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Velocity in Mechanisms
(I Center)
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
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
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
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)
Solution
Velocity diagram scale: 10 cm = 1 m/s
• Velocity of C w.r.t D, vCD = 0.385 m/s
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.
Solution
• N AB = 100 r.p.m
• ωAB = 2 π× 100/60 = 10.47 rad/s
• VAB = ωAB x AB = 3.141 m/s
Solution
• vB = ωBC x I13B, I13B = 0.5
• ωBC = 6.282 rad/s

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Velocity in mechanisms By Instantaneous center method (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