Theory of Machines MCQ Quiz - Objective Question with Answer for Theory of Machines - Download Free PDF

Explanation:

Rack and Pinion Gear

Definition: A rack and pinion gear system is a type of linear actuator that comprises a circular gear (the pinion) engaging a linear gear (the rack). This system converts rotational motion into linear motion and is widely used in various mechanical applications.

Working Principle: In a rack and pinion system, the pinion rotates, and its teeth engage with the teeth on the rack. As the pinion turns, it moves the rack in a straight line. This conversion of rotational motion to linear motion is precise and efficient, making the rack and pinion system an essential mechanism in many engineering applications.

Advantages:

• Provides precise control of linear motion.
• Simple design and easy to manufacture.
• High efficiency in converting rotational motion to linear motion.

Disadvantages:

• Wear and tear of gears can affect the accuracy over time.
• Requires lubrication and maintenance to ensure smooth operation.

Applications: Rack and pinion systems are commonly used in steering mechanisms of vehicles, CNC machines, and other industrial equipment where precise linear motion control is required.

Concept:

Kinetic energy of a rotating body is given by,

\( KE = \frac{1}{2} I \omega^2 \)

Since moment of inertia (I) is constant,

\( KE \propto N^2 \)

Given:

A flywheel absorbs 24 kJ of energy when the speed increases from 210 rpm to 214 rpm.

We need to find the kinetic energy at 220 rpm.

Calculation:

Let:

\( KE_1 = k \times (210)^2 = 44100k \)

\( KE_2 = k \times (214)^2 = 45796k \)

Given: \( KE_2 - KE_1 = 24 \) kJ

\( \Rightarrow 45796k - 44100k = 1696k = 24 \Rightarrow k = \frac{24}{1696} = 0.01415 \)

Finding KE at 220 rpm:

\( KE = k \times (220)^2 = 0.01415 \times 48400 = 685.86~\text{kJ} \)

Explanation:

Flywheel:

• A flywheel is a mechanical device specifically designed to store rotational energy and regulate the cyclic fluctuations in the speed of an engine. It is typically a heavy wheel that is mounted on the crankshaft of an engine and rotates along with it. The flywheel smoothens the variations in the speed of the crankshaft caused by the intermittent power pulses of the engine by acting as an energy reservoir.
• The flywheel operates by absorbing energy during the power strokes of the engine and releasing it during the non-power strokes. When the engine generates excess energy during the power stroke, the flywheel stores it as rotational kinetic energy. During the other strokes, such as the exhaust, intake, and compression strokes, the flywheel releases the stored energy to maintain a consistent speed. This ensures a smooth operation of the engine and reduces vibrations.

Functions of a Flywheel:

• Regulating Speed Fluctuations: The flywheel minimizes cyclic speed variations by smoothing out the energy fluctuations during different strokes of the engine.
• Energy Storage: It stores kinetic energy during the power stroke and releases it during the other strokes, maintaining a consistent engine speed.
• Starting the Engine: In some cases, the flywheel aids in starting the engine by providing the initial rotational inertia required.
• Balancing: The flywheel helps in balancing the engine and reducing vibrations, contributing to smoother operation.

Advantages:

• Improves the smoothness of engine operation by regulating speed fluctuations.
• Reduces vibrations and noise in the engine.
• Enhances the efficiency and reliability of the engine.

Applications: Flywheels are widely used in various applications, including:

• Internal combustion engines in automobiles.
• Industrial machinery and equipment.
• Energy storage systems.
• Power plants and turbines.

Explanation:

Cam Profile:

• The cam profile is the actual shape or contour of the cam that determines the motion of the follower. It is critical in cam-follower mechanisms to control the timing, displacement, velocity, and acceleration of the follower. These profiles are designed with precision to meet specific motion requirements in machines such as engines, automation systems, and other mechanical devices.
• In cam mechanisms, the primary elements that define the profile include the prime circle, base circle, and trace point, which are used to generate the cam's shape and ensure the desired motion of the follower.

Addendum:

• Addendum is a term commonly used in gear terminology and refers to the radial distance between the pitch circle and the top of the gear tooth. It plays a significant role in the design and functioning of gears but has no relevance to the cam profile or its design parameters.

Additional InformationPrime Circle:

• The prime circle is the smallest circle that can be drawn tangentially to the cam profile.

Trace Point:

• The trace point is a specific point on the follower that is used to define the follower’s motion.

Base Circle:

• The base circle is the smallest circle that can be drawn tangentially to the cam profile, excluding the follower's motion.

