1. The number of degrees of freedom of a planar linkage with 8 links and 9 simple revolute joints is
a) 1
b) 2
c) 3
d) 4
Explanation: Given l= 8, j= 9
We know that, Degree of freedom,
n =3(l − 1)−2j = 3(8 − 1)−2 x 9 = 3.
2. The lengths of the links of a 4-bar linkage with revolute pairs are p,q,r, and s units. given that p<q<r<s. Which of these links should be the fixed one, for obtaining a “double crank” mechanism ?
a) link of length p
b) link of length q
c) link of length r
d) link of length s
Explanation: Given p<q<r<s
“Double crank” mechanism occurs, when the shortest link is fixed. From the given pairs p is the shortest link. So, link of length p should be fixed
3. When a cylinder is located in a Vee-block, the number of degrees of freedom which are arrested is
a) 2
b) 4
c) 7
d) 8
Explanation: Number of degrees of freedom = 2 & movability includes the six degrees of freedom of the device as a whole, as the ground link were not fixed. So, 4 degrees of freedom are constrained or arrested.
4. The minimum number of links in a single degree-of-freedom planar mechanism with both higher and lower kinematic pairs is
a) 2
b) 3
c) 4
d) 5
Explanation: From the Kutzbach criterion the degree of freedom,
n = 3(l − 1) − 2j − h
For single degree of Freedom (n = 1),
1 = 3(l − 1) − 2j − h
3l − 2j − 4 − h = 0 …(i)
The simplest possible mechanisms of single degree of freedom is four-bar mechanism. For this mechanism j = 4, h = 0
From equation (i), we have
3l − 2 x 4 − 4 − 0 = 0
or, l = 4.
5. The total number of instantaneous centres for a mechanism consisting of n links are
a) n/2
b) n
c) n – 1/2
d) n(n – 1)/2
Explanation: The number of instantaneous centres in a constrained kinematic chain is equal to the number of possible combinations of two links. The number of pairs of links or the number of instantaneous centres is the number of combinations of n links taken two at a time. Mathematically, number of instantaneous centres, N = n(n – 1)/2 where n = Number of links.
6. According to Aronhold Kennedy’s theorem, if three bodies move relatively to each other, their instantaneous centres will lie on a
a) straight line
b) parabolic curve
c) ellipse
d) none of the mentioned
Explanation: The Aronhold Kennedy’s theorem states that if three bodies move relatively to each other, they have three instantaneous centres and lie on a straight line.
7. In a mechanism, the fixed instantaneous centres are those centres which
a) remain in the same place for all configurations of the mechanism
b) vary with the configuration of the mechanism
c) moves as the mechanism moves, but joints are of permanent nature
d) none of the mentioned
Explanation: Fixed instantaneous centres remain in the same place for all configurations of the mechanism. The permanent instantaneous centres move when the mechanism moves, but the joints are of permanent nature
8. The instantaneous centres which vary with the configuration of the mechanism, are called
a) permanent instantaneous centres
b) fixed instantaneous centres
c) neither fixed nor permanent instantaneous centres
d) none of the mentioned
Explanation: Fixed instantaneous centres remain in the same place for all configurations of the mechanism. The permanent instantaneous centres move when the mechanism moves, but the joints are of permanent nature. Neither fixed nor permanent instantaneous centres vary with the configuration of the mechanism.
9. When a slider moves on a fixed link having curved surface, their instantaneous centre lies
a) on their point of contact
b) at the centre of curvature
c) at the centre of circle
d) at the pin joint
Explanation: When the slider link moves on fixed link having constant radius of curvature, the instantaneous centre lies at the centre of curvature i.e. the centre of the circle, for all configuration of the links.
10. Which is the false statement about the properties of instantaneous centre?
a) at the instantaneous centre of rotation, one rigid link rotates instantaneously relative to another for the configuration of mechanism considered
b) the two rigid links have no linear velocities relative to each other at the instantaneous centre
c) the two rigid links which have no linear velocity relative to each other at this centre have the same linear velocity to the third rigid link
d) the double centre can be denoted either by O21 or O12, but proper selection should be made
Explanation: The following properties of the instantaneous centre are important from the subject point of view :
1. A rigid link rotates instantaneously relative to another link at the instantaneous centre for the configuration of the mechanism considered.
2. The two rigid links have no linear velocity relative to each other at the instantaneous centre. At this point (i.e. instantaneous centre), the two rigid links have the same linear velocity relative to the third rigid link. In other words, the velocity of the instantaneous centre relative to any third rigid link will be same whether the instantaneous centre is regarded as a point on the first rigid link or on the second rigid link.