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Recent questions and answers in Theory of Machines

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GATE Mechanical 2025 | Question: 16
​​​​​A rigid circular disc of radius $r$ (in $m$ ) is rolling without slipping on a flat surface as shown in the figure below. The angular velocity of the disc is $\omega...
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188
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GATE Mechanical 2026 | Question: 6
A horizontal disk has a radial frictionless slot in which a small block is confined to slide. The disk turns anticlockwise about its centre with a constant angular veloci...
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GATE Mechanical 2026 | Question: 7
A gear train with five gears is shown in the figure below. The number of teeth on each gear is $\mathrm{N}_{1}, \mathrm{~N}_{2}, \mathrm{~N}_{3}, \mathrm{~N}_{4}$, and $\...
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GATE Mechanical 2026 | Question: 10
The rotor of an aeroplane engine has a mass moment of inertia $1.0 \mathrm{~kg} \mathrm{~m}^{2}$. The engine rotates at a speed of $500$ RPM in the clockwise direction if...
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GATE Mechanical 2026 | Question: 12
Worm gearsets are used for transmitting rotary motion betweennon-parallel and non-intersecting shaftsintersecting shaftsparallel shaftsnon-parallel and intersecting shaft...
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Suppose that with a pulley system, youneed to exert a force of 1,400 N to lifta heavy object. But without the pulleysystem, you need to exert 4,200 N tolift the object. W...
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613
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GATE Mechanical 2025 | Question: 19
​​​​​In the context of balancing of rotating and reciprocating masses, which one of the following options is true?An unbalanced rigid rotor can be completely balanced usi...
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465
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GATE Mechanical 2025 | Question: 50
An offset slider-crank mechanism is shown in the figure below. The length of the stroke of the slider is __________ $mm$ (rounded off to nearest integer).
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793
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GATE Mechanical 2024 | Question: 13
​​​​The change in kinetic energy $\Delta E$ of an engine is $300 \mathrm{~J}$, and minimum and maximum shaft speeds are $\omega_{\min }=220 \mathrm{rad} / \mathrm{s}$ and...
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GATE Mechanical 2024 | Question: 42
The Levai type-$\text{A}$ train illustrated in the figure has gears with module $m=8 \mathrm{~mm} /$ tooth. Gears $2$ and $3$ have $19$ and $24$ teeth respectively. Gear ...
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GATE Mechanical 2024 | Question: 44
At the instant when $\text{OP}$ is vertical and $\text{AP}$ is horizontal, the link $\text{OD}$ is rotating counter clockwise at a constant rate $\omega=7 \mathrm{rad} / ...
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GATE Mechanical 2024 | Question: 49
A band brake shown in the figure has a coefficient of friction of $0.3$. The band can take a maximum force of $1.5 \mathrm{kN}$. The maximum braking force $\text{(F)}$ th...
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GATE Mechanical 2023 | Question: 7
The options show frames consisting of rigid bars connected by pin joints. Which one of the frames is non-rigid?
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GATE Mechanical 2023 | Question: 28
The figure shows a wheel rolling without slipping on a horizontal plane with angular velocity $\omega_1$. A rigid bar $\text{PQ}$ is pinned to the wheel at $\text{P}$ whi...
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889
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GATE Mechanical 2022 Set 2 | Question: 7
A massive uniform rigid circular disc is mounted on a frictionless bearing at the end $E$ of a massive uniform rigid shaft $\text{AE}$ which is suspended horizontally in ...
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545
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GATE Mechanical 2022 Set 2 | Question: 42
In the configuration of the planar four-bar mechanism at a certain instant as shown in the figure, the angular velocity of the $2$ $\text{cm}$ long link is $w_{2} = 5$ $...
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538
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GATE Mechanical 2022 Set 1 | Question: 7
The figure shows a schematic of a simple Watt governor mechanism with the spindle $O_{1}O_{2}$ rotating at an angular velocity $\omega$ about a vertical axis. The balls a...
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453
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GATE Mechanical 2022 Set 1 | Question: 21
The plane of the figure represents a horizontal plane. A thin rigid rod at rest is pivoted without friction about a fixed vertical axis passing through $O$. Its mass mome...
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GATE Mechanical 2022 Set 1 | Question: 28
A planar four-bar linkage mechanism with $3$ revolute kinematic pairs and $1$ prismatic kinematic pair is shown in the figure, where $AB \perp CE$ and $FD \perp CE$. The ...
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GATE Mechanical 2022 Set 1 | Question: 43
A schematic of an epicyclic gear train is shown in the figure. The sun $\text{(gear 1)}$ and planet $\text{(gear 2)}$ are external, and the ring gear $\text{(gear 3)}$ is...
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GATE Mechanical 2021 Set 2 | Question: 15
Consider the mechanism shown in the figure. There is rolling contact without slip between the disc and ground.Select the correct statement about instantaneous centers in ...
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GATE Mechanical 2021 Set 2 | Question: 16
The controlling force curves $\text{P, Q,}$ and $\text{R}$ for a spring controlled governor are shown in the figure, where $r_{1}$ and $r_{2}$ are any two radii of rotati...
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GATE Mechanical 2021 Set 2 | Question: 32
A power transmission mechanism consists of a belt drive and a gear train as shown in the figure.Diameters of pulleys of belt drive and number of teeth $\text{(T)}$ on the...
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257
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GATE Mechanical 2021 Set 2 | Question: 54
The torque provided by an engine is given by $T(\theta) =12000+ 2500 \sin(2 \theta) \text{N.m}$, where $\theta$ is the angle turned by the crank from inner dead center. T...
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GATE Mechanical 2021 Set 1 | Question: 16
Consider a reciprocating engine with crank radius $\text{R}$ and connecting rod of length $\text{L}$. The secondary unbalance force for this case is equivalent to primary...
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GATE Mechanical 2021 Set 1 | Question: 24
The figure shows an arrangement of a heavy propeller shaft in a ship. The combined polar mass moment of inertia of the propeller and the shaft is $\text{100 kg.m}^{2}$. T...
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GATE Mechanical 2021 Set 1 | Question: 30
Consider a two degree of freedom system as shown in the figure, where $\text{PQ}$ is a rigid uniform rod of length, $\text{b}$ and mass, $\text{m}$.Assume that the spring...
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GATE Mechanical 2021 Set 1 | Question: 32
A tappet valve mechanism in an $\text{IC}$ engine comprises a rocker arm $\text{ABC}$ that is hinged at $\text{B}$ as shown in the figure. The rocker is assumed rigid and...
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GATE Mechanical 2021 Set 1 | Question: 52
The Whitworth quick return mechanism is shown in the figure with link lengths as follows: $\text{OP = 300 mm, OA = 150 mm, AR = 160 mm, RS = 450 mm}$.The quick return rat...
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GATE2020-ME-2: 29
The sun (S) and the Planet (P) of an epicyclic gear train shown in the figure have identical number of teeth.If the sun (S) and the outer ring (R) gears are rotated in th...
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1 1 answer
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GATE2019 ME-2: 39
A four bar mechanism is shown in the figure. The link numbers are mentioned near the links. Input link $2$ is rotating anticlockwise with a constant angular speed $\omega...
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