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.

P_Solution: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 = ω_AP1 × P₁A = 10 × 0.3 = 3 m/s.

Velocity Diagram

• Choosing appropriate scale; draw vector ap (V_AP1= 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:

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 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’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 y_b' and z_b' intersect at b'. Now the vector p₂' b' represents the acceleration of B with respect to P₂ or the acceleration of B.

Conclusion

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