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ME321 Kinematics and Dynamics of Machines
Steve Lambert Mechanical Engineering, U of Waterloo 9/23/2018
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Kinematics and Dynamics
Position Analysis Velocity Analysis Acceleration Analysis Force Analysis We will concentrate on four-bar linkages 9/23/2018
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Velocity Analysis Can use vector methods or instantaneous centres
Vector equations can be expressed in general form, or specialized for planar problems Graphical Solutions Vector Component Solutions Complex Number Solutions 9/23/2018
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Vector Equations 9/23/2018
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Vector Equations for Velocity
Differentiate Position Vector with respect to Time 9/23/2018
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Vector Velocity Equation
Where: = Total absolute velocity of point = Absolute velocity of local origin = Relative velocity in local system = Angular velocity of Local System = Position of point in local system 9/23/2018
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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 9/23/2018
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Planar Velocity Equations
Becomes: 9/23/2018
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Application to Four-Bar Linkages
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Graphical Solution 9/23/2018
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Velocity Image A’B’ is the velocity image of link AB
And then the velocity of point C, VC, can be obtained directly from the figure as the vector O’C’ 9/23/2018
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Vector Component Solution
But: and Giving: or: 9/23/2018
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Instant Centres An instant centre is a point at which there is no relative velocity between two links in a mechanism, at a particular instant in time 9/23/2018
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Kennedy’s Theorem Kennedy’s theorem states: the three instant centres of three bodies moving relative to one another must lie along a straight line. 9/23/2018
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Kennedy’s Theorem 9/23/2018
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Instant Centre Velocity Analysis
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