Answer to Question #200281 in Mechanical Engineering for Muhammad Idrees

Question

In a pin jointed four bar mechanism ABCD, the lengths of various links are as follows:

A B = 25 mm ; BC = 87.5 mm ; CD = 50 mm and AD = 80 mm. The link AD is fixed and the angle BAD = 135°. If the velocity of B is 1.8 m/s in the clockwise direction, find 1. velocity and acceleration of the mid point of BC, and 2. angular velocity and angular acceleration of link CB and CD

Answer 1

$V_{BA}=1.8m/sec; V_{BC}=2*0.5=1m/sec;V_{C} =V_{CD}=3.1*0.5=1.55m/sec$

$V_{E}=34*0.5=1.7m/sec$

For angular velocity of BC and CD

$BC= \frac{V_{BC}}{BC}= \frac {{1}}{0.0875}=11.43rad/sec; CD= \frac{V_{CD}}{CD}= \frac {{1.55}}{0.050}=31rad/sec$

$a^r_{BA}=\frac{(V_BA)^2}{BA}=\frac{(1.8)^2}{0.025}=129.6m/sec$

$a^r_{CB}=\frac{(V_CB)^2}{CB}=\frac{(1)^2}{0.0875}=11.43m/sec$

$a^r_{CD}=\frac{(V_CD)^2}{CD}=\frac{(1.55)^2}{0.0.050}=48.05m/sec$

No Tangential component of BA

$a_e=8.9*12=106.8m/sec$

For angular$\space acc^n$ of BC and CD

$a^t_{BC}=6.3*12=75.6m/sec$

$a^t_{BC}=(BC). \alpha_{BC}=\frac{75.6}{0.0875}=864rad/sec$

$a^t_{CD}=5.2*12=62.4m/sec^2=\frac{a^t_{CD}}{CD}=\frac{62.4}{0.050}=1248rad/sec^2$