Biomedical Engineering Reference
In-Depth Information
10 kHz
a
(
t,f
)
0 Hz
750 N
F
(
t
)
0 N
|
t
= 1.2 s
Fig. 12.3
Vibration spectrogram
a
(
t
,
f
)
and normal force
F
(
t
)
measured from one footstep onto
rock gravel (Authors' recording). Note the discrete (impulsive) broadband impact events evidenced
by
vertical lines
in the spectrogram
F
e
Force,
F
e
(
t
)
F
e
m
Slip energy,
Slip
transient
R
2
R
1
b
E
(
)
k
2
k
1
Time,
t
(a)
(b)
(c)
Fig. 12.4
Normal force texture synthesis.
a
A fracture mechanics approach is adopted. A visco-
elasto-plastic body undergoes shear sliding fracture due to applied force
F
e
.
b
A simple mechanical
analog for the generation of slip events
in response to
F
e
.
c
For vibrotactile display, each slip
event is rendered as an impulsive transient using an event-based approach [
108
]
ΞΎ(
t
)
12.3.2.2 Stepping on Disordered Heterogeneous Materials
Due to the continuous coupling of acoustic and vibromechanical signals with force
input in examples such as that described above, there is no straightforward way to
convincingly use recorded footsteps for acoustic or vibrotactile rendering, although
more flexible granular sound-synthesis methods could be used [
6
,
18
]. For the model-
ing of simpler interactions, involving impulsive contact with solid materials, recorded
transient playback techniques could be used [
55
].
A simple yet physically-motivated approach that can be used in the haptic synthe-
sis of interaction with complex, compressible surfaces is based on a minimal fracture
mechanics model [
108
]. Similar approaches have proved useful for modeling other
types of haptic interaction involving damage [
42
,
64
]. Figure
12.4
illustrates the
continuum model and a simple mechanical analog used for synthesis.
In the stuck state, the surface has stiffness
K
k
1
+
k
2
, effective mass
m
and
damping constant
b
. It undergoes a displacement
x
in response to a force
F
,as
=
