All questions of Theory of Machines (TOM) for Mechanical Engineering Exam

A planar mechanism has 8 links and 10 rotary joints. The number of degrees of freedom of the mechanism, using Grubler's criterion, is   
  • a)
    0
  • b)
    1
  • c)
    2
  • d)
    3
Correct answer is option 'B'. Can you explain this answer?

Amar Gupta answered
Whatever may be the number of links and joints Grubler's criterion applies to mechanism with only single degree freedom. Subject to the condition 3l-2j-4=0 and it satisfy this condition.
Degree of freedom is given by
 

Beam engine mechanism is an example of 
  • a)
     double crank mechanism 
  • b)
     double lever mechanism 
  • c)
     crank and lever mechanism
  • d)
     none of the above
Correct answer is option 'C'. Can you explain this answer?

Sagarika Patel answered
The different types of four bar inversions are as follows:

1) Double crank mechanism: This is the second inversion of four bar chain. It is used for transmitting rotary motion from one crank to the other crank. Coupled wheels of locomotive is an example of this inversion.

2) Crank and lever mechanism: This is the first inversion of four bar chain. It is used to convert rotary motion of input link into oscillatory motion of output link. Beam engine mechanism is an example of this inversion and it consists of four links. The crank rotates about a fixed centre and the lever oscillates at another fixed centre.

3) Double lever mechanism: This is the third inversion of four bar chain. It is used for transmitting oscillatory motion from one lever to another. Ackermann steering gear mechanism is an example of double lever mechanism. 

Can you explain the answer of this question below:The minimum number of links in a single degree-of-freedom planar mechanism with both higher and lower kinematic pairs is:
A: 2
B: 3
C: 4
D: 5
The answer is b.

From the Kutzbach criterion the degree of freedom,
n = 3(l − 1) − 2j − h
For single degree of Freedom (n = 1),
1 = 3(l − 1) − 2j − h
3l − 2j − 4 − h = 0 …(i)
The simplest possible mechanisms of single degree of freedom is four-bar mechanism. For this mechanism j = 4, h = 0
From equation (i), we have
3l − 2 x 4 − 4 − 0 = 0
or, l = 4.

The minimum number of links in a single degree-of-freedom planar mechanism with both higher and lower kinematic pairs is 
  • a)
    2
  • b)
    3
  • c)
    4
  • d)
    5
Correct answer is 'C'. Can you explain this answer?

Rajeev Sharma answered
From the Kutzbach criterion the degree of freedom,
n = 3(l − 1) − 2j − h
For single degree of Freedom (n = 1),
1 = 3(l − 1) − 2j − h
3l − 2j − 4 − h = 0 …(i)

The simplest possible mechanisms of single degree of freedom is four-bar mechanism. For this mechanism j = 4, h = 0

From equation (i), we have
3l − 2 x 4 − 4 − 0 = 0
or, l = 4.

The figure below shows a planar mechanism with single degree of freedom. The instant centre 24 for the given configuration is located at a position[GATE-2004]
a)L 
b)M
c)N 
d)∞
Correct answer is option 'D'. Can you explain this answer?

Sagarika Patel answered
The Correct nswer is d.
Given planar mechanism has degree of freedom, N = 1 and two infinite parallel lines meet at infinity. So, the instantaneous centre I24 will be at N , but for single degree of freedom, system moves only in one direction.
Hence, I24 is located at infinity(∞)

A uniform rigid rod of mass m = 1 kg and length L = 1 m is hinged at its centre and laterally supported at one end by a spring of constant k = 300 N/m. The natural frequency (ωn in rad/s is
  • a)
    10
  • b)
    20
  • c)
    30
  • d)
    40
Correct answer is option 'A'. Can you explain this answer?

Milan Goyal answered
A uniform rigid rod of mass m = 1 kg and length L = 1 m is hinged at its centre & laterally supported at one end by a spring of spring constant k = 300N/m. The natural frequency ωn in rad/s is 10

Match the following
 
  • a)
    P-2   Q-3   R-1   S-4
  • b)
    P-3  Q-2   R-4 S-1
  • c)
    P-4  Q-1  R-2  S-3
  • d)
    P-4  Q-3  R-1  S-2
Correct answer is 'C'. Can you explain this answer?

