Kinematics Question - Double Cardan Joint

[dr29715]

Kinematics Question -- Double Cardan Joint

Homework Statement

What is the angular speed of a driven shaft whent he drive shaft is 40.34774 RPM? Assume that the cardan joints are offset by 45 degrees or less.

Homework Equations

Angular Velocity relationship

w2/w1 = cos(d)/(1-sin^2(o2)*sin^2(d)

w = angular velocity of shaft (1 is input and 2 is output)
d = angle between the shafts
o2= output shaft rotation angle

The Attempt at a Solution

I tried to use this equation to calculate the angluar velocity of the shaft between the two cardan joints and then apply that velocity using the same equation to calculate the angualr velocity of the output shaft. However, it seems that I am missing some information. Specifically, I assumed the angle between shafts is 45 degrees in each situation. What Am I missing?

 

[KataKoniK]

Hello,

Thank you for your question. To accurately solve for the angular velocity of the driven shaft, we need to know the angle between the cardan joints and the length of the driven shaft. This information is necessary because the angle between the cardan joints will affect the output shaft rotation angle and therefore the angular velocity of the driven shaft.

To find the angle between the cardan joints, we can use the Law of Cosines. This states that c^2 = a^2 + b^2 - 2ab*cos(C), where c is the length of the driven shaft, a and b are the lengths of the two shafts connected by the cardan joints, and C is the angle between the cardan joints. Once we have this angle, we can then use the equation you provided to solve for the angular velocity of the driven shaft.

I hope this helps. Let me know if you have any further questions.