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ABCD is a four bar mechanism. AD is fixed link. At the instant AB and DC are vertical whereas BC is horizontal. AB is shorter than DC by 300 mm. The angular velocity of AB and DC are 5 radian per second and 2 radian per second respectively. The length of AB is?
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ABCD is a four bar mechanism. AD is fixed link. At the instant AB and ...
Solution:
Given data:
- AD is fixed link
- AB and DC are vertical
- BC is horizontal
- AB is shorter than DC by 300 mm
- Angular velocity of AB = 5 rad/s
- Angular velocity of DC = 2 rad/s
Step 1: Draw a diagram
Draw a diagram of the four bar mechanism ABCD.
Step 2: Find the angle between AB and AD
Since AB and DC are vertical and BC is horizontal, we can find the angle between AB and AD as follows:
Angle ABD = Angle DCA (Alternate angles)
Angle BAC = Angle CDA (Alternate angles)
Angle ABD + Angle BAC + Angle BCA = 180 degrees (Sum of angles in a triangle)
Angle ABD + Angle BAC + 90 degrees = 180 degrees (Angle BCA is a right angle)
Angle ABD + Angle BAC = 90 degrees
Therefore, the angle between AB and AD is 90 degrees.
Step 3: Find the length of BC
Since AB is shorter than DC by 300 mm, we can express the length of DC as follows:
DC = AB + 300
Let the length of BC be x. Then we can use the cosine rule to find the length of BC as follows:
x^2 = AB^2 + DC^2 - 2ABDCcos(ABD)
x^2 = AB^2 + (AB + 300)^2 - 2AB(AB + 300)cos(90 degrees)
x^2 = AB^2 + AB^2 + 600AB + 90000 - 600AB
x^2 = 2AB^2 + 90000
x = sqrt(2AB^2 + 90000)
Step 4: Find the length of AB
We know that the angular velocity of AB is 5 rad/s and the length of BC is x, so we can find the angular velocity of BC as follows:
Angular velocity of BC = (Length of AB / Length of BC) x Angular velocity of AB
2 rad/s = (AB / x) x 5 rad/s
AB = 0.4x
Substituting the value of x from Step 3, we get:
AB = 0.4 sqrt(2AB^2 + 90000)
Squaring both sides and simplifying, we get:
0.16(2AB^2 + 90000) = AB^2
AB^2 - 288AB - 562500 = 0
(AB - 750)(AB + 750) = 0
Since AB cannot be negative, we have:
AB = 750 mm
Therefore, the length of AB is 750 mm.
Given data:
- AD is fixed link
- AB and DC are vertical
- BC is horizontal
- AB is shorter than DC by 300 mm
- Angular velocity of AB = 5 rad/s
- Angular velocity of DC = 2 rad/s
Step 1: Draw a diagram
Draw a diagram of the four bar mechanism ABCD.
Step 2: Find the angle between AB and AD
Since AB and DC are vertical and BC is horizontal, we can find the angle between AB and AD as follows:
Angle ABD = Angle DCA (Alternate angles)
Angle BAC = Angle CDA (Alternate angles)
Angle ABD + Angle BAC + Angle BCA = 180 degrees (Sum of angles in a triangle)
Angle ABD + Angle BAC + 90 degrees = 180 degrees (Angle BCA is a right angle)
Angle ABD + Angle BAC = 90 degrees
Therefore, the angle between AB and AD is 90 degrees.
Step 3: Find the length of BC
Since AB is shorter than DC by 300 mm, we can express the length of DC as follows:
DC = AB + 300
Let the length of BC be x. Then we can use the cosine rule to find the length of BC as follows:
x^2 = AB^2 + DC^2 - 2ABDCcos(ABD)
x^2 = AB^2 + (AB + 300)^2 - 2AB(AB + 300)cos(90 degrees)
x^2 = AB^2 + AB^2 + 600AB + 90000 - 600AB
x^2 = 2AB^2 + 90000
x = sqrt(2AB^2 + 90000)
Step 4: Find the length of AB
We know that the angular velocity of AB is 5 rad/s and the length of BC is x, so we can find the angular velocity of BC as follows:
Angular velocity of BC = (Length of AB / Length of BC) x Angular velocity of AB
2 rad/s = (AB / x) x 5 rad/s
AB = 0.4x
Substituting the value of x from Step 3, we get:
AB = 0.4 sqrt(2AB^2 + 90000)
Squaring both sides and simplifying, we get:
0.16(2AB^2 + 90000) = AB^2
AB^2 - 288AB - 562500 = 0
(AB - 750)(AB + 750) = 0
Since AB cannot be negative, we have:
AB = 750 mm
Therefore, the length of AB is 750 mm.
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ABCD is a four bar mechanism. AD is fixed link. At the instant AB and DC are vertical whereas BC is horizontal. AB is shorter than DC by 300 mm. The angular velocity of AB and DC are 5 radian per second and 2 radian per second respectively. The length of AB is?
Question Description
ABCD is a four bar mechanism. AD is fixed link. At the instant AB and DC are vertical whereas BC is horizontal. AB is shorter than DC by 300 mm. The angular velocity of AB and DC are 5 radian per second and 2 radian per second respectively. The length of AB is? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about ABCD is a four bar mechanism. AD is fixed link. At the instant AB and DC are vertical whereas BC is horizontal. AB is shorter than DC by 300 mm. The angular velocity of AB and DC are 5 radian per second and 2 radian per second respectively. The length of AB is? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABCD is a four bar mechanism. AD is fixed link. At the instant AB and DC are vertical whereas BC is horizontal. AB is shorter than DC by 300 mm. The angular velocity of AB and DC are 5 radian per second and 2 radian per second respectively. The length of AB is?.
ABCD is a four bar mechanism. AD is fixed link. At the instant AB and DC are vertical whereas BC is horizontal. AB is shorter than DC by 300 mm. The angular velocity of AB and DC are 5 radian per second and 2 radian per second respectively. The length of AB is? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about ABCD is a four bar mechanism. AD is fixed link. At the instant AB and DC are vertical whereas BC is horizontal. AB is shorter than DC by 300 mm. The angular velocity of AB and DC are 5 radian per second and 2 radian per second respectively. The length of AB is? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABCD is a four bar mechanism. AD is fixed link. At the instant AB and DC are vertical whereas BC is horizontal. AB is shorter than DC by 300 mm. The angular velocity of AB and DC are 5 radian per second and 2 radian per second respectively. The length of AB is?.
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