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MEEG439
MEEG439
SPRING2006
Chapter 6 Velocity Analysis
6.0 Introduction
•
Use position and velocity analysis as stepping stones to acceleration (and hence
force) analysis
•
We can use velocities to look at energies and power losses in a system
•
Note: we won’t be covering the graphical velocity analysis techniques in any depth
•
Also, we won’t be using the complex number approach for velocity and acceleration
analysis
6.1 Definition of Velocity
•
Velocity is the rate of change of position with respect to time
•
Velocity is a vector quantity
•
Angular velocity for 2D can be considered a scalar quantity (even though it is
really a vector about the z axis)
,
d
d
dt
dt
θ
ϖ
=
=
=
=
r
v
r
&
&
•
Given a position vector
(cos
sin
)
a
b
=
+
r
i
j
( sin
cos
)
a
=

+
r
i
j
&
•
Note that for this case (rotation about a fixed point) the velocity vector is
perpendicular to the position vector
θ
r
r
.
•
Recall our position equation
or
P
A
PA
PA
P
A
=
+
=

r
r
r
r
r
r
•
Differentiating with respect to time
or
P
A
PA
PA
P
A
=
+
=

v
v
v
v
v
v
•
Now, if points
P
and
A
are on the same body,
v
PA
is the velocity difference
•
If
P
and
A
are on different bodies,
v
PA
is the relative velocity
•
I will tend to call both of these relative velocity
6.2 Graphical Velocity Analysis
•
Before calculators, had to solve such problems graphically
•
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 Spring '11
 SCF

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