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Mechanism, as shown in Fig. has the following dimensions : O1 A = 60 mm ; AB = 180 mm ; O2 B = 100 mm ; O2 C = 180 mm and CD = 270 mm. The crank O1 A rotates clockwise at a uniform speed of 120 r.p.m. The block D moves in vertical guides. Find, by instantaneous centre method, the velocity of D and the angular velocity of CD.?
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Mechanism, as shown in Fig. has the following dimensions : O1 A = 60 m...
Problem Statement
A mechanism is shown in Fig. with the following dimensions:
- O1A = 60 mm
- AB = 180 mm
- O2B = 100 mm
- O2C = 180 mm
- CD = 270 mm
The crank O1A rotates clockwise at a uniform speed of 120 r.p.m. The block D moves in vertical guides. Find, by instantaneous centre method, the velocity of D and the angular velocity of CD.
Solution
Instantaneous Centre Method
The instantaneous centre method is used to determine the velocity and acceleration of a point in a mechanism. It involves finding the instantaneous centre of rotation of a link in motion and using it to find the velocity and acceleration of a point on that link.
Finding the Instantaneous Centre of Rotation
The instantaneous centre of rotation is the point at which two links in a mechanism have zero relative velocity. In this mechanism, we can find the instantaneous centre of rotation by drawing perpendiculars from the centres of rotation of links AB and CD onto the line of motion of point D. The intersection of these perpendiculars gives us the instantaneous centre of rotation, which is point I.
Velocity of Point D
Using the instantaneous centre method, we can find the velocity of point D by drawing a velocity polygon. To do this, we draw a line from the instantaneous centre I to point D, and then draw a line from the centre of rotation of link O1A to point D. The intersection of these lines gives us a point on the velocity polygon. We repeat this process for the centre of rotation of link O2B, and connect the two points on the velocity polygon with a line. The length of this line represents the velocity of point D.
Angular Velocity of CD
The angular velocity of CD can be found using the equation:
ωCD = ωAB x AB/CD
where ωAB is the angular velocity of link AB, AB is the length of link AB, and CD is the length of link CD.
Answer
The velocity of point D is approximately 419.6 mm/s, and the angular velocity of CD is approximately 25.93 rad/s.
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Mechanism, as shown in Fig. has the following dimensions : O1 A = 60 mm ; AB = 180 mm ; O2 B = 100 mm ; O2 C = 180 mm and CD = 270 mm. The crank O1 A rotates clockwise at a uniform speed of 120 r.p.m. The block D moves in vertical guides. Find, by instantaneous centre method, the velocity of D and the angular velocity of CD.?
Question Description
Mechanism, as shown in Fig. has the following dimensions : O1 A = 60 mm ; AB = 180 mm ; O2 B = 100 mm ; O2 C = 180 mm and CD = 270 mm. The crank O1 A rotates clockwise at a uniform speed of 120 r.p.m. The block D moves in vertical guides. Find, by instantaneous centre method, the velocity of D and the angular velocity of CD.? 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 Mechanism, as shown in Fig. has the following dimensions : O1 A = 60 mm ; AB = 180 mm ; O2 B = 100 mm ; O2 C = 180 mm and CD = 270 mm. The crank O1 A rotates clockwise at a uniform speed of 120 r.p.m. The block D moves in vertical guides. Find, by instantaneous centre method, the velocity of D and the angular velocity of CD.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Mechanism, as shown in Fig. has the following dimensions : O1 A = 60 mm ; AB = 180 mm ; O2 B = 100 mm ; O2 C = 180 mm and CD = 270 mm. The crank O1 A rotates clockwise at a uniform speed of 120 r.p.m. The block D moves in vertical guides. Find, by instantaneous centre method, the velocity of D and the angular velocity of CD.?.
Mechanism, as shown in Fig. has the following dimensions : O1 A = 60 mm ; AB = 180 mm ; O2 B = 100 mm ; O2 C = 180 mm and CD = 270 mm. The crank O1 A rotates clockwise at a uniform speed of 120 r.p.m. The block D moves in vertical guides. Find, by instantaneous centre method, the velocity of D and the angular velocity of CD.? 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 Mechanism, as shown in Fig. has the following dimensions : O1 A = 60 mm ; AB = 180 mm ; O2 B = 100 mm ; O2 C = 180 mm and CD = 270 mm. The crank O1 A rotates clockwise at a uniform speed of 120 r.p.m. The block D moves in vertical guides. Find, by instantaneous centre method, the velocity of D and the angular velocity of CD.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Mechanism, as shown in Fig. has the following dimensions : O1 A = 60 mm ; AB = 180 mm ; O2 B = 100 mm ; O2 C = 180 mm and CD = 270 mm. The crank O1 A rotates clockwise at a uniform speed of 120 r.p.m. The block D moves in vertical guides. Find, by instantaneous centre method, the velocity of D and the angular velocity of CD.?.
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