Game Development Reference
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Figure 9.5 S system looped on two passive 1-ports
v a , v c
F a
F h
M m
B m V a
Figure 9.6 1D haptic device
This property can be verified by applying the result shown by (Adams &
Hannaford, 1999), called Llewellyn criterion in network theory.
Theorem 3: For admittance, impedance or hybrid quadripole, the “unconditional
stability in coupled mode'' is guaranteed by the following necessary and sufficient
conditions:
Q is stable and has single imaginary poles.
Re ( q 11 )
0, Re ( q 22 )
0
(9.6)
≥|
|+
2 Re ( q 11 ) Re ( q 22 )
q 21 q 12
Re ( q 21 q 12 )
ω
0
9.3.3 Application to the single degree of freedom problem
The one-dimensional problem, although simple, helps to quite simply understand a
good number of concrete problems related to the haptic sense (Adams & Hannaford,
1999). Please note that the objective of transparency can be reformulated in the form
of the following hybrid matrix:
F h
01
v h
F e
=
(9.7)
v e
10
 
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