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In a cam-follower mechanism, the follower needs to rise through 20 mm during 60o of cam rotation, the first 30o with a constant acceleration and then with a deceleration of the same magnitude. The initial and final speeds of the follower are zero. The cam rotates at a uniform speed of 300 rpm. The maximum speed of the follower is?
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In a cam-follower mechanism, the follower needs to rise through 20 mm ...
Cam-Follower Mechanism: Maximum Speed of Follower
To determine the maximum speed of the follower in a cam-follower mechanism, we need to calculate the acceleration and deceleration phases during the cam rotation.
Given Data:
- Rise of follower: 20 mm
- Cam rotation: 60 degrees
- Initial and final speeds: 0
- Cam rotation speed: 300 rpm
Step 1: Calculate the Angle of Constant Acceleration and Deceleration
Since the follower rises through 20 mm during 60 degrees of cam rotation, we can determine the angle of constant acceleration and deceleration.
Total rise = 20 mm
Total angle = 60 degrees
The angle for constant acceleration and deceleration is half of the total angle, i.e., 30 degrees.
Step 2: Calculate the Time Required for the Rise
To calculate the time required for the rise, we need to find the time taken for the acceleration phase and the time taken for the deceleration phase.
Acceleration phase:
- Initial speed: 0
- Final speed: ?
- Angle of rotation: 30 degrees
Using the formula for linear motion with constant acceleration:
v^2 = u^2 + 2as
Where:
v = final speed
u = initial speed
a = acceleration
s = distance
Since the initial speed is 0, the equation simplifies to:
v^2 = 2as
The distance covered during the acceleration phase is half of the total rise, i.e., 10 mm or 0.01 m.
v^2 = 2 * a * 0.01
v^2 = 0.02a
Deceleration phase:
- Initial speed: ?
- Final speed: 0
- Angle of rotation: 30 degrees
Using the same formula as above:
0 = u^2 + 2as
The distance covered during the deceleration phase is also 10 mm or 0.01 m.
0 = u^2 + 2 * (-a) * 0.01
0 = u^2 - 0.02a
Step 3: Calculate the Time Required for One Revolution of the Cam
The time required for one revolution of the cam can be calculated using the cam rotation speed.
Cam rotation speed = 300 rpm
Since one revolution is 360 degrees, the time required for one revolution is:
Time for one revolution = 1 / (300/60) = 0.2 seconds
Step 4: Calculate the Maximum Speed of the Follower
To calculate the maximum speed of the follower, we need to find the rate of change of speed during the acceleration and deceleration phases.
Acceleration phase:
Rate of change of speed = (final speed - initial speed) / time
Deceleration phase:
Rate of change of speed = (initial speed - final speed) / time
Step 5: Determine the Maximum Speed
The maximum speed occurs at the midpoint of the rise, where the acceleration and deceleration phases meet. At this point, the rate of change of speed is zero.
Setting the rate of change of speed during the acceleration and deceleration phases equal to zero, we can solve for the final and initial speeds.
Acceleration phase
To determine the maximum speed of the follower in a cam-follower mechanism, we need to calculate the acceleration and deceleration phases during the cam rotation.
Given Data:
- Rise of follower: 20 mm
- Cam rotation: 60 degrees
- Initial and final speeds: 0
- Cam rotation speed: 300 rpm
Step 1: Calculate the Angle of Constant Acceleration and Deceleration
Since the follower rises through 20 mm during 60 degrees of cam rotation, we can determine the angle of constant acceleration and deceleration.
Total rise = 20 mm
Total angle = 60 degrees
The angle for constant acceleration and deceleration is half of the total angle, i.e., 30 degrees.
Step 2: Calculate the Time Required for the Rise
To calculate the time required for the rise, we need to find the time taken for the acceleration phase and the time taken for the deceleration phase.
Acceleration phase:
- Initial speed: 0
- Final speed: ?
- Angle of rotation: 30 degrees
Using the formula for linear motion with constant acceleration:
v^2 = u^2 + 2as
Where:
v = final speed
u = initial speed
a = acceleration
s = distance
Since the initial speed is 0, the equation simplifies to:
v^2 = 2as
The distance covered during the acceleration phase is half of the total rise, i.e., 10 mm or 0.01 m.
v^2 = 2 * a * 0.01
v^2 = 0.02a
Deceleration phase:
- Initial speed: ?
