Mechanisms and Machines MCQ Quiz - Objective Question with Answer for Mechanisms and Machines - Download Free PDF

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:

Ball and Socket Joint

• A ball and socket joint is a type of mechanical joint where a spherical-shaped component (the "ball") fits into a concave-shaped socket. This arrangement allows for rotational motion in multiple directions, making it a highly versatile joint in terms of movement. Ball and socket joints are commonly found in both mechanical systems and biological structures, such as the human hip and shoulder joints.
• In a ball and socket joint, the ball component is free to rotate within the socket. This freedom allows for movement around multiple axes, including flexion, extension, abduction, adduction, and rotation. The joint enables a high degree of mobility while maintaining a stable connection between the components.

Mechanical Example: In mechanical systems, ball and socket joints are often used in universal joints, robotic arms, and certain types of couplings where multi-directional movement is required.

Characteristics:

• Provides rotational movement around multiple axes.
• Allows for a wide range of motion, including circular and angular movements.
• Ensures a stable yet flexible connection between the components.

Spherical Pair

• A ball and socket joint is categorized as a spherical pair because it involves a spherical component (the ball) moving within a concave socket. This type of joint allows for rotational motion in three degrees of freedom (DOF): pitch, yaw, and roll. The motion characteristics of the ball and socket joint align perfectly with the definition of a spherical pair in kinematics.

Additional Information

Turning Pair

• A turning pair involves two components that are constrained to rotate relative to each other about a single axis. An example of a turning pair is a hinge or a rotating shaft.

Sliding Pair

• A sliding pair involves two components that move relative to each other in a linear direction. An example of a sliding pair is a piston moving within a cylinder. A ball and socket joint does not exhibit linear motion; instead, it allows for rotational motion in multiple directions, making this option incorrect.

Screw Pair

• A screw pair consists of two components where one component moves helically relative to the other, combining rotational and linear motion. An example of a screw pair is a lead screw in a lathe machine. A ball and socket joint does not involve helical motion, so this option is not applicable.

Explanation:

Whitworth Quick Return Mechanism

• The Whitworth Quick Return Mechanism is a mechanical device used to convert rotational motion into reciprocating motion. This mechanism is particularly known for its ability to produce a faster return stroke compared to the forward stroke, making it highly efficient for certain applications such as in shaping and slotting machines.
• The Whitworth Quick Return Mechanism consists of a rotating crank, a slotted lever (link), and a slider. When the crank rotates, it drives the slotted lever. The slider, which is attached to the tool or working element, moves back and forth due to the motion of the slotted lever. The geometry of the mechanism ensures that the time taken for the forward stroke is longer than the time taken for the return stroke.
• By fixing link 2 and making link 3 the crank, the resulting motion and characteristics align with the quick return mechanism, where the return stroke is quicker than the forward stroke. This forms Whitworth Quick Return Mechanism.

Advantages:

• Increased efficiency due to the faster return stroke, reducing the overall cycle time of the machine.
• Simplicity in design and ease of implementation in various mechanical systems.

Disadvantages:

• Non-uniform motion of the slider, which might not be suitable for applications requiring constant speed.
• Potential for increased wear and tear due to the quick motion during the return stroke.

Applications: The Whitworth Quick Return Mechanism is commonly used in shaping machines, slotting machines, and other machinery where a faster return stroke enhances productivity.

Explanation:

Mechanism ABCD Analysis

• In the context of mechanisms, especially those involving linkages, various configurations can exist such as crank-rocker, double-crank, and double-rocker mechanisms.
• The identification of these configurations depends on the relative lengths of the links and their ability to complete full rotations or limited oscillations.
• For the mechanism ABCD where link BC is fixed, it is essential to understand the movement constraints and capabilities of the other links (AB, CD, and AD) to determine the type of mechanism.
• The classification into crank-rocker, double-crank, or double-rocker mechanisms is based on the Grashof's criterion and the motion of individual links.

Correct Option Analysis:

The correct option is:

Option 1: It is a double-rocker mechanism.

