Four Bar Chain Laboratory Experiment PDF

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Four Bar Chain Laboratory Experiment Full Report with data discussion and conclusion...

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SRI LANKA INSTITUTE OF INFORMATION TECHNOLOGY

Faculty of Engineering

ME2021 - Mechanics of Machines LAB 3 : Four-Bar Chain

Name: EN Number: Date of Performance: 06-04-2021 Date of Submission: 17-04-2021

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Procedure • • • • • •

First the parts of the 4-bar linkage was identified as crank, frame, coupler and the follower. Rocker length was adjusted using the knurled screw. Bars should be moved freely so the screw should not be tightened. Then using the ruler lengths of the crank, follower, rocker and the frame were measured. From 0 degree of the crank, position of the rocker bar was noted. 𝑂A𝐷 was measured. Rotating the crank angle was changed accordingly 0,10,20,30,40, and 45. And the rocker angle and the OAD was measured.

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Observations

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Calculations Degrees of Freedom= 3(N-1)-2L-H = 3*3-2*4-0 =1

1. 𝑉B = (

𝑂A𝐷 ) ∗ 𝑉A 𝑂A𝐴

22 =( )∗1 40 = 0.55 m/s 2. 𝑉B = (

𝑂A𝐷

𝑂A𝐴

) ∗ 𝑉A

27 =( )∗1 40 = 0.675 m/s 3. 𝑉B = (

𝑂A𝐷 ) ∗ 𝑉A 𝑂A𝐴

32 =( )∗1 40 = 0.8 m/s

4. 𝑉B = (

𝑂A𝐷

𝑂A𝐴

) ∗ 𝑉A

35 =( )∗1 40 = 0.875 m/s 5. 𝑉B = (

𝑂A𝐷 ) ∗ 𝑉A 𝑂A𝐴

38 =( )∗1 40 4

= 0.95 m/s 6.

𝑂A𝐷 ) ∗ 𝑉A 𝑂A𝐴 40 =( )∗1 40

𝑉B = (

= 1 m/s

Results OA=40mm AB=175mm OB=100mm

𝑉B = (

θº ϕ OAD (mm) VB (m/s)

0 68 22 0.55

10 71 27 0.675

𝑂A𝐷 ) ∗ 𝑉A 𝑂A𝐴

20 73 32 0.8

Plot VB against θ

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30 76 35 0.875

40 80 38 0.95

45 81 40 1

VB Vs θ 1.2 1 0.8 0.6 0.4 0.2 0 0

10

20

30 VB

Plot ωAB vs θº

2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0

10

20

30

40

45

6

40

45

For the crank angle of θº =45 and for a coupler point M, midway on the follower, draw the cognate linkages to scale.

Find the rocking angle for the link OB. Minimum = 64º Maximum =118º Rocking angle= 118-64 = 56 º

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Discussion Explain some practical applications of using four bar chain. One of the uses of four bar chain is locking pliers. The four-bar linkage is used for locking pliers. The B-C and C-D relations are set at a nearly 180-degree angle. The angle between the bonds is less than 180 degrees when force is applied to the handle. The jaws try to hold the handle open as a result of the impact.

Oil wells must constantly pump up the oil in places where underground oil is not under enough pressure to drive it all the way to the surface. A pumpjack, which consists of a four-bar connection, is a drive mechanism for accomplishing this. The strong spinning counterweight is positioned so that it falls as the pump does its up-stroke, raising the oil toward gravity.

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Bicycles use a four-bar linkage to convert reciprocating human motion into rotary motion. Just two of the four connections in the bicycle linkage are realistic pin joint versions. Only compression is permitted at the pedal and seat, since there is no way for the rider to pull up on the pedal or seat. On racing bikes, the feet are clipped to the pedals and each foot will pull up as well as step down, which is a different strategy.

