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Translation

This procedure demonstrates how to analyze the direction of x and y, establish velocities and accelerations, and solve for angular velocity while considering rotation in plane motion. Using the example of a rolling bicycle wheel, find centers of zero velocity and instant centers of zero velocity for different points, along with locating the line of action of velocities. Detailed steps and equations are provided for a comprehensive understanding.

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Translation

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  1. Translation Position Velocity Acceleration

  2. Rotation

  3. General Plane Motion

  4. i + j k Procedure for Analysis • Establish the direction of x and y • Indicate the direction of VA, VB, w, and rB/A • Apply VB= VA+ w x rB/Ain a vector form • Evaluate the cross product • Equate the respective i and j components to obtain two scalar equation • Solve for w and VB

  5. y x Indicate the direction of velocities of points A, B, C

  6. y x Indicate the direction of velocities of points A, B, C

  7. i + j k Example 16-9

  8. Rolling wheels C Rolls without slipping

  9. For example, the Ie for the bicycle wheel in Fig. 16-17 is at the contact point with the ground. There the spokes are somewhat visible, whereas at the top of the wheel they become blurred. If one imagines that the wheel is momentarily pinned at this point, the velocities of various points can be found using v = wr. Here the radial distances shown in the photo,

  10. Center of Zero Velocity B A Permanent Center of zero velocity

  11. D C IC Instantaneous center of zero velocity

  12. Location of IC Knowing vA and w

  13. Location of IC knowing the line of action of vA and vB

  14. Location of IC knowing the line of action of vA and vB

  15. Example 16-10 IC rB/IC w rC/IC q

  16. Example 16-10 C Translation

  17. Example 16-11

  18. Example

  19. Example 16-12

  20. Thank You

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