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Theory of Machines & Vibrations

Theory of Machines & Vibrations for GATE Mechanical Engineering, one topic per lesson: the theory in plain words, the formulas, a solved example, and GATE-style questions (MCQ, MSQ and NAT) whose numerical answers are recomputed by a program when the site is built.

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1Mechanisms

  1. Mechanisms, Kinematic Pairs and Degrees of FreedomLinks, kinematic pairs and chains, Grübler's criterion for degrees of freedom, Grashof's law, inversions of the four-bar and slider-crank chains, and quick-return mechanisms.
  2. Velocity, Acceleration and CamsRelative velocity method, instantaneous centres and Kennedy's theorem, Coriolis acceleration, slider-crank kinematics, and cam follower motions and terminology.

2Power Transmission

  1. Gears and Gear TrainsGear terminology, the law of gearing, involute teeth, module, interference and minimum teeth, and speed ratios of simple, compound and epicyclic gear trains.
  2. Flywheels, Governors, Balancing and GyroscopeTurning moment diagrams and flywheel size, coefficient of fluctuation, governors (Watt, Porter, Hartnell) and their sensitivity, balancing of rotating and reciprocating masses, and gyroscopic couple.

3Vibrations

  1. Free, Damped and Forced VibrationsNatural frequency of single-degree-of-freedom systems, damping ratio and logarithmic decrement, forced vibration and resonance, transmissibility, vibration isolation and critical speed of shafts.