Theory of Machines Test 1

Result

Theory of Machines Test 1

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Question 1
1 / -0

A mechanism is to be constructed constructing of only lower pairs. What is the minimum number of links which can be used to form this?

A
4-4

B
44-41

C
47-46

D
49-42

Solution

Concept:
Degree of freedom of a mechanism, F = 3(n - 1) – 2j – h – F_r
n = number of links, j = number of binary joints, h = number of higher pairs
F_r = number of redundant links
for minimum number of links we use, j >1 and degree of freedom =1
Calculation:
F = 3(n - 1) – 2j - h – F_r
1 = 3n – 3 -2j
∴ 3n – 2j = 4
\(\therefore \;n\; = \frac{{4\; + \;2j}}{3}\)
j > 1, for a mechanism to be formed we have to take any higher value, more than 1 but since we want an integer value and also we have to use the minimum possible joints hence we will check by trial and error method until we get an integer value.
Hence 2, 3 cannot be the answer but when you substitute 4 you will get the value as 4.
Hence n = 4 at j = 4