Theory of Machines - 2 - Mechanical Engineering MCQ

A link is defined as a member or a combination of members of a mechanism, connecting other members and having motion relative to them. Thus, a link may consist of one or more resistant bodies.

Links can be classified into binary, ternary and quaternary depending upon their ends.

Rack and pinion gears are used to convert rotation into linear motion. The ‘pinion’ is the normal round gear and the ‘rack’ is straight or flat.

A perfect example of this is the steering system on many cars.

Self-closed pair:

When the two elements of a pair are connected together mechanically. The contact between the two can be broken only by destruction of at least one of the members.

All lower pairs and some higher pairs are closed pairs. Sliding pairs, turning pairs, spherical pairs and screw pairs are also closed pairs.

Forced-closed pair:

When two links of a pair are in contact either due to force of gravity or some spring action. In this, the links are not held together mechanically e.g. cam and follower pair (because spring is used to keep the motion constrained).

Slider-crank mechanism does not require such force.

For Watt Governor:

i.e height is inversely proportional to (speed)²

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The turning moment diagram also known as crank effort diagram.

• It is the graphical representation of the turning moment or torque or crank effort (X-axis) for various position of crank (Y-axis).
• The area under the turning moment diagram gives the work done per cycle.
• The work done per cycle when divided by the crank angle per cycle gives mean torque T_m.

Base Circle: It is the smallest circle, drawn tangential to cam profile. The base circle decides the overall size of the cam and thus is fundamental feature.

Pitch Curve: If we hold the cam fixed and rotate the follower in a direction opposite to that of the cam, then the curve generated by the locus of the trace point is called pitch curve. For a knife edge follower, the pitch curve and the cam profile are same whereas for a roller follower, they are separated by the radius of the roller.

Pitch Point: Pitch point corresponds to the point of maximum pressure angle, and a circle drawn with its centre at the cam centre, to pass through the pitch point, is known as the pitch circle.

Prime Circle: It is the smallest circle that can be drawn from the centre of the cam and tangent to the pitch curve.

The damping ratio (ζ = c/c_c) is a system parameter, that can vary from un-damped (ζ = 0), under-damped (ζ < 1) through critically damped (ζ = 1) to over-damped (ζ > 1)

For the effect of gyroscopic couple to occur, the axis of precession should always be perpendicular to the axis of spin. If, however, the axis of precession becomes parallel to the axis of spin, there will be no effect of the gyroscopic couple acting on the body of the ship.In case of rolling of a ship, the axis of precession (i.e. longitudinal axis) is always parallel to the axis of spin for all positions. Hence, there is no effect of the gyroscopic couple acting on the body of a ship.

Conditions of complete balancing of reciprocating parts of an engine:

• Primary forces must balance i.e., primary force polygon is enclosed.
• Primary couples must balance i.e., primary couple polygon is enclosed.
• Secondary forces must balance i.e., secondary force polygon is enclosed.
• Secondary couples must balance i.e., secondary couple polygon is enclosed.

Methods of elimination of Gear tooth Interference:

• Use of a larger pressure angle (having a larger pressure angle results in a smaller base circle. As a result, more of the tooth profiles become involute)
• Under-cutting of tooth (A portion of teeth below the base circle is cut off. When teeth are produced by this process, the tip of one tooth of a gear will not contact the non-involute portion of the tooth of other gear)
• Tooth stubbing (In this process a portion of the tip of the teeth is removed, thus preventing that portion of the tip of tooth in contacting the non-involute portion of the other meshing tooth).
• Increasing the number of teeth on the gear can also eliminate the chances of interference.
• Increasing slightly the center distance between the meshing gears would also eliminate interference.
• Tooth profile modification or profile shifting (Using profile shifted gears (gears with non-standard profile) can also be an option to eliminate interference. In profile shifted meshing gears, the addendum on the pinion is shorter compared with standard gears).

A governor is said to be sensitive when it readily responds to a small change of speed.

Stiffness is inversely proportional to sensitiveness. Therefore, if stiffness is greater, the governor will be less sensitive.

A simple pendulum is one which can be considered to be a point mass suspended form a string or rod of negligible mass.

The period

So the statement the time period is proportional to its length is wrong.

We know that coefficient of fluctuation of speed (C₁) is

Or, C₁ ω_max + C₁ ω_min = 2ω_max – 2ω_min

T_P = 16, T_G = 40, m = 12

C = r_P + r_G

 336 mm

Tangential Acceleration a_t = rα

α = Angular acceleration = 60 rad/s²

r = radius of crank = 15 cm

∴ a_t = rα = 60 × 0.15 = 9 m/s

Kinetic energy of the flywheel is given by:

I is mass moment of inertia of the flywheel about its axis of rotation in kg-m² = m.k²

Angle of Dwell: It is the angle through which the cam turns while the follower remains stationary at the highest or the lowest position.

Crank and slotted lever quick return motion mechanism is an inversions of Single Slider Crank Chain which is a modification of the basic four bar chain.

Number of instantaneous centres:

where L is number of links.

If a straight line is rolled round a circle or a polygon without slipping or sliding, points on line will trace out involutes.

Or Involute of a circle is a curve traced out by a point on a tights string unwound or wound from or on the surface of the cylinder.

In vibration isolation system, the ratio of the force transmitted to the force applied is known as the isolation factor or transmissibility

then ϵ = 1 for all values of damping factor c/c_c.