LECTUR~18_16.5 - RELATIVE MOTION ANALYSIS VELOCITY Todays...

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Today s Objec-ves : Students will be able to: 1. Describe the velocity of a rigid body in terms of transla;on and rota;on components. 2. Perform a rela;ve-­‐mo;on velocity analysis of a point on the body. RELATIVE MOTION ANALYSIS: VELOCITY In-Class Activities : Check Homework Reading Quiz Applications Translation and Rotation Components of Velocity Relative Velocity Analysis Concept Quiz Group Problem Solving Attention Quiz
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READING QUIZ 1. When a rela;ve-­‐mo;on analysis involving two sets of coordinate axes is used, the x -­‐ y coordinate system will A) be aEached to the selected point for analysis. B) rotate with the body. C) not be allowed to translate with respect to the fixed frame. D) None of the above. 2. In the rela;ve velocity equa;on, v B/A is A) the rela;ve velocity of B with respect to A. B) due to the rota;onal mo;on. C) ω × r B/A . D) All of the above.
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APPLICATIONS As the slider block A moves horizontally to the left with v A , it causes the link CB to rotate counterclockwise. Thus v B is directed tangent to its circular path. Which link is undergoing general plane motion? Link AB or link BC? How can the angular velocity, ω , of link AB be found?
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APPLICATIONS (continued) Planetary gear systems are used in many automobile automatic transmissions. By locking or releasing different gears, this system can operate the car at different speeds. How can we relate the angular velocities of the various gears in the system?
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RELATIVE MOTION ANALYSIS (Section 16.5) When a body is subjected to general plane motion, it undergoes a combination of translation and rotation . d r B = d r A + d r B/A Disp. due to translation and rotation Disp. due to translation Disp. due to rotation Point A is called the base point in this analysis. It generally has a known mo;on. The x -­‐ y frame translates with the body, but does not rotate. The displacement of point B can be wriEen:
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