Advanced Engineering Dynamics 2010 Part 9 potx
Advanced Engineering Dynamics 2010 Part 9 potx
...
is of the order unity equation (6. 190 ) is, to a close approximation,
W’
=
(Kla)’
(6. 191 )
w2
=
K2q
1
+
qa2
Returning to the dimensional form
k
(6. 192 )
c2 rc2
~=-k=-
a
R,2
from ... written as
and differentiating partially with respect to
x
gives
(6.126)
(6.127)
or
This
is
known
as
the
Emoshenko beam equation.
Waves in a helical
spring
1 69
Fig.
6.40
F...
Advanced Engineering Dynamics 2010 Part 1 pdf
... Arm Dynamics
8.1 Introduction
8.2 Typical arrangements
8.3 Kinematics of robot
arms
8.4
Kinetics of a robot arm
9 Relativity
9. 1
9. 2
9. 3
9. 4
9. 5
9. 6
9. 7
9. 8
9. 9
9. 10
9. 1
1
9. 12 ...
176
177
178
1 79
184
186
1 89
192
194
194
194
197
223
235
235
235
240
24
1
242
246
2 49
250
252
254
256
258
261
272
281
288
Bibliography...
Advanced Engineering Dynamics 2010 Part 2 doc
...
a group
of
particles
15
1.13
Newton's
laws
for
a
group
of
particles
Consider a group of
n
particles, three
of
which are shown in Fig.
1.1
1, where the ith parti-
cle has ... on the particle
is
the vector sum of the forces due
to
each other particle in the
group and the resultant of the external forces. If
&
is the force on particle
i
due
to
particle ......
Advanced Engineering Dynamics 2010 Part 3 ppt
... the time integral will be integrated by
Parts
because
6u
=
0
at
t,
and
t2.
The second term in equation (3.18) is
Integrating by parts gives
(3. 19)
50
Hamilton
S
principle
Thus
the ... choice
of reference axes
m(ap)i
2
at
(Y2
at
*)
E=
m0+U
-V
(2.39b)
mo2
2
at
(
1
Fig.
2.6
Moving co-ordinates
39
from which we see that there are fictitious Coriolis force...
Advanced Engineering Dynamics 2010 Part 4 pot
...
which discusses robot dynamics. The fact is easily demonstrated by reference to Fig.
4.3,
depicting three consecutive
90 "
rotations. The line
OP
is rotated
90 '
about the
x ... momentum about some origin
0
is
L,
=
C
r,
x
m,i;
(4 .9)
(4.10)
From Fig. 4.5
r~
=
rA
+
PI
where
p,
is the position vector of particle
i
relative to
A.
For a rigid body equat...
Advanced Engineering Dynamics 2010 Part 5 pdf
... constant
1
1 1
2 2 2
E
=
-
ZIe2
+
-
Z,b2sin2B
+
-
Z3
(91
cos 8
+
\irf
+
rngh
cos
8
(4.88)
Fig.
4.18
92
Dynamics
of
vehicles
and therefore
dr du
-
= L
dt de
and ...
from
P.
ne
symmetn'cal
body
79
Therefore
Z,e
=
(-Z3azb
+
Z,S2
cos
8
+
mgh
)
sin
8
=
0
-13azb +
llb2
cos8
+
mgh
=
0
(4 .93 )
(4 .94 )
For
6
=
0
and
8
no...
Advanced Engineering Dynamics 2010 Part 6 docx
...
I:
L*’
-
-
K
(5. 39)
2Pr
and when the radial component of the velocity is zero
(i
=
0)
equation (5. 39) becomes the
quadratic
96
Dynamics
of
vehicles
2E .9
+
2Kr
-
L*2
=
0 ...
W+O
(5 .92 )
z
=
m(6
-
qv
=
m(6
-
itu
(5 .93 )
M
=
Bq
=
r,e
(5 .94 )
where
q
=
6
and
B
=I,,.
Consider first the aircraft in straight and level flight. Figure
5. 19...
Advanced Engineering Dynamics 2010 Part 8 docx
... frequencies are very close together then,
in
the limit,
(6 .92 )
00
phase velocity
cp
=
-
k0
and
do
dk
groupvelocity
cg
=
-
(6 .93 )
A
graph of
o
versus
k
is called the dispersion ...
cs
-
or
0,
=
c,(k,
-
43)
+
wo
(6 .94 )
Now a typical wave in this region is
u
=
U,
COS
(o,t
-
k,x)
Substituting
from
equation (6 .94 ) gives
u
=
U,
COS
{
[cg
(...
Advanced Engineering Dynamics 2010 Part 11 pps
... shall only be con-
cerned with the overall dynamics and not with the detail. This is a vast subject area
of
which
dynamics is a substantial and vital part.
8.2
Typical arrangements
8.2.1
CARTESIAN ...
SUCCESSIVE ROTATIONS ABOUT FIXED AXES
8
Robot
Arm
Dynamics
8.1
Introduction
In
this chapter we examine the way in which three-dimensional dynamics is applied to
a
sys-...
Advanced Engineering Dynamics 2010 Part 12 pdf
...
d
1
90
'
-90 '
0
D,
=O
2
60
'
90 "
0
0
3
0
0
0
0.8
With reference
to
the data sheet the three
A
matrices are
ce,
o
sel
o
&41,=[;
;l
9& apos; ...
ann
dynamics
(4
Fig.
8.25
(a)
and
(b)
Now
a
is the rotation of one
z
axis relative to the previous
z
axis
so
aI
=
-90 "
and
a,
=
The table is
as
follows:
90 &quo...
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