Shubham Chik answered
For q it is 1 because the geneva mechanism is used in ship so continuous motion is not there so there they prefer mechanism which can be stop or start at any moment

A linkage is shown below in the figure in which links ABC and DEF are ternary Jinks whereas AF, BE and CD are binary links.
The degrees of freedom of the linkage when link ABC is fixed are
[IES-2002]
  • a)
    0
  • b)
    1
  • c)
    2
  • d)
    3
Correct answer is option 'A'. Can you explain this answer?

Telecom Tuners answered
To calculate the degrees of freedom (DOF) of the given linkage, we can use Gruebler's equation for planar mechanisms:
F=3(n−1)−2j−h
Where:
  • F is the degrees of freedom.
  • n is the number of links in the mechanism.
  • j is the number of lower pairs (revolute or prismatic joints).
  • h is the number of higher pairs (if any, typically ignored in simple linkages).
Step 1: Count the number of links (nnn)
In the figure:
  • Links ABC and DEF are ternary links (each connects three joints), so we count each as one link.
  • Links AF, BE, and CD are binary links (each connects two joints).
Thus, the total number of links nnn is:
n=2(ternary links)+3(binary links)=5
Step 2: Count the number of joints (j)
In the figure:
  • There are six revolute joints, one at each intersection of the links: A, F, B, E, C, and D.
Thus, the total number of lower pairs (joints) j is:
j=6
Step 3: Apply Gruebler’s equation
Substitute the values into Gruebler’s equation:
F=3(n−1)−2j
F=3(5−1)−2(6)
F=3(4)−12
F=12−12=0
Conclusion:
The degrees of freedom of the linkage is F=0, meaning the linkage is a structure and does not have any mobility when the link ABC is fixed.
Thus, the correct answer is:
Option 1: 0.

What are the minimum number of kinematic pairs required in a kinematic chain?
  • a)
     2 kinematic pairs
  • b)
     3 kinematic pairs
  • c)
     4 kinematic pairs 
  • d)
     None of the above​
Correct answer is option 'C'. Can you explain this answer?

Neha Joshi answered
  • If there is all pairs are lower pair of a kinematic chain then 4 pairs required to make a chain.
  • But, if there is atleast one higher pair involved then minimum 3 pairs required to make a kinematic chain. Cam and follower is example of a kinematic chain and it includes total 3pairs.
One higher pair = two lower pair.

A shaft has two heavy rotors mounted on it. The transverse natural frequencies, considering each of the rotor separately, are 100 Hz and 200 Hz respectively. The lowest critical speed is
  • a)
    5367 r.p.m.
  • b)
    6000 r.p.m.
  • c)
    9360 r.p.m.
  • d)
    2000 r.p.m.
Correct answer is option 'A'. Can you explain this answer?

Aniket Saini answered
Calculation of Lowest Critical Speed of Shaft with Two Rotors

Given data:
Transverse natural frequency of first rotor (f1) = 100 Hz
Transverse natural frequency of second rotor (f2) = 200 Hz

Step 1: Calculation of Critical Speed of Each Rotor

- Critical speed of the rotor is the speed at which the frequency of rotation coincides with the natural frequency of the rotor.
- The critical speed of each rotor can be calculated using the formula:
Critical speed (Nc) = (f * 60) / p
Where,
f = natural frequency of the rotor
p = number of poles of the motor

For the first rotor:
Nc1 = (100 * 60) / 2 = 3000 rpm

For the second rotor:
Nc2 = (200 * 60) / 2 = 6000 rpm

Step 2: Calculation of Lowest Critical Speed of Shaft

- The lowest critical speed of the shaft is the speed at which the natural frequencies of both rotors coincide.
- The natural frequencies of the rotors are in the ratio of 1:2, which means that at some speed, their frequencies will become equal.
- Let the lowest critical speed of the shaft be Nc.

Then, (f2 / f1) = (Nc / Nc1)^2

(Nc / Nc1)^2 = 2

Nc / Nc1 = √2

Nc = Nc1 * √2

Nc = 3000 * √2 = 5367 rpm (approx.)

Therefore, the lowest critical speed of the shaft with two rotors mounted on it is 5367 rpm. The correct answer is option (a).

When two shafts are neither parallel nor intersecting, power can be transmitted by using
  • a)
    A pair of spur gears
  • b)
    a pair of helical gears
  • c)
    An Oldham's coupling
  • d)
    a pair of spiral gears
Correct answer is option 'D'. Can you explain this answer?

