Questions
6–8 MCQs per paper
Difficulty
Medium-Hard
Importance
Core — never skip
Overview
Theory of Machines (TOM) is the core mechanical engineering discipline dealing with the study of relative motion, forces, and dynamic behavior of machine components. For PSU exams, it is a high-yield topic because it bridges the gap between basic kinematics and machine design, frequently appearing in recruitment papers for BHEL, NTPC, and ONGC. Mastering this requires a firm grasp on the mathematical modeling of motion and the balancing of dynamic forces.
Kinematics of Mechanisms
This sub-topic focuses on the geometry of motion and the mobility of links connected in a kinematic chain. Understanding Grubler's and Kutzbach criteria is essential for determining the degrees of freedom in common mechanical linkages.
- Grubler's criterion: F = 3(n-1) - 2j - h
- Kutzbach criterion: F = 3(n-1) - 2j1 - 1j2
- Inversions of four-bar chain: Beam engine, Coupling rod, Watt's indicator
- Grashof's law: s + l <= p + q for continuous rotation
- Coriolis acceleration: ac = 2 * omega * v
Gear Trains and Flywheels
Gear trains involve analyzing speed ratios in simple, compound, and epicyclic arrangements, while flywheels are used to regulate cyclic fluctuations in energy. Focus on the coefficient of fluctuation of speed and energy.
- Epicyclic gear ratio: N = (Na - Nc) / (Nb - Nc)
- Coefficient of fluctuation of speed (Cs) = (w1 - w2) / w_mean
- Max fluctuation of energy (Delta E) = I * w_mean^2 * Cs
- Tractive effort in gear systems
- Sun and planet gear constraints
Governors
Governors regulate the mean speed of an engine under varying load conditions by controlling the fuel supply. The study of sensitivity, isochronism, and hunting is vital for understanding governor performance.
- Watt governor: h = 895 / N^2
- Porter governor: h = (m + M/2) / m * (895 / N^2)
- Proell governor: spring-loaded mechanism
- Sensitivity = (N2 - N1) / N_mean
- Hunting occurs in overly sensitive governors
Balancing and Vibrations
Balancing involves the elimination of unbalanced forces and couples in rotating and reciprocating masses to prevent excessive vibrations. Vibrations analysis covers free, forced, and damped motion, which are critical for rotating machinery stability.
- Static balancing: Sum of forces = 0
- Dynamic balancing: Sum of couples = 0
- Primary unbalance force = m * omega^2 * r * cos(theta)
- Magnification factor (MF) = 1 / sqrt((1 - r^2)^2 + (2 * zeta * r)^2)
- Transmissibility ratio TR = sqrt((1 + (2 * zeta * r)^2) / ((1 - r^2)^2 + (2 * zeta * r)^2))
Formula Sheet
F = 3(n-1) - 2j - h
ac = 2 * omega * v
h = 895 / N^2 (Watt)
h = (m+M/2)/m * (895/N^2) (Porter)
Delta E = I * omega^2 * Cs
Magnification Factor = 1 / sqrt((1-r^2)^2 + (2*zeta*r)^2)
Natural frequency wn = sqrt(k/m)
Critical damping Cc = 2 * sqrt(k*m)
Exam Tip
Always memorize the formulas for the height of various governors (Watt, Porter, Proell) as these are direct 'plug-and-play' question favorites in PSU exams.
Common Mistakes
- Confusing primary and secondary balancing forces for reciprocating masses.
- Neglecting the impact of friction in damped vibration problems.
- Miscalculating the number of joints or lower/higher pairs in complex kinematic linkages.
More Revision Notes
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