1. ME321 Kinematics and Dynamics of Machines
Steve Lambert
Mechanical Engineering,
U of Waterloo
12/9/2018

2. Kinematics and Dynamics
Position Analysis
Velocity Analysis
Acceleration Analysis
Force Analysis
We will concentrate on four-bar linkages
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3. 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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4. Vector Equations
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5. Vector Equations for Velocity
Differentiate Position Vector with respect to Time
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6. Vector Equation for Acceleration
Differentiate velocity equation:
To obtain acceleration relation:
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7. Acceleration Equations
Where:
- Acceleration of origin
- Acceleration in local frame
- Coriolis acceleration
- Angular acceleration
- Centripetal acceleration
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8. 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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9. Planar Velocity Equations
Becomes:
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10. Planar Acceleration Equations
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11. Application to Four-Bar Linkages
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12. Graphical Solution
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13. Vector Component Solution
But:
and
Giving:
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14. Coriolis Acceleration
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15. Coriolis Direction
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