Theory of Machines Important Questions
Theory of Machines (TOM) is a core mechanical engineering subject that deals with the study of motion and forces in mechanical systems. For R20 JNTU students, it’s a scoring subject that combines both theory and practical application — useful for understanding automotive systems, machinery design, robotics, and manufacturing automation.
This guide provides unit-wise key theory questions, numerical focus areas, formulas, and exam tips — everything needed to prepare effectively for your Theory of Machines exam.
Theory of Machines Unit-wise Important Questions
Unit 1: Kinematics of Machines
Key Theory Questions
Define link, pair, and chain in kinematic systems.
Explain the difference between mechanism and machine.
What are lower and higher pairs? Give practical examples.
Define Grashof’s Law and its significance.
State and explain Gruebler’s Criterion for mobility.
What is a kinematic inversion? Explain with examples.
Explain the four-bar mechanism and its types.
Describe the single slider crank mechanism and its inversions.
Explain the double slider crank chain and list its applications.
Define quick return mechanism.
What is an elliptical trammel?
Explain beam engine and oscillating cylinder mechanism.
Define coupler curve and its significance.
What are pantograph mechanisms?
Explain straight-line generating mechanisms.
Differentiate between mechanism and structure.
Explain Ackermann steering gear mechanism.
Describe types of motion in kinematics.
Write short notes on toggle mechanism.
What is the difference between open and closed kinematic chains?
Numerical Focus Areas
Velocity ratio (VR) calculations for different mechanisms.
Gruebler’s criterion problems.
Velocity and acceleration of links in four-bar and slider-crank mechanisms.
Instantaneous center method for velocity analysis.
Important Formulas
Mobility:
F = 3(n−1)−2j−hAngular velocity:
ω = V / rRelative velocity:
V_B/A = ω × rTransmission angle (μ):
μ = tan⁻¹(V₂/V₁)
Unit 2: Velocity and Acceleration Analysis of Mechanisms
Key Theory Questions
Define absolute, relative, and link velocities.
What is the Coriolis component of acceleration?
Explain Klein’s construction with neat diagrams.
Derive the acceleration of a point on a rotating link.
Explain analytical method for velocity and acceleration.
Define angular acceleration and its physical meaning.
Explain link polygon and vector diagrams.
Describe instantaneous center method for acceleration analysis.
Write short notes on centripetal and tangential acceleration.
Discuss velocity polygons for simple mechanisms.
Explain Coriolis acceleration formula (2ωvr).
Define relative acceleration between two points on a link.
What are rotating slider mechanisms?
Explain the procedure for constructing acceleration diagrams.
Describe mechanism synthesis using graphical method.
Numerical Focus Areas
Velocity and acceleration of piston in slider-crank mechanisms.
Determination of Coriolis acceleration.
Angular velocity and acceleration analysis using Klein’s method.
Acceleration of connecting rod and crank pin in mechanisms.
Important Formulas
Tangential acceleration:
a_t = r × αCentripetal acceleration:
a_c = ω² × rCoriolis acceleration:
a_c = 2ωvr
Unit 3: Dynamics of Machines
Key Theory Questions
Explain D’Alembert’s Principle.
Define inertia force and inertia torque.
What is a turning moment diagram?
Define flywheel and explain its function.
What are fluctuations of energy?
Explain governor mechanism and its purpose.
Differentiate between flywheel and governor.
What is a centrifugal governor?
Define coefficient of fluctuation of speed.
Explain Porter and Proell governors.
What are isochronous and sensitive governors?
Explain hunting in governors.
Discuss balancing of rotating masses.
Derive conditions for complete balancing.
Define mass moment of inertia (I = m·k²).
What is a crank effort diagram?
Explain energy stored in a flywheel with formula.
Describe flywheel design considerations.
Numerical Focus Areas
Problems on energy stored in a flywheel (E = ½ Iω²).
Governor effort and power calculations.
Fluctuation of speed and energy.
Turning moment diagrams for engines.
Balancing of rotating masses using graphical method.
Important Formulas
Energy stored:
E = ½ I (ω₁² − ω₂²)Fluctuation of speed:
(N₁ − N₂) / N_meanGovernor height (Watt):
h = 895 / N²
Unit 4: Gear Trains and Cams
Key Theory Questions
Define gear train and its types.
What is a simple gear train?
Explain compound and reverted gear trains.
Describe epicyclic gear trains.
Explain the law of gearing.