Rajeev Menon answered
When helical gears are used to drive non-parallel and non-intersecting shafts, they are commonly called spiral gears. The exact nature of the action between such gears is not generally understood. On spiral gear drives, the unique condition exists that gear of the pair has two circular pitches and two pitch surfaces; one pitch surface is a cylinder while the other is a plane.

When the shafts are at right angles, each gear has one circular pitch in its plane of rotation and another circular pitch in the direction of its axis. The second circular pitch is called the axial pitch. Each gear of the pair has a pitch cylinder whose diameter is determined by its number of teeth and circular pitch in the plane of rotation, and a pitch plane whose travel is controlled by the axial pitch. The axial pitch of any such gear is constant at all diameters, while its circular pitch in the plane of rotation is the same as the axial pitch of the mating gear.

The minimum number of links in a single degree-of-freedom planar mechanism with both higher and lower kinematic pairs is 
  • a)
    2
  • b)
    3
  • c)
    4
  • d)
    5
Correct answer is option 'C'. Can you explain this answer?

Anirban Khanna answered
From the Kutzbach criterion the degree of freedom,
n = 3(l − 1) − 2j − h
For single degree of Freedom (n = 1),
1 = 3(l − 1) − 2j − h
3l − 2j − 4 − h = 0 …(i)
The simplest possible mechanisms of single degree of freedom is four-bar mechanism. For this mechanism j = 4, h = 0
From equation (i), we have
3l − 2 x 4 − 4 − 0 = 0
or, l = 4.

In a plate cam mechanism with reciprocating roller follower, the follower has a constant acceleration in the case of  
[GATE-1993]
  • a)
    cycloidal motion
  • b)
    simple harmonic motion
  • c)
    parabolic motion
  • d)
    3-4-5 polynomial motion
Correct answer is option 'C'. Can you explain this answer?

Tanvi Sarkar answered
For uniform acceleration and retardation, the velocity of the follower must change at a constant rate and hence the velocity diagram of the follower consists of sloping straight lines. The velocity diagram represents everywhere the slope of the displacement diagram, the later must be a curve whose slope changes at a constant rate. Hence the displacement diagram consists of double parabola.

In a 4-stroke I.C. engine, the turning moment during the compression stroke is
  • a)
    positive throughout
  • b)
    negative throughout
  • c)
    positive during major portion of the stroke
  • d)
    negative during major portion of the stroke.
Correct answer is option 'A'. Can you explain this answer?

Aditya Chavan answered
Explanation:

The 4-stroke internal combustion engine has four strokes, which are Intake stroke, Compression stroke, Power stroke, and Exhaust stroke. During the compression stroke, the piston moves from bottom dead center (BDC) to top dead center (TDC), compressing the air-fuel mixture in the combustion chamber. The turning moment during the compression stroke is the torque produced by the engine to rotate the crankshaft.

Positive Turning Moment:

The turning moment during the compression stroke is positive throughout. This means that the torque produced by the engine is in the same direction as the rotation of the crankshaft. The reason for the positive turning moment is that the air-fuel mixture in the combustion chamber is compressed, increasing the pressure and temperature. This increase in pressure and temperature causes the molecules of the air-fuel mixture to move faster and collide more frequently, producing a force that acts on the piston and rotates the crankshaft.

Negative Turning Moment:

If the turning moment during the compression stroke is negative, it means that the torque produced by the engine is opposite to the direction of rotation of the crankshaft. This is not possible in a 4-stroke internal combustion engine because the engine needs to compress the air-fuel mixture to ignite it during the power stroke. If the turning moment during the compression stroke is negative, it means that the engine is not compressing the air-fuel mixture, and the combustion will not take place during the power stroke.

Conclusion:

In conclusion, the turning moment during the compression stroke of a 4-stroke internal combustion engine is positive throughout. The positive turning moment is due to the compression of the air-fuel mixture, which increases the pressure and temperature, producing a force that acts on the piston and rotates the crankshaft.

The speed of an engine varies from 210 rad/s to 190 rad/s. During the cycle the change in kinetic energy is found to be 400 Nm. The inertia of the flywheel in kg/m2 is
  • a)
    0.10
  • b)
    0.20
  • c)
    0.30
  • d)
    0.40
Correct answer is 'A'. Can you explain this answer?

