Theory of Machines - 1 - Mechanical Engineering MCQ

When a point on one link is sliding along another rotating link, then the Coriolis component of the acceleration is to be calculated.

ac=2ωV

Due to interference, the tip of one of the gear of the pair will tend to dig into portions of the flank of the tooth of the other member of the pair.

Whirling speed or Critical speed of a shaft is defined as the speed at which a rotating shaft will tend to vibrate violently in the transverse direction if the shaft rotates in horizontal direction. In other words, the whirling or critical speed is the speed at which resonance occurs.

Some examples of different sound intensities as expressed in dB:

• 180 dB: Rocket at take-off
• 140 dB: Jet engine at take-off
• 120 dB: Rock band
• 110 dB: Loud thunder
• 90 dB: City traffic
• 80 dB: Loud radio
• 60 dB: Ordinary conversation
• 30 dB: Soft whisper
• 0 dB: Softest sound a person can hear

The ratio of the length of arc of contact to the circular pitch is known as contact ratio i.e. number of pairs of teeth in contact.

When one of the links of a kinematic chain is fixed, the chain is known as mechanism. It may be used for transmitting or transforming motion. A mechanism with four links is known as simple mechanism, and the mechanism with more than four links is known as compound mechanism. Simplest possible mechanism is four bar chains consisting of four links, each of them forms a turning pair.

A cylindrical cam or barrel cam is a cam in which the follower rides on the surface of a cylinder. In the most common type, the follower rides in a groove cut into the surface of a cylinder. These cams are principally used to convert rotational motion to linear motion parallel to the rotational axis of the cylinder.

A governor is said to be stable when for every speed within the working range there is a definite configuration i.e. there is only one radius of rotation of the governor balls at which the governor is in equilibrium. For a stable governor, if the equilibrium speed increases, the radius of governor balls must also increase. A governor is said to be unstable, if the radius of rotation decreases as the speed increases.

When the two elements of a pair are connected in such a way that one element (with spherical shape) turns or swivels about the other fixed element, the pair formed is called a spherical pair. The ball and socket joint, attachment of a car mirror, pen stand etc., are the examples of a spherical pair.

Height of the governor:

let S be the stiffness of the spring, h be the lift of governor, F₁ and F₂ are the force exerted on sleeve at lowest and highest equilibrium speed

Addendum: It is the radial distance of a tooth from the pitch circle to the top of the tooth.

Dedendum: It is the radial distance of a tooth from the pitch circle to the bottom of the tooth.

Pitch circle: It is an imaginary circle which by pure rolling action, would give the same motion as the actual gear.

Pitch circle diameter: It is the diameter of the pitch circle. The size of the gear is usually specified by the pitch circle diameter. It is also called as pitch diameter.

Module: It is the ratio of the pitch circle diameter in millimetres to the number of teeth.

Module, m = D / T

When a vehicle takes a turn, its other rear wheel covers a greater distance than inner rear wheel. Hence differential gears are used so that both the rear wheel can rotate at different speed. This is achieved with the help of elliptical gear train.

Mass moment of inertia of the flywheel:

I = mk² = 3250 × 1² = 3250 kg-m²

Starting torque of the engine: T = I.α

Angular acceleration of the flywheel:

α = T/I = 4500/3250 = 18/13 = 1.38 rad/s²

When the axes of the first gear and the last gear are co-axial, then the gear train is known as reverted gear train. The reverted gear trains are used in automotive transmissions, lathe back gears, industrial speed reducers, and in clocks (where the minute and hour hand shafts are co-axial).

The epicyclic gear trains are useful for transmitting high velocity ratios with gears of moderate size in a comparatively lesser space. The epicyclic gear trains are used in the back gear of lathe, differential gears of the automobiles, hoists, pulley blocks, wrist watches etc.

For cantilever beam

Pressure Angle is the measure of steepness of the cam profile. The angle between the direction of the follower movement and the normal to the pitch curve at any point is called pressure angle. Pressure angle varies from maximum to minimum during complete rotation.

The pressure should not exceed 30^० in case of cams with translating followers (and angle should be less than 45^० for low speed cam mechanisms with oscillating followers).

Exact Straight-Line Motion Mechanisms Made up of Turning Pairs: Peaucellier mechanism, Hart’s mechanism

Exact Straight-Line Motion Consisting of One Sliding Pair: Scott Russell’s Mechanism

Approximate Straight-Line Motion Mechanisms: Watt’s mechanism, Modified Scott-Russel mechanism, Grasshopper mechanism, Roberts mechanism

A flywheel controls the speed variation caused by the engine whereas governor maintains a constant speed during load variation on the engine.