing. At the same rotor speed, dynamic reaction on the left bearing in the new arrangement will”. This question is standard in competitive examination syllabi for Theory Of Machine.

Two lower pairs and one additional link is the correct answer to “The relation $$I = \frac{2}{3}\left( {{\text{j}} + 2} \right)$$ apply only to kinematic chains in which lower pairs are used. This may be used to kinematic chains in which higher pairs are used, but each higher pair may be taken as equivalent to”. This question is standard in competitive examination syllabi for Theory Of Machine.

Complex conjugate is the correct answer to “The equation of motion for a vibrating system with viscous damping is $$\frac{{{d^2}x}}{{d{t^2}}} + \frac{c}{m} \times \frac{{dx}}{{dt}} + \frac{s}{m} \times x = 0,$$ if the roots of the equation are __________ then the system will be under damped.”. This question is standard in competitive examination syllabi for Theory Of Machine.

$$\frac{1}{2}$$μWR is the correct answer to “The frictional torque transmitted in a flat pivot bearing, considering uniform wear, is (where μ = Coefficient of friction, W = Load over the bearing and R = Radius of bearing surface)”. This question is standard in competitive examination syllabi for Theory Of Machine.

Universal coupling is the correct answer to “The type of coupling used to join two shafts whose axes are neither in same straight line nor parallel, but intersect is”. This question is standard in competitive examination syllabi for Theory Of Machine.

Base circle is the correct answer to “The size of cam depends upon”. This question is standard in competitive examination syllabi for Theory Of Machine.

$${\omega ^2}\left( {{\text{R}} - {{\text{r}}_1}} \right)\cos \theta $$ is the correct answer to “The acceleration of a flat-faced follower when it has contact with the flank of a circular arc cam, is given by”. This question is standard in competitive examination syllabi for Theory Of Machine.

$${\omega ^2}\left( {{{\text{r}}_1} + {{\text{r}}_2}} \right)\left( {\frac{{2 - {{\cos }^2}\theta }}{{{{\cos }^3}\theta }}} \right)$$ is the correct answer to “The acceleration of the reciprocating roller follower when it has contact with the straight flanks of the tangent cam, is given by”. This question is standard in competitive examination syllabi for Theory Of Machine.

$$\omega \left( {{\text{R}} - {{\text{r}}_1}} \right)\sin \theta $$ is the correct answer to “The velocity of a flat-faced follower when it has contact with the flank of a circular arc cam, is given by”. This question is standard in competitive examination syllabi for Theory Of Machine.

Crank has a uniform angular velocity is the correct answer to “Klein's construction can be used when”. This question is standard in competitive examination syllabi for Theory Of Machine.

A large value of pressure angle is the correct answer to “For the same lift and same angle of ascent, a smaller base circle will give”. This question is standard in competitive examination syllabi for Theory Of Machine.