Four Bar Mechanism MCQ Quiz - Objective Question with Answer for Four Bar Mechanism - Download Free PDF

Explanation:

According to Grashof’s Law:

"A four-bar mechanism has at least one revolving link if the sum of the lengths of the largest and shortest links is less than the sum of lengths of the other two links".

• The mechanism in which no link makes a complete revolution will not be useful.
• In a four-bar chain, one of the links, in particular, the shortest link, will make a complete revolution relative to the other three links, if it satisfies Grashof ’s law. Such a link is known as a crank or driver i.e. AD (link 4 ) is a crank.
• The link BC (link 2) which makes a partial rotation or oscillates is known as lever or rocker or follower and the link CD (link 3) which connects the crank and lever is called connecting rod or coupler. 
• The fixed link AB (link 1) is known as the frame of the mechanism.
• When the crank (link 4) is the driver, the mechanism is transforming rotary motion into oscillating motion.

Additional Information

(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 if 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 a double rocker mechanism is possible.

Explanation: 

Revolute Pair (R-pair):

• A revolute pair has one degree of freedom and permits a rotational motion about an axis. A revolute pair is often called a pin joint. 
• Example: Lathe spindle in the headstock.

Helical Pair (H-pair)

• A helical pair has one degree of freedom and permits rotational and translational motion. These motions are, however, related by the pitch value of the helical pair. A helical pair is often called a screw pair
• Example: Motion between the bolt and fixed nut

​Rolling pair: 

• A pair of two links having a rolling motion relative to each other is called rolling pair
• Example: Ball bearing, contact between the ball or roller, etc.

Globular or Spherical pair:  

• In a spherical pair, one link is constrained to swivel in or about the other fixed point. 
• Example: Ball in the socket

Important Points

1. Sliding pair: In this pair two links are so connected that one is constrained to have sliding motion relative to another e.g. crosshead and guide.
2. Turning pair: In this pair two links are so connected that one is constrained to turn or revolve about a fixed axis of another e.g. crankshaft turning in a bearing

Explanation:

The Peaucellier mechanism is a mechanical linkage that converts rotational motion into straight-line motion with high accuracy. It is a planar mechanism, meaning that it operates in a two-dimensional plane.

The linkage consists of eight links, each of which is connected by a revolute joint (a joint that allows rotation around a fixed axis). There are nine revolute joints in total, forming a closed loop. The linkage is named after its inventors, French mathematician Charles-Nicolas Peaucellier and Russian engineer Yom Tov Lipman Lipkin.

The Peaucellier-Lipkin linkage operates by using the principle of inversion of a circle. Inversion is a mathematical transformation that maps circles and lines in a plane to other circles and lines. The linkage uses the fact that the inversion of a circle with respect to a fixed point on the plane is a straight line passing through that point.

In the Peaucellier-Lipkin linkage, one of the links (the input link) is driven by a rotating crank. The other end of the input link is connected to two other links (the connecting links) through a pair of pivots. The connecting links are connected to two more links (the output links) through another pair of pivots. The output links are connected to a fixed point on the plane through a final pivot.

As the input link rotates, the position of the output point (the fixed point on the plane) moves along a straight line. This straight-line motion is achieved through the complex interaction of the eight links and nine pivots, which causes the inversion of a circle with respect to the fixed point.

Explanation:

According to Grashof’s Law:

"A four-bar mechanism has at least one revolving link if the sum of the lengths of the largest and shortest links is less than the sum of lengths of the other two links".

• The mechanism in which no link makes a complete revolution will not be useful.
• In a four-bar chain, one of the links, in particular, the shortest link, will make a complete revolution relative to the other three links, if it satisfies Grashof ’s law. Such a link is known as a crank or driver i.e. AD (link 4 ) is a crank.
• The link BC (link 2) which makes a partial rotation or oscillates is known as lever or rocker or follower and the link CD (link 3) which connects the crank and lever is called connecting rod or coupler. 
• The fixed link AB (link 1) is known as the frame of the mechanism.
• When the crank (link 4) is the driver, the mechanism is transforming rotary motion into oscillating motion.

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 if 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 a double rocker mechanism is possible.

Hence, the Bicycle mechanism is associated with a four-bar linkage. as it is similar to parallelogram linkage.

