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# How to Prepare Theory of Machines for GATE Mechanical Engineering

I am writing this blog on Theory of Machines (TOM) and Vibration for the GATE Mechanical/Production & Industrial aspirants. Theory of Machines (TOM) & Vibration is a very important subject from the GATE exam point of view.

This blog will be very useful for those aspirants who are doing self-study. The problem in this subject is the newly added topics which becomes a bit problematic for the aspirants as they don’t get relevant questions to practice.

Follow this blog to prepare Theory of Machines for GATE exam.

Note: In this blog, the time duration and day wise analysis are given, the so, time taken by any aspirants may vary that depends on the aspirant’s intellectual.

## Marks analysis of Theory of Machines according to previous year questions has been shown below:

1. Displacement, velocity and acceleration analysis of plane mechanisms – 102 marks
 Marks No. of questions 1 mark 30 2 marks 31 5 marks 4

2. Dynamic analysis of linkages – 25 marks

 Marks No. of questions 1 mark 3 2 marks 7 5 marks 2

3. Gears and gear trains – 66 marks

 Marks No. of questions 1 mark 15 2 marks 19 5 marks 3

4.Flywheel – 31 marks

 Marks No. of questions 1 mark 3 2 marks 10 5 marks 2

5.Balancing of rotating & reciprocating masses – 12 marks

 Marks No. of questions 1 mark 1 2 marks 3 5 marks 1

6.Vibration – 144 marks

 Marks No. of questions 1 mark 30 2 marks 44 5 marks 6

7. CAMS – 4 marks

 Marks No. of questions 1 mark 1 2 marks 4

## Tips & Tricks and Strategy to Prepare Theory of Machines for GATE Exam

Below mentioned are some of the important topics that you need to study wholeheartedly to prepare Theory of Machines

Displacement, velocity and acceleration analysis of plane mechanisms (Duration-4 days)

Day-1

TOPICS: Mechanism and Machine, Types of constrained motion, Rigid and resistant Bodies, Link, Kinematic Pair (Lower pairs, higher pairs etc.), Types of joints, Degree of Freedom(DOF), Classification of Kinematics Pairs, Kinematics Chain, Linkage, Mechanism and structure, Mobility of Mechanisms, Application of Kutzbach Criterion to plane mechanisms, Grubler’s criterion for plane mechanisms.

Tips and Instructions: Questions on Degree of freedom(mobility) should be practiced a lot & should attempt Chapter wise test. After attempting test note down the mistakes in a separate copy and new formula which you learned from the test. This pattern of test should be followed for all the units.

In this section, visualization will help you to solve some tricky questions of DOF. Don’t forget to learn the difference between redundant DOF and redundant link.

There is a good number of questions that has been asked in GATE so practicing those questions is highly recommended.

No. of hours required for clearing concepts & solving questions: 10-12 hours

Books: Khurmi & Gupta or SS Rattan. SS. Rattan is more preferred for both Concept and Questions.

Day-2

Solve lots of questions of the “Day-1” topics from the standard books which are mentioned.

TOPICS: Equivalent Mechanisms, The Four-bar Chain, Mechanical Advantage, Transmission angle, The slider-crank Chain & its inversion, Double Slider-crank chain & its inversion, Miscellaneous Mechanisms.

Tips and Instructions: Practice numerical from the standard books as mentioned below and solve previous year GATE questions as much as possible. In this section try to memorize the names of all the inversions of slider-crank and double slider crank.

No. of hours required for clearing concepts & solving questions: 8-10 hours

Books: Khurmi & Gupta and SS Rattan.

Day-3

Velocity analysis

TOPICS: Absolute and relative motion, Vectors, Addition and subtraction of vectors, Motion of a link, Four-link Mechanism, the Angular velocity of links, Velocity of rubbing, Velocity in the slider-crank mechanism, Crank & slotted lever mechanism, Kennedy’s theorem, Locating I-centers, Angular velocity theorem.

Tips and Instructions: This is the favorite topic of the GATE as questions from this topic is very much probable of coming in GATE, so it is necessary to practice more no. of numerical from this topic. Almost every year the question comes from this topic and the questions are quite tricky but easy to practice as many as problems.