- Final speed: 0
- Angle of rotation: 30 degrees
Using the same formula as above:
0 = u^2 + 2as
The distance covered during the deceleration phase is also 10 mm or 0.01 m.
0 = u^2 + 2 * (-a) * 0.01
0 = u^2 - 0.02a
Step 3: Calculate the Time Required for One Revolution of the Cam
The time required for one revolution of the cam can be calculated using the cam rotation speed.
Cam rotation speed = 300 rpm
Since one revolution is 360 degrees, the time required for one revolution is:
Time for one revolution = 1 / (300/60) = 0.2 seconds
Step 4: Calculate the Maximum Speed of the Follower
To calculate the maximum speed of the follower, we need to find the rate of change of speed during the acceleration and deceleration phases.
Acceleration phase:
Rate of change of speed = (final speed - initial speed) / time
Deceleration phase:
Rate of change of speed = (initial speed - final speed) / time
Step 5: Determine the Maximum Speed
The maximum speed occurs at the midpoint of the rise, where the acceleration and deceleration phases meet. At this point, the rate of change of speed is zero.
Setting the rate of change of speed during the acceleration and deceleration phases equal to zero, we can solve for the final and initial speeds.
Acceleration phase
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In a cam-follower mechanism, the follower needs to rise through 20 mm during 60o of cam rotation, the first 30o with a constant acceleration and then with a deceleration of the same magnitude. The initial and final speeds of the follower are zero. The cam rotates at a uniform speed of 300 rpm. The maximum speed of the follower is?
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In a cam-follower mechanism, the follower needs to rise through 20 mm during 60o of cam rotation, the first 30o with a constant acceleration and then with a deceleration of the same magnitude. The initial and final speeds of the follower are zero. The cam rotates at a uniform speed of 300 rpm. The maximum speed of the follower 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 In a cam-follower mechanism, the follower needs to rise through 20 mm during 60o of cam rotation, the first 30o with a constant acceleration and then with a deceleration of the same magnitude. The initial and final speeds of the follower are zero. The cam rotates at a uniform speed of 300 rpm. The maximum speed of the follower is? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a cam-follower mechanism, the follower needs to rise through 20 mm during 60o of cam rotation, the first 30o with a constant acceleration and then with a deceleration of the same magnitude. The initial and final speeds of the follower are zero. The cam rotates at a uniform speed of 300 rpm. The maximum speed of the follower is?.
In a cam-follower mechanism, the follower needs to rise through 20 mm during 60o of cam rotation, the first 30o with a constant acceleration and then with a deceleration of the same magnitude. The initial and final speeds of the follower are zero. The cam rotates at a uniform speed of 300 rpm. The maximum speed of the follower 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 In a cam-follower mechanism, the follower needs to rise through 20 mm during 60o of cam rotation, the first 30o with a constant acceleration and then with a deceleration of the same magnitude. The initial and final speeds of the follower are zero. The cam rotates at a uniform speed of 300 rpm. The maximum speed of the follower is? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a cam-follower mechanism, the follower needs to rise through 20 mm during 60o of cam rotation, the first 30o with a constant acceleration and then with a deceleration of the same magnitude. The initial and final speeds of the follower are zero. The cam rotates at a uniform speed of 300 rpm. The maximum speed of the follower is?.
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In a cam-follower mechanism, the follower needs to rise through 20 mm during 60o of cam rotation, the first 30o with a constant acceleration and then with a deceleration of the same magnitude. The initial and final speeds of the follower are zero. The cam rotates at a uniform speed of 300 rpm. The maximum speed of the follower is?, a detailed solution for In a cam-follower mechanism, the follower needs to rise through 20 mm during 60o of cam rotation, the first 30o with a constant acceleration and then with a deceleration of the same magnitude. The initial and final speeds of the follower are zero. The cam rotates at a uniform speed of 300 rpm. The maximum speed of the follower is? has been provided alongside types of In a cam-follower mechanism, the follower needs to rise through 20 mm during 60o of cam rotation, the first 30o with a constant acceleration and then with a deceleration of the same magnitude. The initial and final speeds of the follower are zero. The cam rotates at a uniform speed of 300 rpm. The maximum speed of the follower is? theory, EduRev gives you an
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