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In the mechanism shown in Figure (II.5), the crank AB is 75 mm long and rotates clockwise at 8 rad/s. L(BC) = 300 mm and L(BD)=L(CD) =L (DE). Find the velocity and acceleration of pistons C and E.?
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In the mechanism shown in Figure (II.5), the crank AB is 75 mm long an...
Velocity and Acceleration Analysis of Mechanism
Given Data:
- Crank AB length (L(AB)) = 75 mm
- Angular velocity of crank AB (ω) = 8 rad/s
- Length of BC (L(BC)) = 300 mm
- Lengths of BD, CD, DE are equal
1. Velocity Analysis:
- Velocity of point B (V(B)) = L(AB) * ω
- Velocity of point C (V(C)) = V(B) + ω * L(BC) (direction perpendicular to BC)
- Velocity of point D (V(D)) = V(B) + ω * L(BD) (direction perpendicular to BD)
- Velocity of point E (V(E)) = V(D) + ω * L(DE) (direction perpendicular to DE)
2. Acceleration Analysis:
- Acceleration of point B (A(B)) = L(AB) * α
- Acceleration of point C (A(C)) = A(B) + α * L(BC) - ω^2 * L(BC) (direction perpendicular to BC)
- Acceleration of point D (A(D)) = A(B) + α * L(BD) - ω^2 * L(BD) (direction perpendicular to BD)
- Acceleration of point E (A(E)) = A(D) + α * L(DE) - ω^2 * L(DE) (direction perpendicular to DE)
3. Solution:
- Calculate V(B) = 75 mm * 8 rad/s = 600 mm/s
- Calculate V(C) = 600 mm/s + 8 rad/s * 300 mm = 2400 mm/s
- Calculate V(D) = 600 mm/s + 8 rad/s * L(BD)
- Calculate V(E) = V(D) + 8 rad/s * L(DE)
- Calculate A(B) = 75 mm * α
- Calculate A(C) = A(B) + α * 300 mm - 8^2 * 300 mm
- Calculate A(D) = A(B) + α * L(BD) - 8^2 * L(BD)
- Calculate A(E) = A(D) + α * L(DE) - 8^2 * L(DE)
By following the above steps, you can determine the velocity and acceleration of pistons C and E in the given mechanism.
Given Data:
- Crank AB length (L(AB)) = 75 mm
- Angular velocity of crank AB (ω) = 8 rad/s
- Length of BC (L(BC)) = 300 mm
- Lengths of BD, CD, DE are equal
1. Velocity Analysis:
- Velocity of point B (V(B)) = L(AB) * ω
- Velocity of point C (V(C)) = V(B) + ω * L(BC) (direction perpendicular to BC)
- Velocity of point D (V(D)) = V(B) + ω * L(BD) (direction perpendicular to BD)
- Velocity of point E (V(E)) = V(D) + ω * L(DE) (direction perpendicular to DE)
2. Acceleration Analysis:
- Acceleration of point B (A(B)) = L(AB) * α
- Acceleration of point C (A(C)) = A(B) + α * L(BC) - ω^2 * L(BC) (direction perpendicular to BC)
- Acceleration of point D (A(D)) = A(B) + α * L(BD) - ω^2 * L(BD) (direction perpendicular to BD)
- Acceleration of point E (A(E)) = A(D) + α * L(DE) - ω^2 * L(DE) (direction perpendicular to DE)
3. Solution:
- Calculate V(B) = 75 mm * 8 rad/s = 600 mm/s
- Calculate V(C) = 600 mm/s + 8 rad/s * 300 mm = 2400 mm/s
- Calculate V(D) = 600 mm/s + 8 rad/s * L(BD)
- Calculate V(E) = V(D) + 8 rad/s * L(DE)
- Calculate A(B) = 75 mm * α
- Calculate A(C) = A(B) + α * 300 mm - 8^2 * 300 mm
- Calculate A(D) = A(B) + α * L(BD) - 8^2 * L(BD)
- Calculate A(E) = A(D) + α * L(DE) - 8^2 * L(DE)
By following the above steps, you can determine the velocity and acceleration of pistons C and E in the given mechanism.
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In the mechanism shown in Figure (II.5), the crank AB is 75 mm long and rotates clockwise at 8 rad/s. L(BC) = 300 mm and L(BD)=L(CD) =L (DE). Find the velocity and acceleration of pistons C and E.?
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In the mechanism shown in Figure (II.5), the crank AB is 75 mm long and rotates clockwise at 8 rad/s. L(BC) = 300 mm and L(BD)=L(CD) =L (DE). Find the velocity and acceleration of pistons C and E.? 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 In the mechanism shown in Figure (II.5), the crank AB is 75 mm long and rotates clockwise at 8 rad/s. L(BC) = 300 mm and L(BD)=L(CD) =L (DE). Find the velocity and acceleration of pistons C and E.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the mechanism shown in Figure (II.5), the crank AB is 75 mm long and rotates clockwise at 8 rad/s. L(BC) = 300 mm and L(BD)=L(CD) =L (DE). Find the velocity and acceleration of pistons C and E.?.
In the mechanism shown in Figure (II.5), the crank AB is 75 mm long and rotates clockwise at 8 rad/s. L(BC) = 300 mm and L(BD)=L(CD) =L (DE). Find the velocity and acceleration of pistons C and E.? 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 In the mechanism shown in Figure (II.5), the crank AB is 75 mm long and rotates clockwise at 8 rad/s. L(BC) = 300 mm and L(BD)=L(CD) =L (DE). Find the velocity and acceleration of pistons C and E.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the mechanism shown in Figure (II.5), the crank AB is 75 mm long and rotates clockwise at 8 rad/s. L(BC) = 300 mm and L(BD)=L(CD) =L (DE). Find the velocity and acceleration of pistons C and E.?.
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