The human knee joint is a kind of biological hinge that can only shift in one direction. The femur (upper leg bone) and tibia (larger of the two lower leg bones) are connected by the knee, which allows them to spin freely along a single axis. To hold the two legs bones attached to each other while also allowing rotation, a mechanism is required. A four-bar linkage is used to do this in the human knee. (A. B. Zavatsky & J. J. O'Connor, 1992)

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One of the inventors of the steam engine was James Watt. He also devised a connection that could create motion in a straight line. As seen below, this is widely found in suspension structures.

And also in old vehicles they used four bar chain mechanism for wipers.

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Describe the Grashof’s criteria give example.

Grashof's theorem, published in 1883, was the first to discuss the mobility problem of planar four-bar mechanisms, especially those with all revolute joints. Consider a four-link kinematic chain, where is the shortest link length, l is the longest link length, p and q are the other two connections' link lengths, and 1 > p q > s is the longest link length. Grashof stated that there exists at least one link which can fully revolve with respect to the other three links if, l+s≤p+q and none of the four links can make a full revolution if, l+s>p+q No relation would be able to complete a revolution if s + l > p + q. The resulting mechanism is known as a triple rocker mechanism.

l + s ≤ p + q can be divided into two parts 1. l + s < p + q 2. l + s = p + q according to the changes of lengths mechanisms are named differently. Crank rocker, double crank, double rocker, parallelogram linkage and deltoid linkage are named.

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Explain the other arrangements of the mechanism, such as Parallelogram, Crank Rocker, Drag Link, and Double rocker while referring to different dimensions of the links. I.

The mechanism obtained in this case is known as crank rocker mechanism.

II.

The mechanism obtained in this case is known as double crank mechanism.

III.

The mechanism obtained in this case is known as double rocker mechanism.

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I.

Example: ‘s’ is 1 unit, ‘l’ is 4 units, ‘p’ is 2 units and ‘q’ is 3 units. In this case, s + l = p + q = 5 units. In this case, all the inversions obtained are the same as in the case ‘s + l < p + q’.

a. b. c.

II.

Crank rocker: The link adjacent to the shortest link is fixed. Double crank: The shortest link is fixed. Double rocker: The shortest link is opposite to the fixed link.

Example: p = s = 1 unit and l = 4 units. Now for ‘s + l = p + q’, q = l = 4 units. So, we have two pairs of equal length. In this case, the links can be joined in two ways:

a. Equal links opposite to each other: The linkage so obtained is parallelogram linkage. b. Equal links adjacent to each other: The linkage so obtained is deltoid linkage.

The drag-link refers to a four-bar linkage in which both rotating links (cranks) make complete revolutions. As long as you keep the points that control the lengths of the links within the rectangle and approximately the same length, there will be no dead-point positions and both cranks will turn freely. (Phelps, n.d.) (Anon., 2020) (Anon., n.d.)

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Conclusion From this experimental we learnt about 4 bar linkages and their applications. Different types of mechanisms due to the length of the 4 bars. The relation between follower length and the rocking angle. It has inverse proportional relation. Using instantaneous center is hard to find the velocities for this experiment. But it was easy to get the velocity of point B using the given procedure. Experimental was successfully done.

References A. B. Zavatsky & J. J. O'Connor, 1992. A model of human knee ligaments in the sagittal plane: Part 1: Response to passive flexion. Proceedings of the Institution of Mechanical Engineers, Part H. Journal of Engineering in Medicine, 206(September 1, 1992), p. 3. Anon., 2018. Slide Share. [Online] Available at: https://www.slideshare.net/ManthanChavda2/inversion-of-4-bar-chain-mechanism [Accessed 17 April 2021]. Anon., 2020. Free Aptitude. [Online] Available at: https://www.freeaptitudecamp.com/grashof-law/ [Accessed 16 April 2021]. Anon., n.d. Mechdesigner. [Online] Available at: http://mechdesigner.support/index.htm?md-kinematics-grashoff-criterion.htm [Accessed 16 April 2021]. Phelps, S., n.d. GeoGebra. [Online] Available at: https://www.geogebra.org/m/zZ5Bt9hX [Accessed 16 April 2021].

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