ME321 Kinematics and Dynamics of Machines

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ME321 Kinematics and Dynamics of Machines

• Steve Lambert
• Mechanical Engineering,
• U of Waterloo

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Kinematics and Dynamics

• Position Analysis
• Velocity Analysis
• Acceleration Analysis
• Force Analysis

We will concentrate on four-bar linkages
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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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Force Analysis
Define the centre of mass
And apply Newtons Law
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Force Analysis
Resolve forces into single applied force
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DAlemberts Principle
where
Dynamic
Kinetostatic
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Equivalent Force Systems
We can replace the inertia torque by applying the
inertia force at a distance
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Four-Bar Linkage
If we can assume only one link has mass, the
solution is simplified
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Free Body Diagrams
How many unknowns?
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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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Analysis of Coupler
Moment equilibrium gives direction of F23
Force equilibrium gives magnitudes for F23 and
F43
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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