Answer to Question #200281 in Mechanical Engineering for Muhammad Idrees

Question #200281

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



1
Expert's answer
2021-06-07T05:45:41-0400

"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"


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