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162A. Position and
Displacement in
Mechanisms
Chapter 2:
Position &
Displacement
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s
Position and Displacement
Notation
s
Consider a fixed reference
coordinate system O
xyz
or simply
O
xy
if we have a 2d reference
system.
O is the origin from
which positions are measured
s
The position of a point P in the
coordinate system is represented
as
R
PO
which is a vector
verbalized as “R P to O”.
Remember: tiptotail.
This
R
PO
vector is sometimes simply written
as
R
P
, when it is w.r.t. the origin.
s
Vector
R
P
is written with R in bold
(or with a line above or below the
letter) to connote it is a vector.
Without bold (or a line), it
connotes just the magnitude
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s
Absolute Position
of a point
is its position with respect to
the origin of the coordinate
system
s
Relative Position
between
two points P and Q can be
expressed as position
ifference between those
difference between those
two points
R
PQ
=
R
PO

R
QO
s
Apparent Position
of a
point P is the position of the
point P relative to the
observer
s
Absolute and Relative
Positions are related as
:
R
PO
=
R
QO
+
R
PQ
We’ll employ two methods for
position analysis
s
Graphical Method
b
Intuitive
b
Inexact
s
Complex Algebra Method
b
Analytic
b
Exact
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The Loop Closure Equation
s
Loop Closure Equation: A vector equation
representing all or part of mechanism
formulated according to the fact:
The
vector sum of a closed polygon equals
zero.
s
That is, the sum of vectors to close the
loop is
0
, or,
LoopClosure Equation
s
Applying the loop closure equation to the
handoperated clamp
A
B
C
D
R
BA
+
R
CB
+
R
DC
+
R
AD
=
0
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This note was uploaded on 08/08/2011 for the course MAE 162A taught by Professor Glenn during the Spring '08 term at UCLA.
 Spring '08
 GLENN

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