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Velocity analysis of 4-bar mechanism

(Instant center method) Lecture –  4

J S Rathore

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2

Velocity analysis

Instantaneous center (I-center) method Planar motion of a rigid body at any given instant can be modelled as pure

rotation

 Johann Bernoulli  (1742) and Chasles (1830)

Primary centers

Total number of I-centers in a planar mechanism and how to locate them?

Kennedy-Aronholdt Theorem

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3

1

2(23)

Some instant centers  can be located by simply inspecting a mechanism. Thesecenters are termed as primary centers.

Instant center of velocity

Or (21)

(13) at ∞ 

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Kennedy-Aronholdt Theorem

If three bodies are in relative planar motion withrespect to one another, the  three relative inst 

ant

centers of velocity are collinear.

Total number of instant centersassociated with n bodies 2

)1(     nn N 

Kennedy-Aronholdt theorem (Kennedy’s rule):

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Locating I-centers

2

3

4

1

(12)

(23)

(34)

(14)(24)

12 13 14

23 24

342

)1(     nn

 N 

ω2

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)1224(ω224   V 

Imagine link 2 is containing point 24 and revolvingabout 12 or A 

)1424(ω424   V 

 Now, Imagine link 4 containing point 24 and revolving

about 14

Angular velocity of link 4 ?

ω2

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1424

1224

ω

ω

2

4

 

  

 

1424

1224ω

)1424(ω 2

244

V 

Angular velocity of link 4 ?

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In a slider crank mechanism, the length of the crank and the connecting rod are200 mm and 800 mm, respectively.

1. Locate all the instantaneous centers of the mechanism for the position of

the crank when it has turned 30° from the inner dead centre.

2. Also, find the velocity of the slider if the crank rotates at 40 rad/s CCW.

Ex 1

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2

3

4

1

(24)

(13)

Find the velocity of the slider  if the crank rotates at 40 rad/s CCW. 

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Figure shows the quick return mechanism of the slotted lever. Locate all the instantcenters and determine the velocity of the cutting tool at S  and the angular velocity of

the links AR and RS . The crank OP  rotates at 10 rpm.

Ex 2

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(12)

(23)

(14)

1

2

3

4

5

6(34) at ∞ 

(45)

(56)

(16) at ∞ 1 2

3

45

6

(15)

(24)(25)

Ex 2

rad/s98.1ωrad/s,25.4ω

m/s66.1

54

6

V