Locate all the instantaneous centers for a four bar mechanism as shown in Fig. (a) The lengths of various links are: AD = 125 mm; AB = 62.5 mm; BC = CD = 75 mm. If the link AB rotates at a uniform speed of 10 rpm in the clockwise direction, find the angular velocity of the links BC and CD.

Solution:

**Solution:**

————————————————————————————————————–

**Given:**

■ Length of *AD = 125 mm = 0.125 m*

■ Length of *AB = 62.5 mm = 0.0625 m*

■ Length of *BC = CD = 75 mm = 0.075 m*

■ Speed of link AB, *NAB = 10 rpm*

■ Angular velocity at link AB ,*ω**AB**= (2**π**N) / 60 = (2 x**π x**10) / 60 =1.0471 rad/s*

————————————————————————————————————–

**Objective:**

Find the Angular velocities of

(1) Link BC

(2) Link CD

————————————————————————————————————–

**Step 1 of 4 │Determine the number of Instantaneous centers**

The given four bar mechanism have four links (i.e n=4), Therefore number of Instantaneous centers is given by

Therefore Six instantaneous centers are in the given four bar mechanics. They are

**I12, I14**are the fixed instantaneous centres and **I13, I23, I24, I34**are varying instantaneous centres (Changes with configuration of links)

————————————————————————————————————–

**Step 2 of 4 │Locate the instantaneous centres on the figure**

Draw the Fourbar mechanism * (Refer Figure.1)* as per the dimension and locate the instantaneous centres. Measure the distance of the instantaneous from the joints.

Figure.1

————————————————————————————————————–

**Step 3 of 4 │Determine the angular velocity of the link BC**

We know that

Therefore velocity at point B in link AB is given by

Substituting known values

Since the point B is also a point on link BC, therefore velocity of point B on link BC is

From the Figure.1,

The distance I13.B =103.83 mm = 0.1038 m

Therefore

————————————————————————————————————–

**Step 4 of 4 │Determine the angular velocity of the link BC**

The instantaneous centre I13 is common for joints B and C, Therefore we can write

From the Figure.1,

The distance I13.B =103.83 mm = 0.1038 m

The distance I13.C =75 mm = 0.075 m

Substituting values

We know that

Therefore

**————————————————————————————————————–****Answer:**

**————————————————————————————————————–**