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ME360 Mechanics of Machinery ميكانيكا الالات

ME360 Mechanics of Machinery ميكانيكا الالات. Dr. Hanafy M. Omar. Chapter 3: Velocity Analysis Analytical Solution. Objective. Determine velocities of links and joints of mechanisms Two techniques will be studies to evaluate the velocity: Analytical Technique Graphical technique

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ME360 Mechanics of Machinery ميكانيكا الالات

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  1. ME360Mechanics of Machineryميكانيكا الالات Dr. Hanafy M. Omar Chapter 3: Velocity Analysis Analytical Solution

  2. Objective • Determine velocities of links and joints of mechanisms • Two techniques will be studies to evaluate the velocity: • Analytical Technique • Graphical technique • The two techniques will be explained first on the four bar mechanism then extended to the other mechanisms

  3. Velocity Definition

  4. Pure Rotation Motion • Velocity of point P Note: In this case, the direction of the velocity is perpendicular to the position vector.

  5. Velocity of General Motion • Velocity Difference / Relative Velocity We can look at VPA as pure rotation around point A, its direction is perpendicular to the vector RPA in the direction of the rotation.

  6. Analytical Velocity Analysis • The goal is to find the rate of change of the output variables 3 and 4 and hence the velocities of all points of the mechanism • The given data include: • The lengths of all links • The crank angle 2 • The rate of change of the crank angle 2 • To determine the velocities, we need to know the angles of mechanism links. • Therefore, we have to perform position analysis before starting the velocity analysis

  7. Velocity Analysis using Vector Loop Method Perform position analysis using any technique described in chapter 2. Write the loop closure equation then differentiate it Solve for angular velocities then determine the speed of any point

  8. Velocity Analysis using Vector Loop Method After writing the loop-closure equation, differentiate it w.r.t time as follows: Solve for the angular velocities

  9. Velocity Analysis using Vector Loop Method The velocity triangle of point B is as shown

  10. Velocity Analysis using Vector Loop Method

  11. Velocity Analytical Analysis- Numerical Example

  12. Velocity Analytical Analysis- Numerical Example We have all the required parameters except We can obtain these angles from the position analysis as explained in chapter 2

  13. Analytical Velocity Analysis of Slider-Crank

  14. Analytical Velocity Analysis of Slider-Crank

  15. Analytical Velocity Analysis of Slider-Crank

  16. Analytical Velocity Analysis of Inverted Slider-Crank

  17. Analytical Velocity Analysis of Inverted Slider-Crank Note: Link4 is perpendicular to link 3 then =90 degree From the geometry + To determine the velocity, differentiate then solve the two equations for the two unknowns

  18. Analytical Velocity Analysis of Inverted Slider-Crank After differentiation Note that: We have two equations in two unknowns, Solve them to get

  19. Analytical Velocity Analysis of Inverted Slider-Crank

  20. Velocity of Slip

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