# Machine Kinematics Questions and Answers – Number of Degrees of Freedom for Plane Mechanisms

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This set of Machine Kinematics Multiple Choice Questions & Answers (MCQs) focuses on “Number of Degrees of Freedom for Plane Mechanisms”.

1. The total number of instantaneous centres for a mechanism consisting of n links are
a) n/2
b) n
c) n-1
d) n(n-1)/2

Explanation: 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-1)/2.

2. According to Kennedy’s theorem, if three bodies move relatively to each other, their instantaneous centres will lie on
a) straight line
b) parabolic curve
c) triangle
d) rectangle

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.

3. Which of the following property of the instantaneous center is correct?
a) A rigid link rotates instantaneously relative to another link at the instantaneous centre for the configuration of the mechanism considered.
b) The two rigid links have no linear velocity relative to each other at the instantaneous centre.
c) The velocity of the instantaneous centre relative to any third link is same whether the instantaneous centre is regarded as a point on the first link or on the second rigid link.
d) all of the mentioned

Explanation: None.

4. The magnitude of velocities of the points on a rigid link is
a) directly proportional to the distance from the points to the instantaneous centre and is parallel to the line joining the point to the instantaneous centre.
b) directly proportional to the distance from the points to the instantaneous centre and is perpendicular to the line joining the point to the instantaneous centre.
c) inversely proportional to the distance from the points to the instantaneous centre and is parallel to the line joining the point to the instantaneous centre.
d) inversely proportional to the distance from the points to the instantaneous centre and is perpendicular to the line joining the point to the instantaneous centre.

Explanation: None.

5. 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.

6. The instantaneous centres, which moves as the mechanism moves but joints are of permanent nature, are called permanent instantaneous centres.
a) True
b) False

Explanation: The permanent instantaneous centres move when the mechanism moves, but the joints are of permanent nature.
Fixed instantaneous centres remain in the same place for all configurations of the mechanism.

7. The instantaneous centres which vary with the configuration of mechanism, are called
a) permanent instantaneous centres
b) fixed instantaneous centres
c) neither fixed nor permanent instantaneous centres
d) none of the mentioned

Explanation: Neither fixed nor permanent instantaneous centres vary with the configuration of the mechanism.

8. When two links are connected by a pin joint, 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: None.

9. The two links are said to have a pure rolling contact, when their instantaneous centre __________ on their point of contact.
a) lies
b) does not lie

Explanation: None

10. When a slider moves on a fixed link having ____________ their instantaneous center lies at infinity.
a) straight surface
b) curved surface
c) oval surface
d) none of the mentioned

Explanation: When a slider moves on a fixed link having curved surface, their instantaneous centre lies at the centre of curvature.
When a slider moves on a fixed link having straight surface their instantaneous center lies at infinity.

11. 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 a slider moves on a fixed link having curved surface, their instantaneous centre lies at the centre of curvature.
When a slider moves on a fixed link having straight surface their instantaneous center lies at infinity.

12. A slider moving on a fixed link having constant radius of curvature will have its instantaneous centre at the center of the circle.
a) True
b) False

Explanation: None.

13. The instantaneous center of a rigid thin disc rolling on a plane rigid surface is located at
a) the centre of the disc
b) the point of contact
c) an infinite distance on the plane surface
d) the point on the circumference situated vertically opposite to the contact point