Game Development Reference
In-Depth Information
v c
v e
K c
F c
F e
B c
Figure 9.8 Mechanical equivalent
The hybrid matrix of the virtual coupling is thus written as:
F c
01
v c
F e
=
(9.14)
v e
11 /Z c ( z )
The hybrid matrix of the haptic tool
+
virtual coupling system thus equals:
F h
Z m ( z ) ZOH ( z )
v h
F e
=
(9.15)
v e
1 /Z c ( z )
Which gives the unconditional stability condition as:
Re ( Z m ( z ))
0 Re (1 /Z c ( z ))
0
(9.16)
1
ZOH ( z ))
2 R e ( Z m ( z ))
cos(
Re (1 /Z c ( z ))
|
ZOH ( z )
|
This second inequality helps to determine the limit K c and B c parameters.
9.4 CONCLUSION
In this chapter, we introduced haptic coupling in the case of a linear system with
one degree of freedom. We can consult different references (Stramigioli, 1998; Lin &
Otaduy, 2005) for the 6 DOF systems.
9.5 ANNEXE: ELEMENTS OF NETWORK THEORY
The formalism of the quadripoles is borrowed from the electronics domain. In general,
practically all the representations of the quadripoles are used. We shall particularly
note:
The “chain'' form, which, as its name suggests, helps to easily construct a system
by simply connecting several quadripoles;
 
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