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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. - PowerPoint PPT Presentation

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<ul><li><p>THREE-DIMENSIONAL KINEMATICS OF RIGID BODIES</p></li><li><p>GENERAL MOTIONThe kinematic analysis of a rigid body which has general three-dimensional motion is best accomplish with the aid of principles of relative motion.</p></li><li><p>Rotating Reference AxesA 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.</p></li><li><p>The expressions for the velocity and acceleration of point A becomeWhere, 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.</p></li><li><p>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. </p></li><li><p>Example 1The 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.</p></li><li><p>Example 2The 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.</p></li></ul>

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