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ME321 Kinematics and Dynamics of Machines

Learn the principles of motion analysis and force calculations in mechanical systems, focusing on four-bar linkages and dynamic force analysis. Topics include position, velocity, and acceleration analysis, as well as Newton's laws and inertia concepts. Explore inverse and direct kinematics, and solve complex problems through equilibrium and superposition methods. Enhance your understanding of machine dynamics with practical examples and applications.

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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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