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

 A slider crank mechanism is shown in the given figure.
Which of the following expressions stand for crank effort?
1. 
2. 
3.  Fs . OM
4. FT.r
Select the correct answer using the codes given below
  • a)
    1 and 3
  • b)
    1,2 and 4
  • c)
    1, 2 and 3
  • d)
    2, 3 and 4
Correct answer is option 'A'. Can you explain this answer?

Sanvi Kapoor answered
Crank effort: Force is exerted on the crank pin as a result of the force on the piston. Crank effort is the net effort (force) applied at the crank pin perpendicular to the crank which gives the required turning moment on the crank shaft

The safe rim velocity of a flywheel is influenced by the
  • a)
    centrifugal stresses
  • b)
    fluctuation of energy
  • c)
    fluctuation of speed
  • d)
    mass of the flywheel
Correct answer is option 'A'. Can you explain this answer?

Avinash Sharma answered
Rim velocity 
where
σ = centrifugal stress of circumferential stress
ρ = density of rim materia!
Hence, rim velocity is the function of centrifugal stress and density of rim material.

The space centrode of a circular disc rolling on a straight path is
  • a)
    a circle
  • b)
    a parabola
  • c)
    a straight line
  • d)
    ellipse
Correct answer is option 'C'. Can you explain this answer?

Arnav Menon answered
Explanation:

The space centrode of a circular disc rolling on a straight path is a straight line.

Definition of Space Centrode:

The space centrode is the locus of the instantaneous centers of rotation of a rolling body. It is a curve that describes the path traced by the point of contact of two bodies in rolling contact. For a disc rolling on a straight path, the space centrode is a straight line.

Derivation:

Consider a circular disc of radius r rolling on a straight path. Let O be the center of the disc, and P be the point of contact between the disc and the path. Let C be the instantaneous center of rotation of the disc, and let Q be the point of contact between the disc and its image in a plane perpendicular to the path.

Now, as the disc rolls, the point P moves along the path, and the point Q moves along a circle of radius r centered at C. Therefore, the locus of C is a straight line passing through the point of contact P.

Hence, the space centrode of a circular disc rolling on a straight path is a straight line.

Applications:

The concept of space centrode is widely used in kinematics and dynamics of machinery. It is used to analyze the motion of rolling bodies, such as gears, cams, and rollers. The knowledge of space centrode helps in designing mechanisms with desired motion characteristics, such as constant velocity, acceleration, and deceleration. It also helps in minimizing wear and tear of the contacting surfaces, by ensuring that the instantaneous centers of rotation lie on the surfaces.

Identity the wrong statement:
  • a)
    Turning-moment-diagram is graphical representation of turning moment or crank effort for various positions of the crank.
  • b)
    The area of turning -moment-diagram represents the work done.
  • c)
    The variation of energy above and below the mean resisting torque line is called fluctuation of energy.
  • d)
    The coefficient of fluctuation of energy is defined as the ratio of work done per cycle to the maximum fluctuation of energy.
Correct answer is option 'D'. Can you explain this answer?

Pranavi Gupta answered
Explanation:

Incorrect Statement:
The coefficient of fluctuation of energy is defined as the ratio of work done per cycle to the maximum fluctuation of energy.

Explanation:
The coefficient of fluctuation of energy is actually defined as the ratio of the difference between the maximum and minimum energies to the mean energy. It gives an indication of how much energy fluctuates above and below the mean energy level during a cycle.

Correct Definition:
The coefficient of fluctuation of energy is given by the formula:
Coefficient of fluctuation of energy = (Emax - Emin) / Emean
Where:
- Emax is the maximum energy during a cycle
- Emin is the minimum energy during a cycle
- Emean is the mean energy during a cycle
This coefficient helps in analyzing the variation in energy levels and is an important parameter in the study of machine dynamics and performance. It provides insights into the efficiency and smooth operation of machines.
Therefore, the correct definition and calculation of the coefficient of fluctuation of energy are crucial in understanding the energy dynamics of a system and optimizing its performance.

The cam follower used in aircraft engies is a
  • a)
    roller follower
  • b)
    flat faced follower
  • c)
    spherical faced follower
  • d)
    knife edged follower
Correct answer is option 'A'. Can you explain this answer?

Automobile engines generally used spherical faced follower, whereas roller followers are used in aircraft engines. Surface stresses are minimum in mushroom follower with spherical face.

Toggle mechanisms have following applications except
  • a)
    stone crushers
  • b)
    gear cutting
  • c)
    embossing presses
  • d)
    switches
Correct answer is option 'B'. Can you explain this answer?

The mechanisms used to overcome a large resistance of a member with a small driving force are known as snap action or toggle mechanisms. They find their use in a variety of machines such as stone crushers, embossing presses, switches etc.

The transmission angle is minimum and maximum respectively, when the crank angle with the fixed link is
  • a)
    00 and 2700
  • b)
    900 and 2700
  • c)
    00 and 1800
  • d)
    00 and 900
Correct answer is option 'C'. Can you explain this answer?

Rohan Singh answered
Explanation:

The transmission angle is defined as the angle between the coupler link and the output link. It is an important parameter that determines the smoothness of motion in a four-bar linkage mechanism. The optimal transmission angle is 0°, which means that the coupler and output links are aligned. However, in practice, it is not always possible to achieve this ideal condition. Therefore, the transmission angle is usually designed to be as close to 0° as possible.

