Mid Sem Question Paper

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ME-352 Theory of Mechanisms and Machines Mid Semester Examination

20th September, 2015 Maximum Marks: 100 6:00 PM-8:00 PM Q1. Objective Type Questions (T/F and fill in the blanks) (10)

a) A double rocker can never be a Grashof linkage.

b) It is possible to make a 9 bar constrained linkage containing only simple hinges.

c) There can be a redundant joint and zero redundant links in a mechanism.

d) Instantaneous centre of zero velocity can be used for acceleration analysis.

e) There can be redundant degree of freedom and zero redundant links in a mechanism

f) Orientation of the coupler is a free choice in a motion generation problem.

g) If 𝑠 + 𝑙 = 𝑝 + 𝑞 in a four bar linkage, the extreme positions of the link with maximum range of angular displacement _____________ (intersect/overlap/interfere/don’t exist).

h) Reciprocating engine is a ______________________ (type/mirror image/kinematic inversion/example) of a 3R-1P mechanism.

i) Your Drafter has _________ degree(s) of freedom. j) Number of cranks (links performing complete rotation) in the given linkage is_______________.

𝐿1 > 𝐿2 > 𝐿3 > 𝐿4

Q.2 Calculate the degrees of freedom of each of the following mechanisms and fill the table provided with appropriate values.

(15)

Mark the links as 1 , 2 , 3 , . . . and joints as “1”,”2”,”3”, . . . .

a)

b)

c)

d)

L1 L2 L3 L4

Name: ____________________ Roll No.:_________________

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e)

f)

g)

h)

n j h nr jr Fr F

a

b

c

d

e

f

g

h

Note: n= number of links, j = number of simple joints, h= number of higer pairs, nr= number of redundant links,

jr=number of redundant joints, Fr= number of redundant dof, F= degree of freedom

Name: ____________________ Roll No.:_________________

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Q.3 Revenge of a Design Engineer! (15)

a) You are the operator sitting on an earth mover which uses three hydraulic actuators to perform its operations. Given is the initial configuration of the earth mover. Determine actuator lengths 𝑧1, 𝑧2 and 𝑧3 corresponding to positions 𝛽 and 𝛾 of the bucket using graphical displacement analysis on the provided diagram so that you can accurately operate this marvel.

z1 (mm) z2 (mm) z3 (mm)

Position β

Position γ

b) Draw extreme positions of 𝐶 on the provided diagram and subsequently calculate the QRR for a given constant angular velocity 𝜔.

QRR =

A

B

C

D

C

C

E

F G

H

C

I

J K

β

γ Z1

Z2

Z3

𝝎

B

A

B

B

C

O1 O2

α

Name: ____________________ Roll No.:_________________

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c)

Can the above mechanism achieve a configuration in which 𝜃 = 45° from the horizontal? Support your answer with

graphical displacement analysis on the provided diagram itself.

d) For the following linkages, determine whether they are Grashof/Non-Grashof linkages:

Grashof Non-Grashof

Figure 1

Figure 2

Figure 3

Yes / No

𝜽

Figure 1

Figure 2

Figure 3

10 27

10 15

15

20

30

Diagram to Scale 10

Name: ____________________ Roll No.:_________________

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Q.4 Which one’s better? (20)

Mechanical advantage (𝑀𝐴) of a mechanism is defined as the ratio of the output torque/force to input torque/force.

a. Express 𝑀𝐴 of the following 4 bar mechanism in terms of the linkage parameters.

b. Find the condition to maximize 𝑀𝐴. How does it relate with the transmission angle?

c. Consider a point 𝑃 on the coupler of the given mechanism, find its velocity using both analytical and graphical

techniques.

d. Calculate the error between the analytical and graphical results.

𝜔2 2 rad/sec

r1 5 cm

r2 3 cm

r3 4 cm

r4 6 cm

a 1.5 cm

b 1 cm

𝝎𝟐 𝝎𝟐 𝝎𝟐 𝝎𝟐 𝜽𝟐

𝜽𝟑

𝜽𝟒

r1

r2

r3

r4

a

b

A

B

C

D

P

Name: ____________________ Roll No.:_________________

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Name: ____________________ Roll No.:_________________

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Q5. Caution! Computation ahead! (10)

Generate a 4 bar linkage which satisfies the function ∅ = 2𝜃2 − 1 for the following values of 𝜃:

𝜋6⁄ , 𝜋 3⁄ and 𝜋 2⁄

where 𝜃, 𝛾 and ∅ represent orientations of the input, coupler and output link respectively with the horizontal.

Take free choices for 𝛾 as 𝜋 4⁄ , 𝜋 2⁄ and 3𝜋4⁄ for the respective configurations.

a. Write down all relevant equations.

b. Determine the initial configuration of the 4 bar linkage.

c. Is the resultant mechanism a Grashof linkage?

Name: ____________________ Roll No.:_________________

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Q.6 In the mechanism below, AB rotates with a constant angular velocity 𝝎𝑨 = 10 𝑟𝑎𝑑/𝑠𝑒𝑐 CW. Determine 𝝎𝑯 and

𝜶𝑯 using graphical velocity and acceleration analysis. The figure is to scale (i.e. link lengths are equal to what you can

measure directly from the figure).

Hint: The acceleration component of a point on a constrained link, in a direction perpendicular to its velocity (called

normal component), is independent of the angular acceleration of the link. (30)

A

E

C

B

F

D

G

H

𝝎𝑨

𝜶𝑯

𝝎𝑯

Name: ____________________ Roll No.:_________________

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Name: ____________________ Roll No.:_________________

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