Inversion MCQ Quiz - Objective Question with Answer for Inversion - Download Free PDF

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:

Bellows Coupling

• A bellows coupling is a type of flexible coupling that is designed to accommodate misalignment between two shafts.
• It features a flexible bellows, typically made of metal, which allows for both radial and axial movement.
• This flexibility makes it ideal for applications where shafts may not be perfectly aligned.
• The bellows in the coupling are designed to flex, allowing the coupling to absorb misalignment and transmit torque efficiently.
• The bellows can handle angular, parallel, and axial misalignment, making it highly versatile.
• The design ensures that the torque is transmitted smoothly, without backlash, which is crucial for precision applications.

Advantages:

• High flexibility: Can accommodate various types of misalignment, including angular, parallel, and axial.
• Precision: Provides smooth torque transmission without backlash, making it suitable for precision applications.
• Durability: Made of metal, usually stainless steel, which provides excellent durability and resistance to corrosion.
• Compact design: The compact size allows for use in applications with limited space.

Disadvantages:

• Cost: Higher initial cost compared to some other types of couplings.
• Complexity: Slightly more complex design and installation process due to the flexible bellows.

Applications: Bellows couplings are commonly used in applications requiring high precision and flexibility, such as in instrumentation, robotics, and servo systems. They are also used in situations where shafts are expected to experience misalignment during operation.

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:

Quick Return Motion Mechanism:

• A quick return motion mechanism is typically used in shaping, slotting, and planing machines.
• It is designed to reduce the idle time of the machine by minimizing the time taken for the return stroke.

In a shaping machine, the tool moves forward slowly during the cutting stroke to cut the material and returns quickly during the return stroke to save time.

Function of Quick Return Mechanism:

• The primary function is to complete the return stroke as quickly as possible to maximize productivity.
• This allows more time for the forward cutting stroke, which is where the actual material removal takes place.

Important Points

The quick return mechanism ensures that the machine's non-productive time is minimized, thereby increasing overall efficiency.

Additional Information

Other mechanisms used in machine tools include:

(1) Crank and Slotted Lever Mechanism:

• Used in shaping machines to provide the reciprocating motion to the tool.

(2) Whitworth Quick Return Mechanism:

• Another type of quick return mechanism used in shaping and slotting machines.

(3) Hydraulic Drive:

• Used in modern machines to provide smoother and more controlled motion.

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:

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:

Scotch yoke mechanism

• The scotch yoke is a basic mechanism that converts rotary motion into reciprocating linear motion using a pin in a moving slot.
• An application for this mechanism is to open and close valves.
• The crank is connected to the slider by the pin, and as the crank turns the pin it moves the slider.
• Though the goal of the slider-crank and scotch yoke mechanisms is the same, their performance differs slightly.
• The scotch yoke mechanism will generate perfect simple harmonic motion (sine wave), whereas the slider-crank mechanism will produce a slightly distorted sine wave.
• Because the output is simple harmonic motion, the scotch yoke mechanism is commonly used in testing equipment to simulate simple harmonic vibration.
• A major disadvantage to a scotch yoke mechanism is the high contact pressure and wear.

Explanation:

Inversion:

• If one of the links is fixed in a kinematic chain, it is called a mechanism. So, we can obtain as many mechanisms as the number of links (n inversions from a kinematic chain having an ‘n’ number of 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 the mechanism.
• In This question, as there are 10 links, hence there will be 10 possible inversions.
• In the process of inversion, the relative motions of the links of the mechanisms produced remain unchanged.

Additional Information

Concept:

A cutting stroke occurs when the crank rotates through an angle β and the return stroke occurs when the crank rotates through an angle α or (360° - β) in the clockwise direction.

\(\frac{{Time~of~cutting~stroke}}{{Time~of~return~stroke}} = \frac{β }{α } = \frac{β }{{\left( {360^\circ - β } \right)}}\)

Calculation:

Given:

Length of the crank, AO = 2 cm

Distance between the center of the crank and slotted lever, OO' = 4 cm

Consider ΔOO'A,

 \(cos \frac{α}{2}=\frac{OA}{OO'}\)

\(cos\frac{α}{2}=\frac{2}{4}=\frac{1}{2}\)

Therefore, α = 120° 

The cutting stroke angle β,

β = 360 - α

β = 360 - 120 = 240°

\(\frac{{Time~of~cutting~stroke}}{{Time~of~return~stroke}} = \frac{β }{α } = \frac{240}{120}=2\)

Explanation:

Single Slider-Crank Chain:

When one of the turning pairs of a four-bar chain replaced by a sliding pair, it becomes a single slider crank chain.

A slider-crank is a kinematic chain having four links. It has one sliding pair and three turning pairs.

• Link 1 is frame (fixed).
• Link 2 has rotary motion and is called 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.

This mechanism is used to convert rotary motion to reciprocating and vice versa. 

Inversion:

Different mechanisms obtained by fixing different links of kinematic chain are called inversions. A slider crank chain has the following inversions.

• 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.
• 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- Hand pump, Pendulum pump or Bull engine, etc.

Explanation:

Crank and Slotted lever mechanism:

The crank and the slotted lever will produce the oscillating motion as shown in the figure.

For the angle θ₁ there will be forward stroke i.e. cutting and for the remaining angle θ₂ there will be a reverse stroke.

Concept:

According to Grashof’s Law:

(1) S + L ≤ P + Q (Class I mechanism)

There will be at least one complete revolution between the two links.

• If the shortest link is fixed: Double Crank Mechanism
• If any of the adjacent links of the shortest link is fixed: Crank rocker mechanism
• If the link opposite to shortest link is fixed: Double Rocker Mechanism

(2) S + L > P + Q (Class II mechanism)

• Only double rocker mechanism is possible.

Calculation:

Given:

PQ = 2.0 m, QR = 3.0 m, RS = 2.5 m and SP = 2.7 m

Length of shortest link = PQ = 2 m, Length of largest link = QR = 3 m,

Grashof's Law: The sum of lengths of the shortest and longest link should be less than or equal to the sum of lengths of the other two links.

Here \(s+l\le p+q \\ 2+3 \le 2.5+2.7\)

Since the smallest link is the best link for rotation and also governs input and output. So, use the smallest link as a coupler to obtain double rocker mechanism.

Hence, for obtaining Rocker – Rocker mechanism, the link opposite to smallest link (RS) must be fixed.

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:

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 a 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 mechanism is 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.
• 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.