No. of hours required for clearing concepts & solving questions: 10-12 hours

Books: Khurmi & Gupta and SS Rattan.

Day-4

Revise & Practice Question of velocity analysis and attempt chapter test as much as possible.

Acceleration analysis

TOPICS: Slider-crank mechanism, Coriolis acceleration component, Crank and slotted-lever mechanism, Practice questions from standard books.

Instructions and Tips: Coriolis acceleration component is the very important topic from the acceleration analysis. In this topic, you must learn how to find the direction of different accelerations.

No. of hours required for clearing concepts & solving questions: 4-5 hours

Books: Khurmi & Gupta and SS Rattan.

Dynamic analysis (Duration-1 Day)

Day-5

TOPICS: D’Alembert’s Principle, Dynamic analysis of slider-crank mechanisms, velocity, and acceleration of a piston, Engine force analysis, turning moment on the crankshaft, Inertia Force in reciprocating engines (Graphical method), Force on connecting rod, Force on Bearing.

Instructions and Tips: Force analysis of slider-crank mechanism for finding the values of forces in different components like connecting rod, gudgeon pin, bearings, turning moment etc. should be done properly from the standard book (Khurmi & Gupta)

No. of hours required for clearing concepts & solving questions: 4-5 hours

Books: Khurmi & Gupta (For concepts and Questions)

Gears and gear trains (Duration- 3 Days)

Day-6 & 7

Gears: This topic covers both theoretical and numerical questions. Solve Previous year GATE questions too.

TOPICS: Classification of Gears, Gear Terminology, Law of Gearing (Diagram is very important), Velocity of sliding, Forms of teeth, Cycloidal & Involute Profile teeth, Path of contact, Arc of contact, Contact Ratio, Interference in Involute gears, Minimum no. of teeth, Interference between Rack and pinion, Undercutting, Comparison of cycloidal and involute Tooth Forms

No. of hours required for clearing concepts & solving questions: 10-12 hours

Books: SS Rattan (For Concept & Questions) and Khurmi & Gupta (For Questions).

Day-7 & 8

Gear Trains: This is the very important topic from the GATE exam point of view, one question is fixed from the Gear train almost every year. Mostly numerical questions are asked about this topic. This is a very scoring topic so don’t dare to leave this topic and try to solve all the examples from the standard books given below. A good number of questions has been asked in GATE from this topic so practicing those questions is highly recommended. Solve previous year GATE question at least 2-3 times.

TOPICS: Types of gear trains, simple gear train, Compound gear train, Epicyclic gear train and its velocity ratio, Compound epicyclic gear train (Sun and planet wheel), Torques in epicyclic gear trains.

No. of hours required for clearing concepts & solving questions: 10-12 hours

Books: SS Rattan (For Concept & Questions) and Khurmi & Gupta (For Questions).

Turning Moment diagrams & flywheel (Duration- 1 Day)

Day-9

This is a very easy and scoring topic. In this topic, you must know the formulas and few important concepts regarding work is done/cycle, power and Turning moment diagrams. Solve questions from the standard book mentioned below and previous year questions at least 2-3 times.

TOPICS: Turning moment Diagram for a four-stroke cycle internal combustion Engine, Turning moment Diagram for a multi-cylinder Engine. Fluctuation of Energy, Determination of Maximum fluctuation of energy, Coefficient of fluctuation of Energy, Coefficient of fluctuation of speed, Energy stored in a Flywheel, Dimensions of Flywheel Rim, Flywheel in punching press.

Though punching press & dimension of flywheel rim are not so important but if you prepare for it, it may give you an extra edge during your exam if a question comes as Gate is unpredictable now a day so you can’t leave any topic.

No. of hours required for clearing concepts & solving questions: 10-12 hours

Books: Khurmi & Gupta (For concepts and Questions)

Balancing of rotating & reciprocating masses (Duration- 1 Day)

Day-10

TOPICS: Static balancing, Dynamic Balancing, balancing of several masses in different planes, Balancing of Reciprocating mass, Primary & secondary unbalanced forces of reciprocating masses, Partial balancing of unbalanced primary force in a reciprocating Engine, Variation of tractive force, Swaying couple, Hammer blow.

