Answer to Question #198982 in Mechanical Engineering for Muhammad Idrees

Question

The crank and connecting rod of a reciprocating engine are 200 mm and 700 mm respectively. The crank is rotating in clockwise direction at 120 rad/s. Find with the help of Klein’s construction: 1. Velocity and acceleration of the piston, 2. Velocity and acceleration of the midpoint of the connecting rod, and 3. Angular velocity and angular acceleration of the connecting rod, at the instant when the crank is at 30° to I.D.C. (inner dead center). [Ans. 15.24 m/s, 2880 m/s2 ; 16.8 m/s, 2779.2 m/s2 ; 29.66 rad/s, 1913.14 rad/s2]

Answer 1

1. Velocity and acceleration of the piston

We know that the velocity of the piston P,

$v_p = ω × OM = 120 × 0.127 = 15.24 m/s$

and acceleration of the piston P.

a_p = ω² × NO = (120)² x 0.2 = 2880 m/s²

Angular velocity and angular acceleration of the connecting rod.

We know that the velocity of the connecting rod PC (i.e. velocity of P with respect).

V_pm = ω × CM = 120 × 0.173 = 20.76 m/s