Explanation:

Quick return mechanism: 

• It is an apparatus to produce a reciprocating motion in which the time taken for travel in return stroke is less than in the forward stroke
• A quick return mechanism converts the circular motion into reciprocating motion (repetitive back and forth linear motion).
• This mechanism is mostly used in shaping, planning, and slotting machines.
• In a slotting, the rotary motion of the drive is converted into reciprocating motion of the ram by the mechanism housed within the column or the machine.
• In a standard slotter, metal is removed in the forward cutting stroke, while the return stroke goes idle and no metal is removed during this period.
• The quick return mechanism is so designed that it moves the ram holding the tool at a comparatively slower speed during the forward cutting stroke, whereas during the return stroke it allows the ram to move at a faster speed to reduce the idle return time.

The reciprocating movement of the ram and the quick return mechanism of the machine is generally obtained by anyone of the following methods:

• Crank and slotted link mechanism.
• Whitworth quick return mechanism.
• Hydraulic shaper mechanism.

Quick return ratio(QRR): It is the ratio of cutting time to the return time.

QRR = 

As the time taken to return is less than advance time, ∴ QRR > 1

Explanation:

The following points are important about the inversion of a kinematic chain:

• The inversions of a kinematic chain are obtained by fixing different links one at a time.
• For a kinematic chain consisting of 4 links, the maximum possible kinematic inversions are four.
• The qualitatively distinct inversions mean that all the inversions should be able to convert the input into a distinct output.

A 4 revolute pair chain is called the Grashof chain if the following condition is satisfied:

l + s

i.e. the sum of the shortest and longest link should not be greater than the other two.

If a Grashof chain with 4 revolute pairs is considered then the following three distinct inversions are possible.

Double crank:

A double-crank results when the shortest link is fixed.

In this mechanism both the driving and the driven links make a complete rotation.

Double rocker:

A double rocker results when the shortest link is made coupler.

In this mechanism, both the driving and the follower links make only oscillations and none of them makes a complete rotation.

Crank-rocker:

If the link adjacent to the shortest link is fixed then it results in a crank-rocker.

In this mechanism, the driving link makes complete rotation and the driven link makes only oscillation.

Class-II four-bar linkage:

When the sum of the lengths of the largest and the shortest links is more than the sum of the lengths of the other two links, the linkage is known as class-II, four-bar linkage i.e. l + s > p + q.

In such links, fixing of any of the links always results in a rocker-rocker or double rocker mechanisms.

In other words, the mechanism and its inversions give the same type of motion i.e. (not distinct).

Explanation:

A kinematic chain is a combination of four or more kinematic pairs, such that the relative motion between the links or elements is completely constrained. The simplest and the basic kinematic chain is a four-bar chain or quadric cycle chain.

It consists of four links, each of them forms a turning pair at A, B, C and D. The four links may be of different lengths.

According to Grashof ’s law: S + L ≤ P + Q

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 if 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 a double rocker mechanism is possible.

Calculation:

Given:

For getting a crank rocker mechanism, any of the adjacent links of the shortest link should be fixed and S + L ≤ P + Q.

Here fixed link is PS = 400 mm which is not the shortest link.

Let's start with incorrect options first.

1. Now consider the length of PQ = 350 mm
   • S + L = 300 + 600 = 900
   • P + Q = 400 + 350 = 750
   • S + L > P + Q.
   • Grashof’s Law not satisfied
2. Now consider the length of PQ = 300 mm
   • S + L = 300 + 600 = 900
   • P + Q = 400 + 300 = 700
   • S + L > P + Q
   • Grashof’s Law not satisfied
3. Now consider the length of PQ = 200 mm
   • S + L = 200 + 600 = 800
   • P + Q = 400 + 300 = 700
   • S + L > P + Q
   • Grashof’s Law not satisfied
4. Now consider the length of PQ = 80 mm

• S + L = 80 + 600 = 680
• P + Q = 400 + 300 = 700
• S + L
• Grashof’s Law is satisfied
• Shortest link is PQ (80 mm). Link adjacent to shortest link is fixed i.e. PS. So it will give crank rocker mechanism.

Explanation:

According to Grashof’s Law:

"A four-bar mechanism has at least one revolving link if the sum of the lengths of the largest and shortest links is less than the sum of lengths of the other two links".

