Game Development Reference

In-Depth Information

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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