1 / 7

THREE-DIMENSIONAL KINEMATICS OF RIGID BODIES

THREE-DIMENSIONAL KINEMATICS OF RIGID BODIES. GENERAL MOTION. The kinematic analysis of a rigid body which has general three-dimensional motion is best accomplish with the aid of principles of relative motion. Rotating Reference Axes.

jaclyn
Download Presentation

THREE-DIMENSIONAL KINEMATICS OF RIGID BODIES

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. THREE-DIMENSIONAL KINEMATICS OF RIGID BODIES

  2. GENERAL MOTION The kinematic analysis of a rigid body which has general three-dimensional motion is best accomplish with the aid of principles of relative motion.

  3. Rotating Reference Axes A more general formulation of the motion of a rigid body in space calls for the use of reference axes which rotate as well as translate. Reference axes whose origin is attached to the reference point B rotate with an absolute angular velocity  which may be different from the absolute angular velocity w of the body.

  4. The expressions for the velocity and acceleration of point A become Where, vrel and arel are the velocity and acceleration of point A measured relative to x-y-z by an observer attached to x-y-z.

  5. We again note that  is the angular velocity of the axes and may be different from the angular velocity w of the body. We observe that, if x-y-z are rigidly to the body, = w and vrel and arel are both zero.

  6. Example 1 The motor housing and its bracket rotate about the Z-axis at the constant rate =3 rad/s. The motor shaft and disk have constant angular velocity of spin p=8 rad/s with respect to the motor housing in the direction shown. If g is constant at 30o, determine the velocity and acceleration of Point A at the top of the disk and the angular acceleration a of the disk.

  7. Example 2 The circular disk is spinning about its own axis (y-axis) at the constant rate p=10p rad/s. Simultaneously, the frame is rotating about Z-axis at the constant rate =4p rad/s. Calculate the angular acceleration a of the disk and acceleration of Point A at the top of the disk. Axes x-y-z are attached to the frame, which has the momentary orientation shown with respect to the fixed axes X-Y-Z.

More Related