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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. Dynamic (Force) Analysis.

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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. Dynamic (Force) Analysis • Determine the reaction forces on pins, etc. as a consequence of a specified motion, • Determine the input force of torque required to achieve a specified motion, or • Determine the motion as a consequence of a specified set of forces and/or torques. • Inverse Kinematics: start with the motion and determine the forces, or • Direct kinematics: start with the forces and determine the motion.

  4. Force Analysis Define the centre of mass: And apply Newton’s Law:

  5. Force Analysis Resolve forces into single applied force:

  6. D’Alembert’s Principle where: Dynamic Kinetostatic

  7. Equivalent Force Systems We can replace the inertia torque by applying the inertia force at a distance

  8. Four-Bar Linkage If we can assume only one link has mass, the solution is simplified

  9. Free Body Diagrams How many unknowns?

  10. Analysis of Coupler • We know: • the magnitude and direction of Fo • the direction of F43 • Therefore, we have 3 equations and three unknowns

  11. Analysis of Coupler Moment equilibrium gives direction of F23 Force equilibrium gives magnitudes for F23 and F43

  12. More Complex Problems • When more than one link has mass: • Solve problem in parts, where only one link at a time has mass, and obtain total solution through superposition • Solve complete problem at once using equilibrium for all links, and solve resulting equations simultaneously in the matrix method

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