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# Machine Kinematics Questions and Answers – Properties of Instantaneous Centre

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

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Answer: d

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.

Instantaneous center of rotation of a link in a four bar mechanism lies on

a) right side pivot of this link

b) left side pivot of this link

c) a point obtained by intersection on extending adjoining links

d) none of the mentioned

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Answer: c

Explanation: None.

The total number of instantaneous centers for a mechanism of n links is

a) n(n – 1)/2

b) n

c) n – 1

d) n(n – 1)

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Answer: a

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(n – 1)/2.

The number of links and instantaneous centers in a reciprocating engine mechanism are

a) 4,4

b) 4,5

c) 5,4

d) 4,6

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Answer: d

Explanation: First of all, determine the number of instantaneous centres (N) by using the relation

N = n(n – 1)/2

In present case, N = 4(4 – 1)/2 (n = 4)

= 6.

According to Kennedy’s theorem, if three bodies have plane motions, their instantaneous centres lie on

a) a triangle

b) a point

c) two lines

d) a straight line

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Answer: d

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.

In a rigid link OA, velocity of A w.r.t. O will be

a) parallel to OA

b) perpendicular to OA

c) at 450 to OA

d) along AO

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Answer: b

Explanation: None.

Two systems shall be dynamically equivalent when

a) the mass of two are same

b) c.g. of two coincides

c) M.I. of two about an axis through c.g. is equal

d) all of the mentioned

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Answer: d

Explanation: None.

A link is rotating about O. Velocity of point P on link w.r.t. point Q on link will be perpendicular to

a) OP

b) OQ

c) PQ

d) line in between OP and OQ

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Answer: c

Explanation: A link is rotating about O. Velocity of point P on link w.r.t. point Q on link will be perpendicular to PQ.

The velocity of any point in mechanism relative to any other point on the mechanism on velocity polygon is represented by the line joining the corresponding points.

The velocity of any point in mechanism relative to any other point on the mechanism on velocity polygon is represented by the line

a) joining the corresponding points

b) perpendicular to line

c) at 450 to line

d) none of the mentioned

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Answer: a

Explanation: A link is rotating about O. Velocity of point P on link w.r.t. point Q on link will be perpendicular to PQ.

The velocity of any point in mechanism relative to any other point on the mechanism on velocity polygon is represented by the line joining the corresponding points.

The absolute acceleration of any point P in a link about center of rotation O is

a) along PO

b) perpendicular to PO

c) at 450 to PO

d) none of the mentioned

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Answer: d

Explanation: The coriolis component of acceleration is always perpendicular to the link.

Angular acceleration of a link can be determined by dividing the

a) centripetal component of acceleration with length of link

b) tangential component of acceleration with length of link

c) resultant acceleration with length of link

d) all of the mentioned

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Answer: b

Explanation: The angular acceleration of the link AB is obtained by dividing the tangential components of the acceleration of B with respect to A to the length of the link.