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A crank rocker mechanism ABCD has dimensions AB = 30 mm, BC = 90 mm, CD = 75 mm and AD (fixed link) = 100 mm. Maximum value of transmission angle will be (in degree) ______.
Correct answer is between '103,103.8'. Can you explain this answer?
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Most Upvoted Answer
A crank rocker mechanism ABCD has dimensions AB = 30 mm, BC = 90 mm, C...
Explanation:
Transmission angle (θ) = arccos [(AD2 + CD2 - BC2)/(2 x AD x CD)]
Cosine (θ) = [(AB2 + CD2 - BC2)/(2 x AB x CD)]
Maximum transmission angle = 180 - 7.9 = 172.1 degrees
The correct answer falls between 103 and 103.8 degrees which is not in agreement with the calculated value. There might be some error in the calculations or some other assumption might have been made to arrive at the given answer.
- The transmission angle is defined as the angle between the coupler link (BC) and the output link (CD) when the mechanism is in motion.
- The maximum value of the transmission angle occurs when the coupler link and the output link are in line with each other.
- This occurs when the crank (AB) and the coupler (BC) are in a straight line with each other.
- The distance between the fixed pivot point and the crank pivot point (AD) is 100 mm.
- The distance between the crank pivot point and the coupler pivot point (BC) is 90 mm.
- The maximum value of the transmission angle can be calculated using the following equation:
Transmission angle (θ) = arccos [(AD2 + CD2 - BC2)/(2 x AD x CD)]
- Substituting the given values, we get:
- θ = arccos [(1002 + 752 - 902)/(2 x 100 x 75)]
- θ = arccos (0.974)
- θ = 12.4 degrees
- However, this is the minimum value of the transmission angle.
- The maximum value occurs when the crank and the coupler are in line with each other.
- At this point, the transmission angle is 180 degrees minus the angle between the crank and the output link.
- The angle between the crank and the output link can be calculated using the law of cosines:
Cosine (θ) = [(AB2 + CD2 - BC2)/(2 x AB x CD)]
- Substituting the given values, we get:
- Cosine (θ) = [(302 + 752 - 902)/(2 x 30 x 75)]
- Cosine (θ) = 0.9889
- θ = 7.9 degrees
- Therefore, the maximum value of the transmission angle is:
Maximum transmission angle = 180 - 7.9 = 172.1 degrees
The correct answer falls between 103 and 103.8 degrees which is not in agreement with the calculated value. There might be some error in the calculations or some other assumption might have been made to arrive at the given answer.
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A crank rocker mechanism ABCD has dimensions AB = 30 mm, BC = 90 mm, C...
103.4
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A crank rocker mechanism ABCD has dimensions AB = 30 mm, BC = 90 mm, CD = 75 mm and AD (fixed link) = 100 mm. Maximum value of transmission angle will be (in degree) ______.Correct answer is between '103,103.8'. Can you explain this answer?
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