Tips and Instructions: This topic is not so important. You will find very fewer questions in the previous year but solving those few questions are highly recommended as it will give you the idea of questions. For practicing question, you can solve previous year ESE questions and standard books. Also, try to attempt a chapter test.

No. of hours required for clearing concepts & solving questions: 5-6 hours

Books: Khurmi & Gupta (For concepts and Questions)

Vibration (Duration- 4 Days)

Day-11 & 12

SECTION-1(LONGITUDINAL VIBRATION)

TOPICS: Free Longitudinal Vibrations, Displacement, Velocity, acceleration, Inertia effect of the mass of spring, Damped Vibrations, Logarithmic decrement, Forced Vibrations, Forced-damped Vibrations, Magnification factor, Vibration Isolation, and transmissibility, forcing due to unbalance, Forcing due to support the motion.

Tips and Instructions: All the topics are important from this unit. Every year 2-3 marks questions are fixed in each of the set of the Mechanical stream. Solve questions from the previous year GATE at least 2-3 times before the GATE exam, standard books mentioned below and attempt online test as much as possible.

Learn the concept from the standard book (“SS Rattan”) and then solve the examples given in it and make notes of all the important formula and concept. There are good questions has been asked in GATE so practicing those questions are highly recommended.

No. of hours required for clearing concepts & solving questions: 10-12 hours/day

Books: SS Rattan (For Concept & Questions) and Khurmi & Gupta (For Questions).

Day-13 & 14

SECTION-2(TRANSVERSE VIBRATION)

SECTION-3(TORSIONAL VIBRATION)

TOPICS: Free Torsional Vibrations (Single Rotor), Inertia effect of the mass of shaft, Free Torsional Vibrations (2 rotor and 3 rotor system), Torsionally equivalent shaft.

Tips and Instructions: Learn concepts from the “SS Rattan” book, make notes from it and solve previous year questions at least 2-3 times before the exam. Also solve questions of Longitudinal Vibration simultaneously.

Books: SS Rattan (For Concept & Questions) and Khurmi & Gupta (For Questions).

No. of hours required for clearing concepts & solving questions: 10-12 hours/day

Note: I will recommend to solve as many as problems of vibration and revise the concepts and formula regularly and try to attempt as many as the test of this unit. It is scoring and an important topic.

Gyroscope (Duration- 1 Day)

Day-15

TOPICS: Angular velocity, Angular acceleration, precessional angular motion, Gyroscopic torque(couple), Effect of Gyroscopic couple on an Aeroplane, Terms used in Naval ships, Effect of Gyroscopic couple on a Naval ship during pitching, rolling, steering, Effect of Gyroscopic couple on a disc Fixed rigidly at a certain angle to a rotating shaft, Stability of a four-wheel drive moving in a curved path, Stability of a two-wheel vehicle taking a turn.

Tips and Instructions: This is the newly added topic in gate mechanical syllabus so few questions have been in the previous year so learn concept from standard books and solve previous year questions ESE and solved examples of standard books. Till now very easy and formula-based question have been asked in GATE.

Books: Khurmi & Gupta or SS Rattan for concepts and questions.

Governor (Duration- 1 Day)

Day-16

TOPICS: Types of Governors, Centrifugal Governors, Terms used in Governors, Watt governors, Porter Governors, Proell governors, Hartnell Governors, Hartung Governors, Wilson-Hartnell Governors, Pickering governors, Sensitiveness of Governors, Stability of Governors, Isochronous Governors, Hunting, Effort and power of a Porter Governor, controlling force, Controlling force Diagram for a Porter governor and spring-controlled governor, coefficient of insensitiveness

Tips and Instructions: This is also a newly added unit in GATE. Till now no questions have been asked in GATE but ESE previous questions are recommended to solve for practice. This is not so important topic but it is recommended to cover this topic as it is probable that GATE authority may ask questions from this topic as the questions from this topic have never been asked after it was included in the syllabus. So be prepared for the worst situation.

No. of hours required for clearing concepts & solving questions: 10-12 hours

Books: Khurmi & Gupta is recommended for solving questions and for learning concept.

So in all it would take approximately 16 days of your serious determination to prepare Theory of Machines. Don’t forget to practice lots and lots of numerical especially previous year questions of mechanical for GATE Preparation.