Double Cardan Joint and angular velocity

[dr29715]

1. 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.


2. 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

3. 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?

 

[Achy47]

I would like to clarify a few things before attempting to solve this problem. First, could you provide more context and background information about the system in question? For example, what type of drive shaft and cardan joints are being used, and what is the purpose of this system? This information can help me better understand the problem and provide a more accurate solution.

Second, it would be helpful to know the units of measurement for the given RPM value. Is it revolutions per minute, radians per minute, or another unit? This will affect the calculation of angular velocity.

Assuming that the given RPM value is in revolutions per minute and the system consists of two identical cardan joints with an angle of 45 degrees between them, I can provide a general solution for the angular velocity of the output shaft. However, this may not be applicable to all systems.

Using the equation you provided, w2/w1 = cos(d)/(1-sin^2(o2)*sin^2(d), we can rearrange it to solve for w2, the angular velocity of the output shaft. This gives us w2 = w1 * cos(d)/(1-sin^2(o2)*sin^2(d)). Plugging in the values, w1 = 40.34774 RPM and d = 45 degrees, we get w2 = 40.34774 * cos(45)/(1-sin^2(o2)*sin^2(45)). However, we still need to know the rotation angle of the output shaft, o2, to fully solve this problem.

In conclusion, more information is needed to accurately solve this problem. I hope this helps and I am happy to assist further once more details are provided.