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and that the magnitude of the retracted unit vector remains at unity
XU YU ZU
2 + 2 + 2 = 1 (6.7)
The angle of inclination (q) of Ur in the yz-plane, which is one of the design variables that
can be used to position the retracted truck assembly to fit into the available stowage space,
is given as
tanq = Y
Z
U
U
(6.8)
The vector components of Ur, and subsequently V4, can then be determined by solving
Eqs (6.6), (6.7), and (6.8) simultaneously.
As shown in Fig. 6.4, the pivot axis that will permit the achievement of the desired
motion is defined by the cross product of the space vectors between the deployed and
retracted positions of the two point locations, in this case points A and B,
V = VB ´ VA (6.9)
where
VA = (X3 - X1)i$ + (Y3 -Y1)j$ + (Z3 - Z1)k$ (6.10)
and
VB = (X4 - X2)i$ + (Y4 - Y2)j$ + (Z4 - Z2)k$ (6.11)
Thus, the direction cosines of the wing-mounted assembly and the angle of rotation can be
determined using Eqs (6.2) and (6.3), respectively. Note that the subscripts in Eq. (6.3)
will be 1 and 3 in this case, i.e., the vectors corresponding to the deployed and retracted
positions of point A, respectively.
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Point A
Point B
Point A’
Point B’
V, pivot axis
VB
VA
y
z
x
Figure 6.4 Wing-mounted assembly pivot axis alignment
6.3.2. Retracted Position of a Given Point Location
In addition to determining the required pivot axis and angle of retraction, the analytic
method is used to establish the retraction path and the stowed position of the landing gear
assembly. Note that the drag and side struts are excluded in the analysis since the retraction
of these items involves additional articulation, e.g., folding and swiveling, that cannot be
modeled by the analysis.
Define point A as an arbitrary point location on the landing gear assembly. Given the
angle of rotation and the direction cosines of the pivot axis as determined above, the
retracted position of point A, denoted here as A’, can be determined by solving the
following system of linear algebraic equations [2, pp. 193-194]
( )
( )
( )
X
Y
Z
c
l lX mY nZ X
m lX mY nZ Y
n lX mY nZ Z
c
mZ nY
nX lZ
lY mX
X
Y
Z
A
A
A
A A A A
A A A A
A A A A
A A
A A
A A
A
A
A
'
'
'
é
ë
êêê
ù
û
úúú=
+ + -
+ + -
+ + -
é
ë
êêê
ù
û
úúú
+
-
-
-
é
ë
êêê
ù
û
úúú
+
é
ë
êêê
ù
û
úúú
1 2 (6.12)
where
c1 = 1- cosf c2 = sinf 0 < f < f full (6.13)
53
Similarly, the retraction path and swept volume of the assembly, as shown in Fig. 6.5, can
be established by calculating several intermediate transit positions at a given interval of
degrees. The above information can then be used to identify possible interference between
the landing gear and surrounding structures during deployment/retraction.
Pivot axis
y
z
x
Figure 6.5 Retraction path and swept volume of the landing gear
6.4. Integration and Stowage Considerations
For future large aircraft, interference between the landing gear assembly and the
surrounding structure is one of the more important considerations in the development of
kinematics. With the large number of doors required to cover the stowage cavity on such
aircraft, a complex deployment/retraction scheme for both the landing gear and doors is
required to ensure that no interference will occur under all conditions. Additionally, the
availability of stowage volume can become a major integration problem as the number of
tires increases with aircraft takeoff weight. Given the conflicting objectives between
maximizing the volume that can be allocated for revenue-generating cargoes and providing
adequate landing gear stowage space, a trade-off study involving crucial design parameters,
54
e.g., pivot axis alignment, angle of retraction, and bogie rotation, is needed to arrive at a
satisfactory compromise with surround structures.
6.4.1. Truck Assembly Clearance Envelope
Clearances are provided to prevent unintended contact between the tire and the adjacent
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