How Can You Determine the Kinematics of Rigid Body BD in a Rotating System?

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SUMMARY

The discussion focuses on determining the kinematics of rigid body BD in a rotating system where crank AB rotates counterclockwise at a constant angular velocity of 160 RPM. The key equations involve converting angular velocity to radians per second and utilizing trigonometric relationships to derive the angular position of rod BD as a function of the angle theta. Participants emphasize the importance of understanding the vertical components of the rods to calculate the angular velocity and acceleration of rod BD, as well as the velocity and acceleration of collar D.

PREREQUISITES
  • Understanding of angular velocity and acceleration in rigid body dynamics
  • Familiarity with trigonometric functions and their applications in mechanics
  • Knowledge of kinematic equations for rotational motion
  • Ability to interpret and manipulate equations involving angles and lengths in a rotating system
NEXT STEPS
  • Study the derivation of angular velocity and acceleration equations for rotating bodies
  • Learn how to apply trigonometric relationships in the context of rigid body motion
  • Explore the use of simulation tools for visualizing kinematics in rotating systems
  • Investigate the application of the Law of Sines and Cosines in solving for unknown angles and lengths in mechanics
USEFUL FOR

Mechanical engineers, physics students, and anyone involved in analyzing the kinematics of rotating systems will benefit from this discussion.

chart2006
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Homework Statement


"Knowing that crank AB has a constant angular velocity of 160rpm counterclockwise, determine and plot, for values of [tex]\theta[/tex] from 0 to 360 degrees, (a) the angular velocity and angular acceleration of rod BD, (b) the velocity and acceleration of collar D.
http://www.mypicx.com/uploadimg/557399749_04082009_1.jpg

Homework Equations



I don't know! :(


The Attempt at a Solution



[tex]\lamda =160rpm=160(\frac{2\pi}{60})rad/s[/tex]

Unfortunately this is as far as I've been able to get. The reason is because I'm not sure as how to derive an equation that would allow me to plug in a value from 0 to 360 for theta and it give me beta (angle of bar BD from the horizontal). If I can just get past that point I can figure the rest out. With any other problem there is a fixed position in which I can just use the triangle method to figure it out but i can't really do that here.
 
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hi chart 2006

you know then length AB & BD and the also the vertical component of AD

the vertical component of AB is AB.Sin(theta) from this you should be able to find the vertical component of BD, ie BD.Sin(beta)...
 

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