Explanation:

• Rotary engine – I inversion of slider-crank mechanism (crank fixed)
• Whitworth quick return motion mechanism – I inversion of slider-crank mechanism so option 3 is correct.
• Crank and slotted lever quick return motion mechanism – II inversion of slider-crank mechanism (connecting rod fixed).
• Oscillating cylinder engine – II inversion of slider-crank mechanism (connecting rod fixed).
• Pendulum pump or bull engine – III inversion of slider-crank mechanism (slider fixed).
• Inversions of double slider crank mechanism:  Elliptical trammel, Oldham coupling
• Inversions of four-bar chain: Crank-rocker mechanism, Drag link mechanism, Double crank mechanism, Double rocker mechanism

Inversions of single slider crank mechanism:

• A slider-crank is a kinematic chain having four links. It has one sliding pair and three turning pairs.
• Link 2 has rotary motion and is called a crank. Link 3 has got combined rotary and reciprocating motion and is called connecting rod. Link 4 has reciprocating motion and is called a slider. Link 1 is a frame (fixed). This mechanism is used to convert rotary motion to reciprocating and vice versa. 

• Inversions of the slider-crank mechanisms are obtained by fixing links 1, 2, 3 and 4.
• First inversion: This inversion is obtained when link 1 (ground body) is fixed.
  • Application-  Reciprocating engine, reciprocating compressor, etc.
• Second inversion: This inversion is obtained when link 2 (crank) is fixed.
  • Application- Whitworth quick returns mechanism, Rotary engine, etc.

Whitworth quick returns mechanism

• Third inversion: This inversion is obtained when link 3 (connecting rod) is fixed.
  • Application - Slotted crank mechanism, Oscillatory engine, etc.
• Fourth inversion: This inversion is obtained when link 4 (slider) is fixed.
  • Application- A hand pump, pendulum pump or Bull engine, etc.

Explanation:

Mechanism and Inversion:

• When one of the links of a kinematic chain is fixed, the chain is known as a mechanism.
• A mechanism with four links is known as a simple mechanism, and a mechanism with more than four links is known as a compound mechanism.
• We can obtain as many mechanisms as the number of links in the kinematic chain by fixing, in turn, different links in a kinematic chain.
• This method of obtaining different mechanisms by fixing different links in a kinematic chain is known as the inversion of a mechanism.

Explanation:

• A kinematic chain is a group of links either joined together or arranged in a manner that permits them to move relative to one another. 

Now, let's take an example of such a mechanism

The above-shown figure is a cam and follower mechanism. 

In this mechanism, there are 2 lower pairs i.e. between links (1,2 and 3,1) and 1 higher pair which is between link (2,3). 

Hence, the minimum number of links that can make a mechanism is 3.

Mistake Points

If it is given in the question that all the pairs are lower pairs then the correct answer will be 4.

If the links are connected in such a way that no motion is possible, it results in a locked chain or structure.

A minimum number of three links is required to form a closed chain but there will be no relative motion between these three links if all are lower pairs. Hence it cannot form a kinematic chain.

So the minimum of four links is necessary to form a kinematic chain when all the lower pairs are used.

Topper’s approach:

The follower turns = 18 × 16/8 = 36 times

Detailed Solution:

Let, the follower turns = x times

According to the question,

⇒ x × 8 = 16 × 18

⇒ x = 16 × 18/8

⇒ x = 36

Concept:

Kutzback equation for DOF is given by

DOF = 3(n - 1) - 2j - h

where n = Number of links, j = Number of joints, h = Number of higher pairs.

Calculation:

Given:

From fig.

n = 10, j = 12, h = 0

DOF can be calculated as 

DOF = 3(n - 1) - 2j - h

DOF= 3(10 - 1) - (2 × 12) - 0

∴ DOF = 3

The number of tertiary links are 3 as shown below.

Explanation:

Kinematic pairs are classified under three headings namely, lower pair, higher pair and wrapping pair.

Lower Pair: 

A pair is said to be a lower pair when the connection between two elements is through the area of contact. Some of the types of Lower pair are:

• Revolute Pair
• Prismatic Pair
• Screw Pair
• Cylindrical Pair
• Planar Pair

Higher Pair: 

A pair is said to be higher pair when the connection between two elements has only a point or line of contact. Examples of higher pairs are:

• A point contact takes place when spheres rest on plane or curved surfaces (in case of ball bearings)
• Contact between teeth of a skew-helical gears
• Contact made by roller bearings
• Contact between teeth of most of the gears
• Contact between cam-follower
• Spherical Pair

Wrapping Pairs:

In a higher pair, the contact between the two bodies has only a line contact or a point contact. Whereas in a wrapping pair, one body completely wraps over the other. The typical example is of a belt and a pulley or a chain and a sprocket where the belt completely wraps around the pulley or the chain completely wraps around the sp

Spherical Pair:

This pair usually look like lower pair but it is multiple point contact pair like wrapping pair which is a higher pair.

