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Kinematics of Machine Lab Experiments

To draw velocity diagram of slider crank mechanism



Aim

To draw velocity diagram of slider crank mechanism

Problem

The crank of a slider crank mechanism rotates clockwise at a constant speed of 300 r.p.m. The crank is 150 mm and the connecting rod is 600 mm long. Determine : 1. Linear velocity and of the midpoint of the connecting rod, and 2. angular velocity of the connecting rod, at a crank angle of 45° from inner dead centre position.

P1A = 300 mm; P2B = 360 mm; AB = 360mm, and P1P2 = 600 mm. The angle AP1P2= 60°. The crank P 1A has an angular velocity of 10 rad/s and an angular acceleration of 30 rad/s 2, both clockwise. Determine the angular velocities of P2B, and AB and the velocity of the joint B.

PSolution:Given:N BO= 300 r.p.m. or ω BO= 2π × 300/60 = 31.42 rad/s; OB = 150 mm =0.15 m ; BA = 600 mm = 0.6m. We know that linear velocity of B with respect to O or velocity of B, v BO= v B= ω BO× O B= 31.42 × 0.15 = 4.713 m/s...(Perpendicular to B O)

Velocities in Slider Crank Mechanism

space-diagram

First of all draw the space diagram, to some suitable scale; as shown in Fig. Now the velocity diagram, as is drawn as discussed below:

  1. Draw vector ob perpendicular to BO, to some suitable scale, to represent the velocity of B with respect to O or simply velocity of B i.e. v BO or v B, such thatvector ob = v BO= v B = 4.713 m/s
  2. From point b, draw vector ba perpendicular to BA to represent the velocity of A withrespect to B i.e. v AB, and from point o draw vector o a parallel to the motion of A (which is along A O)to represent the velocity of A i.e. v A. The vectors ba and oa intersect at a. By measurement, we find that velocity of A with respect to B, v AB = vector ba= 3.4 m / s and Velocity of A ,v A = vector o a= 4 m / s
  3. In order to find the velocity of the midpoint D of the connecting rod A B, divide the vectorba at d in the same ratio as D divides A B, in the space diagram. In other words, bd / ba = BD/BA Since D is the midpoint of A B, therefore d is also midpoint of vector ba.
  4. Join od. Now the vector od represents the velocity of the midpoint D of the connecting rod i.e. v D By measurement, we find that v D = vector od = 4.1 m/s Ans.
  5. The vectors ab and p2b intersect at b.
  6. By measurement, we find that p2b = 2.2 m/s
  7. We know that angular velocity of P2B, and angular velocity of AB:
b-velocity-diagram

Conclusion

The velocity diagram of slider crank was drawn and analysed.