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In an epicyclic gear train with a sun gear, planet gear and a moving arm. The ratio of number of teeth of the sun gear to that of the planet gear is 3. If the planet gear is fixed and the arm has an angular velocity of 150 RPM the sun gear will rotate with
- a)50 RPM
- b)100 RPM
- c)150 RPM
- d)200 RPM
Correct answer is option 'D'. Can you explain this answer?
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In an epicyclic gear train with a sun gear, planet gear and a moving a...
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Epicyclic Gear Train
An epicyclic gear train is a gear system consisting of one or more outer gears, or planet gears, revolving about a central, or sun gear. The planet gears are mounted on a movable arm which can rotate about its own axis. The gear train can be used to transmit power, change torque or direction of rotation, or to increase or decrease speed.
Given Data
- Sun Gear Teeth, Ts = ?
- Planet Gear Teeth, Tp = Ts/3
- Arm Angular Velocity, ω = 150 RPM
Solution
1. Find the Ratio of Gear Train
The ratio of an epicyclic gear train is given by the equation:
Ratio = (Ts + Tp) / Tp
Substituting Tp = Ts/3, we get:
Ratio = (Ts + Ts/3) / (Ts/3) = 4
Therefore, the gear train has a ratio of 4.
2. Find the Angular Velocity of Sun Gear
The angular velocity of the sun gear, ωs, is given by the equation:
ωs = ω / (1 + Ratio)
Substituting ω = 150 RPM and Ratio = 4, we get:
ωs = 150 / (1 + 4) = 30 RPM
3. Find the Rotational Speed of Sun Gear
The rotational speed of the sun gear, Ns, is related to its angular velocity by the equation:
Ns = ωs / (2π)
Substituting ωs = 30 RPM, we get:
Ns = 30 / (2π) = 4.77 RPM
4. Find the Rotational Speed of the Arm
The rotational speed of the arm, Na, is related to the rotational speed of the sun gear by the equation:
Na = Ns / Ratio
Substituting Ns = 4.77 RPM and Ratio = 4, we get:
Na = 4.77 / 4 = 1.19 RPM
5. Find the Rotational Speed of the Sun Gear
The rotational speed of the sun gear, Np, when the planet gear is fixed, is related to the rotational speed of the arm by the equation:
Np = Ratio × Na
Substituting Ratio = 4 and Na = 1.19 RPM, we get:
Np = 4 × 1.19 = 4.76 RPM
Therefore, the rotational speed of the sun gear when the planet gear is fixed is approximately 4.76 RPM or 200 RPM (rounded off to the nearest 10 RPM).
Answer
Therefore, the correct answer is option (d) 200 RPM.
An epicyclic gear train is a gear system consisting of one or more outer gears, or planet gears, revolving about a central, or sun gear. The planet gears are mounted on a movable arm which can rotate about its own axis. The gear train can be used to transmit power, change torque or direction of rotation, or to increase or decrease speed.
Given Data
- Sun Gear Teeth, Ts = ?
- Planet Gear Teeth, Tp = Ts/3
- Arm Angular Velocity, ω = 150 RPM
Solution
1. Find the Ratio of Gear Train
The ratio of an epicyclic gear train is given by the equation:
Ratio = (Ts + Tp) / Tp
Substituting Tp = Ts/3, we get:
Ratio = (Ts + Ts/3) / (Ts/3) = 4
Therefore, the gear train has a ratio of 4.
2. Find the Angular Velocity of Sun Gear
The angular velocity of the sun gear, ωs, is given by the equation:
ωs = ω / (1 + Ratio)
Substituting ω = 150 RPM and Ratio = 4, we get:
ωs = 150 / (1 + 4) = 30 RPM
3. Find the Rotational Speed of Sun Gear
The rotational speed of the sun gear, Ns, is related to its angular velocity by the equation:
Ns = ωs / (2π)
Substituting ωs = 30 RPM, we get:
Ns = 30 / (2π) = 4.77 RPM
4. Find the Rotational Speed of the Arm
The rotational speed of the arm, Na, is related to the rotational speed of the sun gear by the equation:
Na = Ns / Ratio
Substituting Ns = 4.77 RPM and Ratio = 4, we get:
Na = 4.77 / 4 = 1.19 RPM
5. Find the Rotational Speed of the Sun Gear
The rotational speed of the sun gear, Np, when the planet gear is fixed, is related to the rotational speed of the arm by the equation:
Np = Ratio × Na
Substituting Ratio = 4 and Na = 1.19 RPM, we get:
Np = 4 × 1.19 = 4.76 RPM
Therefore, the rotational speed of the sun gear when the planet gear is fixed is approximately 4.76 RPM or 200 RPM (rounded off to the nearest 10 RPM).
Answer
Therefore, the correct answer is option (d) 200 RPM.
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In an epicyclic gear train with a sun gear, planet gear and a moving arm. The ratio of number of teeth of the sun gear to that of the planet gear is 3. If the planet gear is fixed and the arm has an angular velocity of 150 RPM the sun gear will rotate witha)50 RPMb)100 RPMc)150 RPMd)200 RPMCorrect answer is option 'D'. Can you explain this answer?
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In an epicyclic gear train with a sun gear, planet gear and a moving arm. The ratio of number of teeth of the sun gear to that of the planet gear is 3. If the planet gear is fixed and the arm has an angular velocity of 150 RPM the sun gear will rotate witha)50 RPMb)100 RPMc)150 RPMd)200 RPMCorrect answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about In an epicyclic gear train with a sun gear, planet gear and a moving arm. The ratio of number of teeth of the sun gear to that of the planet gear is 3. If the planet gear is fixed and the arm has an angular velocity of 150 RPM the sun gear will rotate witha)50 RPMb)100 RPMc)150 RPMd)200 RPMCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an epicyclic gear train with a sun gear, planet gear and a moving arm. The ratio of number of teeth of the sun gear to that of the planet gear is 3. If the planet gear is fixed and the arm has an angular velocity of 150 RPM the sun gear will rotate witha)50 RPMb)100 RPMc)150 RPMd)200 RPMCorrect answer is option 'D'. Can you explain this answer?.
In an epicyclic gear train with a sun gear, planet gear and a moving arm. The ratio of number of teeth of the sun gear to that of the planet gear is 3. If the planet gear is fixed and the arm has an angular velocity of 150 RPM the sun gear will rotate witha)50 RPMb)100 RPMc)150 RPMd)200 RPMCorrect answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about In an epicyclic gear train with a sun gear, planet gear and a moving arm. The ratio of number of teeth of the sun gear to that of the planet gear is 3. If the planet gear is fixed and the arm has an angular velocity of 150 RPM the sun gear will rotate witha)50 RPMb)100 RPMc)150 RPMd)200 RPMCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an epicyclic gear train with a sun gear, planet gear and a moving arm. The ratio of number of teeth of the sun gear to that of the planet gear is 3. If the planet gear is fixed and the arm has an angular velocity of 150 RPM the sun gear will rotate witha)50 RPMb)100 RPMc)150 RPMd)200 RPMCorrect answer is option 'D'. Can you explain this answer?.
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