1. ME321 Kinematics and Dynamics of Machines
Steve Lambert
Mechanical Engineering,
U of Waterloo
7/16/2019

2. Kinematics and Dynamics
Position Analysis
Velocity Analysis
Acceleration Analysis
Force Analysis
We will concentrate on four-bar linkages
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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.
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4. Force Analysis Define the centre of mass: And apply Newton’s Law:
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5. Force Analysis
Resolve forces into single applied force:
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6. D’Alembert’s Principle
where:
Dynamic
Kinetostatic
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7. Equivalent Force Systems
We can replace the inertia torque by applying the inertia force at a distance
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8. Four-Bar Linkage If we can assume only one link has mass,
the solution is simplified
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9. Free Body Diagrams
How many unknowns?
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10. Analysis of Coupler We know: the magnitude and direction of Fo
the direction of F43
Therefore, we have 3 equations and three unknowns
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11. Analysis of Coupler Moment equilibrium gives direction of F23
Force equilibrium gives magnitudes for F23 and F43
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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
7/16/2019