chapter6-a-student_0-3 - MEEG439 MEEG439 SPRING2006 Chapter...

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 2-D 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
•