This option correctly identifies the mechanism type for the given configuration. In a double-rocker mechanism, neither of the two links connected to the fixed link (in this case, links AB and CD) can make a complete revolution, and both only oscillate back and forth. Here’s a detailed explanation to support this conclusion:

• Grashof’s Criterion: According to Grashof’s law, for a four-bar linkage consisting of four links, where one of the links is fixed, the system is classified based on the sum of the shortest and longest links compared to the sum of the other two links.
• If the sum of the shortest and longest links is less than the sum of the remaining two links, at least one link can make a complete revolution. If not, the mechanism is a double-rocker.

Assuming the lengths of the links in the mechanism ABCD are such that Grashof’s criterion indicates a double-rocker configuration, it implies that:

• Link AB (or BA) and link CD cannot make a complete revolution around their respective joints B and C.
• Instead, both links can only oscillate within a limited range, qualifying the mechanism as a double-rocker.

Explanation:

Oldham's Coupling

• Oldham's coupling is a mechanical device used to connect two shafts in such a way that torque can be transmitted while accommodating small amounts of misalignment between the shafts. This coupling is particularly useful in applications where shafts are slightly misaligned or where the alignment may shift during operation.
• Oldham's coupling consists of three main components: two hubs, each attached to one of the shafts, and an intermediate floating disc. The key feature of Oldham's coupling is the design of the intermediate disc, which has matching grooves on either side that engage with corresponding projections on the hubs. This configuration allows the disc to slide and rotate, compensating for misalignment between the shafts while still transmitting torque.
• The intermediate disc effectively acts as a mediator between the two hubs, ensuring that any misalignment is absorbed by the sliding action of the disc. This allows the coupling to maintain a constant transmission of torque despite the misalignment. The design also ensures that the forces are evenly distributed, reducing the stress on the shafts and the coupling itself.

Advantages:

• Ability to accommodate angular, parallel, and axial misalignments.
• Simple and compact design, making it easy to install and maintain.
• Provides smooth and continuous torque transmission.
• Reduces the risk of damage to the connected machinery due to misalignment.

Disadvantages:

• Limited to applications with relatively low torque and speed requirements.
• Not suitable for high-precision applications where exact alignment is critical.

Applications: Oldham's coupling is commonly used in various applications, including:

• Machine tools and automation equipment.
• Pumps and compressors.
• Conveyors and material handling systems.
• Printing and packaging machinery.

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.

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:

The degree of freedom (DOF) of a mechanical system is the number of independent parameters that define its configuration.

The position and orientation of a rigid body in space are defined by three components of translation and three components of rotation, which means that it has six degrees of freedom.

• We have 3 components of rotation and 3 components of translation. 

Concept:

From Gruebler's criterion, we have Degree of freedom (F) is given by:

F = 3(N - 1) - 2P₁ - 1P₂ - F_r

where, N = number of links, P₁ = number of pairs with 1 degree of freedom, P₂ = number of pairs with 2 degrees of freedom, F_r = number of redundant pairs.

Calculation:

Given:

We have N = 4, P₁ = 3, P₂ = 1, F_r = 1

where F_r = Number of redundant kinematic pair.

Redundant kinematic pair:

The main purpose of the roller follower is to reduce friction. It is not playing any role in the transfer of relative motion. Oscillation of follower ϕ is the function of rotation of cam θ.i.e ϕ = f(θ ). Hence we can say that there is a redundant pair in this mechanism. After considering the redundant pair we shall get a degree of freedom.

F = 3(N - 1) - 2P1 - 1P2 - F_r

F_r = 1, Kinematic pair between roller and cam.

F = 3 × (4 - 1) - (2 × 3) - (1 × 1) - 1 = 1

Hence, the degree of freedom of the mechanism is 1.

If we neglect the count of redundant kinematic pair

Degree of freedom (F) is given by:

F = 3(N - 1) - 2P1 - 1P2 

So, F = 3 × (4 - 1) - (2 × 3) - (1 × 1) 

F = 2

So the answer will come 2, which is wrong,

Since there is a redundant link present in the system. 

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 the 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:

Kinematic pair:

A kinematic pair or simply a pair is a joint of two links having relative motion between them.

Kinematics pair can be classified according to:

• Nature of contact
• Nature of relative motion
• Nature of mechanical constraint

Kinematic pairs according to Nature of Contact:

Additional Information

Kinematic pair according to nature of relative motion:

According to the nature of mechanical constraint: