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ME321 Kinematics and Dynamics of Machines

ME321 Kinematics and Dynamics of Machines. Steve Lambert Mechanical Engineering, U of Waterloo. Kinematics and Dynamics. Position Analysis Velocity Analysis Acceleration Analysis Force Analysis. We will concentrate on four-bar linkages. Acceleration Analysis. Use vector loop equations

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ME321 Kinematics and Dynamics of Machines

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  1. ME321 Kinematics and Dynamics of Machines Steve Lambert Mechanical Engineering, U of Waterloo

  2. Kinematics and Dynamics • Position Analysis • Velocity Analysis • Acceleration Analysis • Force Analysis We will concentrate on four-bar linkages

  3. Acceleration Analysis • Use vector loop equations • Vector equations can be expressed in general form, or specialized for planar problems • Graphical Solutions • Vector Component Solutions • Complex Number Solutions (in text)

  4. Vector Equations

  5. Vector Equations for Velocity Differentiate Position Vector with respect to Time

  6. Vector Equation for Acceleration Differentiate velocity equation: To obtain acceleration relation:

  7. Acceleration Equations Where: - Acceleration of origin - Acceleration in local frame - Coriolis acceleration - Angular acceleration - Centripetal acceleration

  8. Planar Velocity Equations • Assume: • Motion is restricted to the XY plane • Local frame is aligned with and fixed to link • Therefore: •  becomes the angular velocity of the link, and • local velocity becomes the change in length of the link

  9. Planar Velocity Equations Becomes:

  10. Planar Acceleration Equations

  11. Application to Four-Bar Linkages

  12. Graphical Solution

  13. Vector Component Solution But: and Giving:

  14. Coriolis Acceleration

  15. Coriolis Direction

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