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G
N
G
A
P=mg
A
N
M
M
Fig. 8. Power lift gate topological graph
Nodes
(external)
1010
Branches
(internal)
C=(-1)
0 1 1 0
1001




A
M
N
G
AN
MN
AG
 
Fig. 9. Connection matrix and geometry (Nodes towards branches)
structure. This global structure connects nodes and branches of the graph, and may
include physical parameters governing the behaviour of the system. This method has
been thoroughly described in previous papers [5], [9].
Thus, the transposed matrix C T can be used to express (Fig. 10) the connection
between internal and external mechanical forces and moments, defined with their
associated static screws, with T A standing for “screw of external mechanical action on
point A” and T AN standing for “screw of internal mechanical action on AN structure”:
10 1
010
C=(-1) 110
001
T
T
T
+
T
  
A
AN
AG
  
T
T
T
 
 
 
T
T
AN
  
M
M N
=
  
T
−−
T
T
MN
N
AN
M N
  
T
T
  
AG
G
AG
Fig. 10. Connection matrix and mechanical actions (Branches towards nodes)
10 1
010
C=(-1) 110
001
R=R R
R=R
R=R R
R=R
M=M M
M=M
M=M M
M=M
+
A
AN
AG
 
R
M
R
M
R
M
AN
AN
T
M N
 
−−
A
N
AN
MN
 
G
AG
MN
MN
 
+
 
A
AN
AG
A
 
M
N
AG
AG
 
−−
 
N
AN
MN
A
G
AG
A
Fig. 11. Equations system
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