Define addendum, dedendum, and module.
What is interference in gears?
Explain gear terminology with diagrams.
What is a cam and follower?
Differentiate between radial and cylindrical cams.
Explain uniform velocity, simple harmonic, and cycloidal motion.
Define pitch circle and pressure angle.
Explain displacement diagram for a cam.
What are follower types and their motion curves?
Define cam profile and list design considerations.
Numerical Focus Areas
Problems on gear ratio (N₂/N₁ = T₁/T₂).
Train value of simple, compound, and epicyclic gear trains.
Cam profile and displacement analysis.
Involute profile calculations for gears.
Important Formulas
Velocity ratio:
VR = T₂/T₁Module:
m = D / TTrain value:
TV = N₁/N₂
Unit 5: Governors and Flywheels
Key Theory Questions
Define governor and explain its purpose.
Explain Porter, Proell, Watt, and Hartnell governors.
Define sensitivity, stability, and isochronism.
Derive height of governor formula (h = 895/N²).
Explain working of centrifugal governors.
Discuss spring-loaded governors.
Differentiate between inertia and centrifugal governors.
Explain hunting and stability of governors.
Define coefficient of speed regulation.
Explain flywheel function and energy storage principle.
Describe fluctuation of energy and speed.
Explain turning moment diagram and its significance.
Discuss design parameters of flywheels.
Numerical Focus Areas
Height of governor and controlling force calculations.
Flywheel energy storage and moment of inertia problems.
Fluctuation of speed calculations.
Unit 6: Balancing of Machines
Key Theory Questions
Explain static and dynamic balancing.
Why is balancing important in engines?
Describe balancing of several rotating masses in one plane.
Explain balancing of reciprocating masses.
Derive conditions for complete balancing.
What are primary and secondary unbalanced forces?
Discuss balancing of V-engines and inline engines.
Explain couples in dynamic balancing.
Define balancing machine and its operation.
Discuss effects of unbalanced forces on bearings.
Explain balancing of multi-cylinder engines.
Numerical Focus Areas
Graphical balancing (polygon method).
Primary and secondary force calculations.
Reciprocating mass balancing in engines.
Unit 7: Vibration Analysis
Key Theory Questions
Define vibration and list its types.
Explain free, forced, and damped vibrations.
Derive equation of motion for simple harmonic vibration.
Define natural frequency and resonance.
Explain damping ratio and logarithmic decrement.
What is critical damping coefficient?
Explain torsional vibration.
Describe vibration isolation and transmissibility.
Discuss whirling speed of shafts.
Define critical speed and its effect on rotors.
Explain viscous damping and spring-mass systems.
Numerical Focus Areas
Natural frequency (f = 1/2π √(k/m)).
Transmissibility ratio (T = X/Y).
Critical speed and torsional vibration problems.
Logarithmic decrement calculations.
Practice Numerical Questions
A flywheel stores 10 kJ of energy at 300 rpm. Calculate the mass moment of inertia.
Determine the natural frequency of a spring-mass system (k = 2000 N/m, m = 10 kg).
A Watt governor runs at 200 rpm with arms of 300 mm. Find the equilibrium speed for a height of 200 mm.
Two masses 5 kg and 3 kg rotate at radii of 0.2 m and 0.3 m respectively. Find the balancing mass at 0.25 m radius.
In a slider-crank mechanism, crank length is 100 mm and connecting rod is 400 mm. Find the acceleration of the piston when crank angle is 45°.
A simple gear train has driver gear 20 teeth, idler 40 teeth, and driven gear 60 teeth. Find the speed ratio.
A Proell governor runs at 250 rpm. Calculate controlling force when radius is 150 mm.
Determine the flywheel mass required for a machine with fluctuation of energy 5 kJ at 200 rpm.
Preparation Tips for R20 JNTU TOM Exam
Focus on diagram-based questions (cams, governors, gear trains).
Practice balancing and vibration numericals daily.
Revise key formulas and dimension analysis weekly.
Don’t skip previous year question papers — many repeat.
Understand each mechanism practically using animation or models.
Prepare short notes for definitions and laws.
Conclusion
The Theory of Machines is the foundation for all moving systems in mechanical engineering. A strong grip on kinematics, dynamics, balancing, and vibration will help you not only in university exams (R20 JNTU) but also in GATE, PSU, and interview preparation.
With consistent revision, visual understanding, and regular numerical practice, you’ll master both conceptual clarity and application skills in this vital subject.