The transmission angle varies with the crank angle, which is the angle between the fixed link and the crank link. The crank angle determines the position of the mechanism, and it changes as the mechanism moves. The transmission angle is minimum or maximum at specific crank angles, which depend on the geometry of the mechanism.

The transmission angle is minimum when the coupler and output links are parallel, which means that they have the same slope. This occurs when the crank angle is 0° or 180°, which corresponds to the top and bottom dead center positions of the mechanism. At these positions, the coupler link is perpendicular to the fixed link, and the output link is parallel to the fixed link. Therefore, the transmission angle is minimum at crank angles of 0° and 180°.

The transmission angle is maximum when the coupler and output links are perpendicular, which means that they have opposite slopes. This occurs when the crank angle is 90° or 270°, which corresponds to the mid-stroke positions of the mechanism. At these positions, the coupler link is parallel to the fixed link, and the output link is perpendicular to the fixed link. Therefore, the transmission angle is maximum at crank angles of 90° and 270°.

Therefore, the correct answer is option C, which states that the transmission angle is minimum and maximum at crank angles of 0° and 180°, and 90° and 270°, respectively.

The problem of hunting of a centrifugal governor becomes very acute when the governor becomes
  • a)
    less sensitive
  • b)
    highly sensitive
  • c)
    high stable
  • d)
    less stable
Correct answer is option 'B'. Can you explain this answer?

Sensitiveness of a governor is a desirable quality. However, if a governor is too sensitive, it may fluctuate continuously above and below the mean position, it is called hunting of governor.

Klein’s construction is a graphical method of determining
  • a)
    acceleration of various parts
  • b)
    velocity of various parts
  • c)
    displacement of various parts
  • d)
    forces acting on various parts
Correct answer is option 'A'. Can you explain this answer?

Pankaj Joshi answered
Klein’s construction for reciprocating engine mechanism:
(i) has a simpler construction for getting quadrilateral similar to the diagram of mechanism for reciprocating engine.
(ii) is applicable when the crank has uniform angular velocity.
(iii) is used to determine the linear velocity and acceleration of piston.

In a simple gear train, if the number of idle gears is odd, then the motion of driven gear will 
  • a)
    be opposite as that of driving gear 
  • b)
    be same as that of driving gear 
  • c)
    depend upon the number of teeth on the driving gear 
  • d)
    none of the mentioned
Correct answer is option 'B'. Can you explain this answer?

Sanvi Kapoor answered
The speed ratio and the train value, in a simple train of gears, is independent of the size and number of intermediate gears. These intermediate gears are called idle gears, as they do not affect the speed ratio or train value of the system.

Match List - I (Terms) with List - II (Definitions) and select the correct answer using the codes given below the lists:
List-I
A. Module
B. Addendum
C. Circular pitch
List-II
1. Radial distance of a tooth from the pitch circle to the top of the tooth
2. Radial distance of a tooth from the pitch circle to the bottom of the tooth
3. Distance on the circumference of the pitch circle from a point of one tooth to the corresponding point on the next tooth
4. Ratio of pitch circle diameter in mm to the number of teeth
Codes:
     A B C
(a) 4 1 3
(b) 4 2 3
(c) 3 1 2
(d) 3 2 4
  • a)
    (a)
  • b)
    (b)
  • c)
    (c)
  • d)
    (d)
Correct answer is option 'A'. Can you explain this answer?

Explanation:

Module:
- Module is the ratio of pitch circle diameter in mm to the number of teeth.
- It is represented as M = D/N, where M is the module, D is the pitch circle diameter, and N is the number of teeth.

Addendum:
- Addendum is the radial distance of a tooth from the pitch circle to the top of the tooth.
- It is the height of the tooth above the pitch circle.

Circular pitch:
- Circular pitch is the distance on the circumference of the pitch circle from a point of one tooth to the corresponding point on the next tooth.
- It is the distance between corresponding points on adjacent teeth measured along the pitch circle.

Correct answer:
The correct match for each term is:
- Module: Ratio of pitch circle diameter in mm to the number of teeth (4)
- Addendum: Radial distance of a tooth from the pitch circle to the top of the tooth (1)
- Circular pitch: Distance on the circumference of the pitch circle from a point of one tooth to the corresponding point on the next tooth (3)
Therefore, the correct answer is option (a) 4 1 3.

The locus of instantaneous center of a moving body relative to a fixed body is known as the
  • a)
    space centrode
  • b)
    bodycentrode
  • c)
    moving centrode
  • d)
    none of these
Correct answer is option 'A'. Can you explain this answer?

Arnab Saini answered
A centrode is the locus of the I-center of a plane body relative to another plane body for the range of motion specified or during a finite period of time.
Space centrode (or fixed centrode) is the locus of the I-center of the moving body relative to the fixed body.
Body centrode (or moving centrode) is the locus of the I-center of the fixed body relative to the movable body.

The lead screw of a lathe with nut is a
  • a)
    roiling pair
  • b)
    screw pair
  • c)
    turning pair
  • d)
    sliding pair
Correct answer is option 'B'. Can you explain this answer?

Isha Nambiar answered
If two mating links have a turning as well as sliding motion between them, they form a screw pair. This is achieved by cutting matching threads on the two links. The lead screw and the nut of a lathe is a screw pair.

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