• Example. Ball in Socket joint.

Concept:

Mechanical advantage:

• It is a number that tells us how many times a simple machine multiplies the effort force. 
• is defined as the ratio of output force to input force.
• The mechanical advantage of a machine gives its efficiency. 
• Formula, \(MA=\frac{F_0}{F_i}\), where, F₀ = output force, F_i = input force
• It is a unitless and dimensionless quantity.

Efficiency:

• The efficiency of a machine is the ratio of the work done on the load by the machine to the work done on the machine by the effort.
• Thus, it is the ratio of useful work done by the machine output to the work done by the machine input.
• It is represented by the Greek symbol η.
• Formula, efficiency, \(\eta=\frac{mechanical\, \, advantage}{velocity \, \, ratio}\)

Velocity ratio:

• The ratio of the distance moved by the point at which the effort is applied in a simple machine to the distance moved by the point at which the load is applied at the same time.
• Formula, \(velocity\, \, ratio=\frac{distance\, \, moved\,\, by\,\, effort}{distance \,\, moved\,\, by\,\, load}\)
• In the case of an ideal (frictionless and weightless) machine, velocity ratio = mechanical advantage.

Calculation:

Given: mechanical advantage, MA = 2.5, length of load lift, L_R = 2.5 m, length of effort, L_E = 10 m

Velocity ratio, \(v=\frac{10}{2.5}=4\)

Efficiency, \(\eta=\frac{mechanical \, \, advantage}{velocity \,\, ratio}\)

\(\eta=\frac{2.5}{4}=0.625\)

In percentage, the efficiency is 62.50 %.

Concept:

Mechanical Advantage: 

• In a simple machine when the effort(P) balances a load (W), the ratio of the load to the effort is called MA.
• \(M.A = \frac{{Load}}{{Effort}} = \frac{W}{P}\)

Velocity Ratio: 

• It is the ratio between the distance moved by the effort to the distance moved by the load.
• \(V.R = \frac{{distance\;moved\;by\;the\;effort\;\left( {{d_P}} \right)}}{{distance\;moved\;by\;the\;load\;\left( {{d_w}} \right)}}\)

Efficiency: 

• It is the ratio of output to input. In a simple mechanism, it is also defined as the ratio of mechanical advantage to the velocity ratio.
• \(\eta = \frac{{Output}}{{Input}} = \frac{{M.A}}{{V.R}}\)
• In actual machines, a mechanical advantage is less than the velocity ratio
• In an ideal machine, the mechanical advantage is equal to the velocity ratio.

Calculation:

Given:

Effort (P) = 15 units, MA = 3

\(M.A = \frac{W}{P}\)

\(3 = \frac{W}{15}\)

Load, W = 45 units

Explanation:

Reverted gear train:

When the axes of the first gear and the last gear are co-axial, then the gear train is known as a 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).

Advantages:

• 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.

Explanation:

Governor Effort

• It is the force exerted by the governor at the sleeve as the sleeve tends to move.
• When the speed of the governor is constant, the force exerted on the sleeve is zero as the sleeve doesn't tend to move and hence at the constant speed, the effort of the governor is zero, but when the speed changes and the sleeve tends to move to new equilibrium position force is exerted on the sleeve.
• This force gradually diminishes to zero as the sleeves move to a new equilibrium position corresponding to the new speed.
• The mean force exerted on the sleeve during the given change of speed is known as the effort of the governor.
• The given change of speed is generally taken as 1%, hence effort is defined as the force exerted on the sleeve for 1% change of speed.

Explanation:

Isochronous Governor: 

• A governor is said to be isochronous when the equilibrium speed is constant (i.e. range of speed is zero) for all radii of rotation of the balls within the working range, neglecting friction. 
• The isochronism is the stage of infinite sensitivity.
• A spring-loaded governor can only possibly be an Isochronous governor.

Hunting: 

• If a governor is too sensitive, a small variation of speed causes large change in the sleeve movement. Thus, a governor is said to be hunt if the speed of the engine fluctuates continuously above and below the mean speed.

Stability: 

• A governor is said to be stable when for each speed within the working range there is only one radius of rotation of the fly-ball at which governor is in equilibrium.