Amar Desai answered
Given:
The speed of the engine varies from 210 rad/s to 190 rad/s.
The change in kinetic energy during the cycle is 400 Nm.

To find:
The inertia of the flywheel in kg/m2.

Solution:
The kinetic energy of a rotating object is given by the equation:
KE = (1/2) * I * ω2
where KE is the kinetic energy, I is the moment of inertia, and ω is the angular velocity.

We are given that the change in kinetic energy during the cycle is 400 Nm. This can be expressed as:
ΔKE = (1/2) * I * (ω2 - ω1)
where ω2 is the final angular velocity and ω1 is the initial angular velocity.

We are also given that the speed of the engine varies from 210 rad/s to 190 rad/s. This means that ω2 = 190 rad/s and ω1 = 210 rad/s.

Substituting these values in the equation, we have:
400 = (1/2) * I * (1902 - 2102)

Simplifying the equation further:
400 = (1/2) * I * (36100 - 44100)
400 = (1/2) * I * (-8000)
400 = -4000I

Dividing both sides of the equation by -4000, we get:
I = -400/4000
I = -0.1 kg/m2

Since moment of inertia cannot be negative, we take the absolute value of I:
I = 0.1 kg/m2

Therefore, the inertia of the flywheel is 0.1 kg/m2.

Hence, the correct answer is option 'A'.

For the planar mechanism shown in figure select the most appropriate choice for the motion of link 2 when link 4 is moved upwards.
  • a)
    Link 2 rotates clockwise
  • b)
    Link 2 rotates counter – clockwise
  • c)
    Link 2 does not move
  • d)
    Link 2 motion cannot be determined 
Correct answer is option 'B'. Can you explain this answer?

Ankit Kumar answered
When link 4 is moved upwards, it will push link 3 upwards but since link 3&4 are joined by a revolute joint, the link will have to rotate in anticlockwise direction to move upwards. Since link 2&3 are joined, link 2 will show the same motion as link 3. So link will rotate in counter clockwise direction

The number of inversions for a slider crank mechanism is 
  • a)
    6
  • b)
    5
  • c)
    4
  • d)
    3
Correct answer is option 'C'. Can you explain this answer?

Shivam Sharma answered
The four different mechanisms can be obtained by four different inversions of the chain. Slider Crank mechanism.
It has four binary links, three revolute pairs, one prismatic pair.By fixing links 1, 2, 3 in turn we get various inversions.

Consider the following statements:
1. Flywheel and governor of an engine are the examples of an open loop control system
2. Governor is the example of closed loop control system
3. The thermostat of a refrigerator and relief valve of a boiler are the examples of closed loop control system
Which of these statements is/are correct?
  • a)
    1 only
  • b)
    2 and 3
  • c)
    3 only
  • d)
    2 only
Correct answer is option 'C'. Can you explain this answer?

Aditya Chavan answered
Closed Loop and Open Loop Control Systems

Closed loop and open loop control systems are the two types of control systems used in engineering. A closed loop control system is a system in which the output is controlled by measuring the feedback and comparing it with the desired output. An open loop control system is a system in which the output is not controlled by feedback.

Examples

1. Flywheel and governor of an engine are the examples of an open loop control system
2. Governor is the example of closed loop control system
3. The thermostat of a refrigerator and relief valve of a boiler are the examples of closed loop control system

Explanation

Statement 1: Flywheel and governor of an engine are the examples of an open loop control system.

This statement is incorrect. The flywheel and governor of an engine are examples of closed loop control systems. The governor controls the engine speed by measuring the feedback from the engine and adjusting the fuel supply accordingly.

Statement 2: Governor is the example of closed loop control system.

This statement is correct. The governor is an example of a closed loop control system. The governor measures the feedback from the engine and adjusts the fuel supply to maintain the desired engine speed.

Statement 3: The thermostat of a refrigerator and relief valve of a boiler are the examples of closed loop control system.

This statement is correct. The thermostat of a refrigerator and relief valve of a boiler are examples of closed loop control systems. The thermostat measures the temperature inside the refrigerator and adjusts the cooling system to maintain the desired temperature. The relief valve of a boiler measures the pressure inside the boiler and adjusts the steam flow to maintain the desired pressure.