• The mechanism in which no link makes a complete revolution will not be useful.
• In a four-bar chain, one of the links, in particular, the shortest link, will make a complete revolution relative to the other three links, if it satisfies Grashof ’s law. Such a link is known as a crank or driver i.e. AD (link 4 ) is a crank.
• The link BC (link 2) which makes a partial rotation or oscillates is known as lever or rocker or follower and the link CD (link 3) which connects the crank and lever is called connecting rod or coupler. 
• The fixed link AB (link 1) is known as the frame of the mechanism.
• When the crank (link 4) is the driver, the mechanism is transforming rotary motion into oscillating motion.

Additional Information

(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 if 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 a double rocker mechanism is possible.

Concept:

Slider crank mechanism:

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. 

The reciprocating engine is an inversion of the slider-crank mechanism with the cylinder as a fixed member.

Explanation:

According to Grashoff’s law:

S + L ≤ P + Q

S + L ≤ P + Q (Class I mechanism)

S + L 

• Shortest link is fixed: Double crank Mechanism
• Link opposite to shortest link is fixed: Double rocker mechanism
• Link adjacent to the shortest link is fixed: crank rocker mechanism

S + L = P + Q

• Shortest link is fixed: double crank mechanism
• Longest link fixed: Double rocker mechanism

S + L > P + Q (class II mechanism)

• Always double rocker mechanism

A pantograph is an instrument used to reproduce to an enlarged or a reduced scale and as exactly as possible the path described by a given point. It consists of four links.

 It is an example of a four-bar kinematic chain. It consists of four links joined in such a way to form a parallelogram ABCD in which AB=CD and AD=BC. In the figure, OAE always remains in a straight line. Pantograph consists of four turning pair. A and E will trace a similar path but of different scale.

Explanation:

Lower pair: When the two elements of a pair have a surface contact when relative motion takes place and the surface of one element slides over the surface of the other, the pair formed is known as lower pair.  Automobile Steering gear, Sliding pairs, turning pairs and screw pairs are the examples of lower pairs.

Higher pair: When the two elements of a pair have a line or point contact when relative motion takes place and the motion between the two elements is partly turning and partly sliding, then the pair is known as higher pair. A pair of toothed gearing, belt and rope drives, ball and roller bearings and cam and follower are the examples of higher pairs.

Grubler’s equation

The Grubler’s criterion is applied to mechanisms with only a single degree of freedom joints where the overall mobility of the mechanism is unity.

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

Shaper is a reciprocating type of machine tool in which the ram moves the cutting tool backward and forwards in a straight line. It is intended primarily to produce flat surfaces. These surfaces may be horizontal, vertical, or inclined.

In a shaper, the rotary motion of the drive is converted into reciprocating motion of the ram by the mechanism housed within the column or the machine.

In a standard shaper, metal is removed in the forward cutting stroke, while the return stroke goes idle and no metal is removed during this period.

The shaper mechanism is so designed that it moves the ram holding the tool at a comparatively slower speed during the forward cutting stroke, whereas during the return stroke it allows the ram to move at a faster speed to reduce the idle return time.

This mechanism is known as the quick return mechanism.

Concept:

Kinematic chain:

When the kinematic pairs are coupled in such a way that the last link is joined to the first link to transmit definite motion (i.e. completely or successfully constrained motion), it is called a kinematic chain.

A relationship between the number of links (l) and the number of joints (j) which constitute a kinematic chain:

• L.H.S. > R.H.S: Locked chain (no relative motion is possible)
• L.H.S. = R.H.S: Constrained kinematic chain/ kinematic chain (the relative motion is completely constrained)
• L.H.S.

Calculation:

Given:

l = 3, j = 3

RHS = 

LHS = 3

∴ LHS > RHS i.e. the chain is locked.

Additional Information

When one of the links of a kinematic chain is fixed, the chain is known as a mechanism.

Concept:

Grashof law: 

For continuous relative motion, the sum of the smallest and longest side must be less than or equal to the summation of adjacent sides. Those mechanisms which follow this law is called as class 1 mechanisms.

s + l  p + q where s= shortest link, l = longest link, p & q = adjacent link

1. If the shortest link is fixed then motion is a double crank.
2. If the shortest link is adjacent to fixed link then motion is the crank rocker.
3. If the shortest link is coupler then the motion is double rocker but continuous because coupler link will become crank.

Calculation:

Given:

Shortest link s =  3, longest link l = 7, p = 5, q = 6

We will check if this mechanism satisfies Grashof's law:

3 + 7  5 + 6 

10  11, the mechanism satisfies the grashof law.

Now, Crank is fixed hence the motion will be double Crank.