Biomedical Engineering Reference
In-Depth Information
TABLE 4-1
Description of Mechanical Blocks
Block
Describing Equation
Energy/Power
1
2
kx
2
Spring
F
=
kx
E
spring
=
1
2
k
θ
2
Torsion spring
T
=
k
θ
E
spring
=
F
=
m
d
dt
=
m
d
2
x
1
2
m
v
2
Mass
E
mass
=
dt
2
=
I
α
=
I
d
dt
=
I
d
2
θ
dt
2
1
2
I
ω
2
=
Moment of inertia
T
E
I
F
=
c
v
=
c
dx
dt
2
Dashpot
P
dash
=
c
v
=
c
ω
=
c
d
dt
2
Rotational damper
T
P
damp
=
c
ω
4.5.2 Mechanical Model
Many models used in biomechatronic systems can be modeled using the building blocks
described in the previous system. For example, consider the actuator that is driving the
incus in a middle ear implantable hearing device (MEIHD), shown in Figure 4-6.
As a first approximation, the driven mass consists of the sum of the mass of the
actuator pin and the ossicles. The spring component results from the springiness of the
flexible linkages between the ossicles and their attachment to the eardrum and the round
window, while the damping component is also determined by the energy absorbed in these
linkages.
In this model, it is assumed that the applied forces all operate in the direction of
movement of the ossicles. Therefore, the net force applied to the mass
m
(kg) is
F
−
kx
−
c
v
,
and it results in an acceleration
a
(m/s
2
)
. Written as an equation
ma
=
F
−
kx
−
c
v
(4.19)
This can be written as a differential equation
m
d
2
x
dt
2
c
dx
dt
=
F
−
kx
−
(4.20)
FIGURE 4-6
Diagram of (a) A
middle ear
implantable
hearing device and
(b) Simplified
free-body diagram
of the system.