Conclusion

In summary, statement 1 is incorrect, statement 2 is correct, and statement 3 is correct. The governor, thermostat, and relief valve are all examples of closed loop control systems.

Effect of friction, at the sleeve of a centrifugal governor is to make it
  • a)
    More sensitive
  • b)
    More stable
  • c)
    Insensitive over a small range of speed
  • d)
    Unstable
Correct answer is option 'C'. Can you explain this answer?

Friction Effect on Centrifugal Governor

Introduction:
A centrifugal governor is a device that is used to control the speed of machines such as engines. The governor works on the principle of centrifugal force and is designed to regulate the amount of fuel going into the engine. The governor consists of a sleeve that rotates around a spindle and is connected to the throttle valve of the engine.

Friction Effect:
Friction is a force that opposes motion between two surfaces that are in contact with each other. The amount of friction depends on the nature of the surfaces and the force pressing them together. In a centrifugal governor, friction occurs between the sleeve and the spindle.

Effect on Sensitivity:
Sensitivity refers to the degree to which the governor responds to changes in speed. Friction at the sleeve of a centrifugal governor reduces its sensitivity over a small range of speed. This is because the frictional force opposes the motion of the sleeve, making it more difficult for the governor to respond to changes in speed. As a result, the governor becomes less sensitive and is unable to control the speed of the engine accurately.

Effect on Stability:
Stability refers to the ability of the governor to maintain a constant speed. Friction at the sleeve of a centrifugal governor makes it more stable. This is because the frictional force acts as a damping force, reducing the amplitude of the oscillations of the sleeve. As a result, the governor is able to maintain a constant speed and is less likely to oscillate or hunt.

Effect on Range of Speed:
The range of speed refers to the range of speeds at which the governor is effective. Friction at the sleeve of a centrifugal governor makes it insensitive over a small range of speed. This is because the frictional force reduces the sensitivity of the governor, making it less effective at controlling the speed of the engine within a certain range of speeds.

Effect on Stability:
Friction at the sleeve of a centrifugal governor can also make it unstable. This happens when the frictional force is too high, causing the sleeve to stick or jam. When this happens, the governor is unable to respond to changes in speed, and the speed of the engine becomes unstable.

Conclusion:
In conclusion, friction at the sleeve of a centrifugal governor has both positive and negative effects on its performance. While it can make the governor more stable, it can also reduce its sensitivity and range of speed. It is therefore important to minimize friction in the governor to ensure that it performs optimally.

The Carioles component of acceleration is present
          [GATE-2002]
  • a)
    4-bar mechanisms with 4 turning pairs
  • b)
    shaper mechanism
  • c)
    slider-crank mechanism
  • d)
    Scotch Yoke mechanism
Correct answer is option 'B'. Can you explain this answer?

Anjali Shah answered
Explanation:
The question is related to the component of acceleration present in different mechanisms. Let's discuss each option and find out the correct answer.

a) 4-bar mechanisms with 4 turning pairs:
A 4-bar mechanism consists of four links connected by four turning pairs. The turning pairs can be revolute or prismatic joints. This mechanism is widely used in various applications such as engines, machines, and robotics. However, the component of acceleration present in this mechanism is not related to the question. Therefore, option A is not correct.

b) Shaper mechanism:
The shaper mechanism is a type of reciprocating machine tool. It is used to produce flat or curved surfaces on a workpiece. This mechanism consists of a ram, a cutting tool, and a worktable. The component of acceleration present in this mechanism is the Carioles component of acceleration. Therefore, option B is correct.

c) Slider-crank mechanism:
The slider-crank mechanism is a type of reciprocating mechanism used in engines, pumps, and compressors. It consists of a piston, a connecting rod, and a crankshaft. The component of acceleration present in this mechanism is the tangential component of acceleration. Therefore, option C is not correct.

d) Scotch Yoke mechanism:
The Scotch Yoke mechanism is a type of reciprocating mechanism used in engines and compressors. It consists of a yoke, a piston, and a crankshaft. The component of acceleration present in this mechanism is the radial component of acceleration. Therefore, option D is not correct.

Conclusion:
From the above explanation, we can conclude that the correct answer is option B, i.e., Shaper mechanism. The Carioles component of acceleration is present in the shaper mechanism.

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