Kinematics of Machine Lab Experiments
To draw acceleration diagram of four bar mechanism
Oct 18 2023
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:
P_{1}A = 300 mm; P_{2}B = 360 mm; AB = 360mm, and P_{1}P_{2} = 600 mm. The angle AP_{1}P_{2}= 60°. The crank P_{1}A has an angular velocity of 10 rad/s and an angular acceleration of 30 rad/s ^{2}, both clockwise. Determine the angular acceleration of P_{2}B, and AB and the velocity of the joint B.
P_{Solution:}Given : ω _{AP1}= 10 rad/s; α _{AP1}= 30 rad/s ^{2}; P _{1}A = 300 mm = 0.3 m ; P _{2}B = 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 = ω_{AP1} × P_{1}A = 10 × 0.3 = 3 m/s.
Velocity Diagram
- Choosing appropriate scale; draw vector ap (V_{AP1}= 3 m/s).
- Draw fixed point P_{1}& P_{2} 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 P_{2} draw vector P_{2}b perpendicular to P_{2}B to represent the velocity of B with respect to P_{2} or velocity of B.
- The vectors ab and p _{2} b intersect at b.
- By measurement, we find that p_{2}b = 2.2 m/s
- We know that angular velocity of P_{2}B, and angular velocity of AB:
Acceleration Diagram
- Since P_{1} and P_{2} are fixed points, therefore these points will lie at one place, in the acceleration diagram. Draw vector p1' x parallel to P_{1}A, to some suitable scale, to represent the radial component of the acceleration of A with respect to P_{1}.
- From point x, draw vector xa' perpendicular to P_{1}A to represent the tangential component of the acceleration of A with respect to P_{1}.
- Join p_{1}' a'. The vector p_{1}' 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 y_{b}' 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’_{2}z parallel to P_{2}B to represent the radial component of the acceleration B with respect to P_{2}.
- From point z, draw vector zb' perpendicular to P_{2}B to represent the tangential component of the acceleration of B with respect to P_{2}.
- The vectors y_{b}' and z_{b}' intersect at b'. Now the vector p_{2}' b' represents the acceleration of B with respect to P_{2} or the acceleration of B.
Conclusion
The acceleration diagram of four bar mechanism was drawn and analysed.