Answer to Question #296480 in Mechanical Engineering for king

Question

Slider crank mechanism as shown in the figure calculate the i) Acceleration of the slider B ii) Acceleration of the point E iii) Angular acceleration of the link AB OA rotates at (30+X) rad/s in counter clockwise direction (10marks) X is the last digit of the student roll no. for example if the student roll no is A09 then X=9 and ω=30+9=39 rad/s. Draw the neat and clean diagram with proper scale. Rough drawings will not be considered

Answer 1

Velocity diagram and Acceleration diagram, 

 and 

Trigonometric relations: for an isosceles triangle two sides are equal.

To find acceleration of the slider crank using exact analysis.

V_A → velocity of A w.r.t. O

V_BA → velocity of B w.r.t. A.

Velocity component of B along x direction = V_BAcos 45

Also due to the constraint on slider V_BA along x = 0 (i.e. V_BA is along y direction only)

⇒ V_BA cos 45 = 0

⇒ V_BA = 0

Also, V_BA = V_B - V_A = 0 ⇒ V_B = V_A

Now, constructing the velocity diagram for given case V_A= rω

Now Constructing the acceleration diagram: