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Answer :
Final answer:
The lengths of crank, coupler, rocker and ground links are 10, 20, 30, and 38, the worst transmission angle of the crank-rocker linkage is 25.34 degrees.
Explanation:
In a crank-rocker linkage, the transmission angle is the angle between the rocker and the ground link.
To find the worst transmission angle, we need to determine the positions at which it occurs.
The transmission angle can be calculated using the law of cosines.
Let's find the worst transmission angle:
Length of crank (a): 10 inches
Length of coupler (b): 20 inches
Length of rocker (c): 30 inches
Length of ground link (d): 38 inches
To calculate the worst transmission angle, we need to find the two positions of the mechanism where the angle is largest.
These positions occur when the coupler and rocker links are in line or almost in line.
We can use the law of cosines to calculate the angles at these positions:
Angle at position 1:
cos(theta1) = (a² + d² - b²)/(2ad)
Substituting the given values, we have:
cos(theta1) = (10² + 38² - 20²)/(2*10*38) = 0.9036
Therefore, theta1 = cos⁻¹(0.9036) = 25.34 degrees
Angle at position 2:
cos(theta2) = (a^2 + d^2 - b^2)/(2ad)
Substituting the given values, we have:
cos(theta2) = (10² + 38² - 20²)/(2*10*38) = 0.9036
Therefore, theta2 = cos⁻¹(0.9036) = 25.34 degrees
The worst transmission angle is the larger of the two angles, so the worst transmission angle of the crank-rocker linkage is 25.34 degrees.
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