This document discusses calculating angular velocities in 4-bar linkage mechanisms. It provides an example of a mechanism where the crank rotates at 120 rpm, with given link lengths. Using the instant centers, it calculates the angular velocity of link CD as 5.024 rad/sec or 0.4019 m/sec. A second problem is presented with different link lengths and a crank rotating at 100 rpm, where the task is to find the angular velocity of link BC using the instant centers.

1. Velocity in Mechanisms
(I Center)

2. Problem 1
• In a 4 bar chain mechanism shown in figure, crank AB rotates
at 120 rpm clockwise direction. Link BC and AD are of equal
length 150 mm. CD and AB lengths are 80 mm and 40 mm
respectively. Angle BAD = 60o. Find angular velocity (ωCD) of
link CD

3. Locate I-centers
• I13B = 410 mm
• I24D= 250 mm
• I24A= 100 mm
A
B
D
C
I24
Link 1
Link 2
Link 4
Link 3
I13
I12
I23
I34
I14

4. Solution
• I24D= 250 mm
• I24A= 100 mm
• = 12.56 rad/sec
A
B
D
C
I24
Link 1
Link 2
Link 4
Link 3
I13
I12
I23
I34
I14

5. Solution
• ωCD = 12.56 x 100 / 250 = 5.024 rad/sec
• vCD = ωCD x CD = 5.024 x 0.08 = 0.4019 m/sec
• vCD = 0.385 m/s (By Relative Velocity Method)

6. Solution
Velocity diagram scale: 10 cm = 1 m/s
• Velocity of C w.r.t D, vCD = 0.385 m/s

7. Problem 2
• In a pin jointed four bar mechanism, as shown in Fig. 6.9, AB =
300 mm, BC = CD = 360 mm, and AD = 600 mm. The angle
BAD = 60°. The crank AB rotates uniformly at 100 r.p.m. Locate
all the instantaneous centres and find the angular velocity of
the link BC.

8. Solution
• N AB = 100 r.p.m
• ωAB = 2 π× 100/60 = 10.47 rad/s
• VAB = ωAB x AB = 3.141 m/s

9. Solution
• vB = ωBC x I13B, I13B = 0.5
• ωBC = 6.282 rad/s