THREE-DIMENSIONAL KINEMATICS OF RIGID ??PPT fileWeb view2011-12-26THREE-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 ...

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  • 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

    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.

  • 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.

  • 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.

  • 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.

  • 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.

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