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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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)

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Vector Equations
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Vector Equations for Velocity
Differentiate Position Vector with respect to Time
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Vector Equation for Acceleration
Differentiate velocity equation
To obtain acceleration relation
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Acceleration Equations
Where
- Acceleration of origin - Acceleration in local
frame - Coriolis acceleration - Angular
acceleration - Centripetal acceleration
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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

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Planar Velocity Equations
Becomes
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Planar Acceleration Equations
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Application to Four-Bar Linkages
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Graphical Solution
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Vector Component Solution
But and
Giving
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Coriolis Acceleration
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Coriolis Direction