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Kinematics of Machine Lab Experiments

To draw acceleration diagram of four bar mechanism



Aim

To draw acceleration diagram of four bar mechanism.

Problem

The dimensions and configuration of the four bar mechanism, shown in Figure, are as follows:

P1A = 300 mm; P2B = 360 mm; AB = 360mm, and P1P2 = 600 mm. The angle AP1P2= 60°. The crank P1A has an angular velocity of 10 rad/s and an angular acceleration of 30 rad/s 2, both clockwise. Determine the angular acceleration of P2B, and AB and the velocity of the joint B.

PSolution:Given : ω AP1= 10 rad/s; α AP1= 30 rad/s 2; P 1A = 300 mm = 0.3 m ; P 2B = AB =360 mm = 0.36 m. We know that the velocity of A with respect to P 1 or velocity of A, V AP1 = VA = ωAP1 × P1A = 10 × 0.3 = 3 m/s.

diagram

Velocity Diagram

  • Choosing appropriate scale; draw vector ap (VAP1= 3 m/s).
  • Draw fixed point P1& P2 by single point in velocity diagram.
  • From point a, draw vector ab perpendicular to AB to represent velocity of B with respect to A.
  • From point P2 draw vector P2b perpendicular to P2B to represent the velocity of B with respect to P2 or velocity of B.
  • The vectors ab and p 2 b intersect at b.
  • By measurement, we find that p2b = 2.2 m/s
  • We know that angular velocity of P2B, and angular velocity of AB:

equation-1
velocity-diagram-1

Acceleration Diagram

  • Since P1 and P2 are fixed points, therefore these points will lie at one place, in the acceleration diagram. Draw vector p1' x parallel to P1A, to some suitable scale, to represent the radial component of the acceleration of A with respect to P1.
  • From point x, draw vector xa' perpendicular to P1A to represent the tangential component of the acceleration of A with respect to P1.
  • Join p1' a'. The vector p1' a' represents the acceleration of A. By measurement, we find that the acceleration of A.
  • From point a', draw vector a' y parallel to AB to represent the radial component of the acceleration of B with respect to A
  • From point y, draw vector yb' perpendicular to AB to represent the tangential component of the acceleration of B with respect to A
  • Now from point p’2 ,draw vector p’2z parallel to P2B to represent the radial component of the acceleration B with respect to P2.
  • From point z, draw vector zb' perpendicular to P2B to represent the tangential component of the acceleration of B with respect to P2.
  • The vectors yb' and zb' intersect at b'. Now the vector p2' b' represents the acceleration of B with respect to P2 or the acceleration of B.

equation-2
acceleration-diagram

Conclusion

The acceleration diagram of four bar mechanism was drawn and analysed.