Biomedical Engineering Reference
In-Depth Information
Figure 8.5
(
a
) Three-segment model of the leg, thigh, and trunk during standing
balance. The feet (ankle) can be perturbed with a horizontal acceleration
x
and the hip
with a horizontal force
F
. The system responds with three joint torques,
T
1
,
T
2
,and
T
3
.(
b
) Link-segment model of (
a
) showing the global reference system and three local
reference systems along with output displacement variables
q
1
,
q
2
,
q
3
,and
q
4
.
¨
are described relative to these points and references. Selecting LRS such
that their origins are segments cg simplifies the formulation of the equations,
but for the sake of generality let the LRS origins be at the distal ends of
the segments. Also, the variables
(θ
2
,
θ
3
,
θ
4
)
can be selected to represent
joint angles, but we'd rather let these variables be segment angles. It is also
assumed that the reaction forces at the joints are not needed. Based on these
choices, the model is completely specified using three LRSs, six points, three
segments, three torques, and one force, as shown in Figure 8.5
b
. They are
stated in the following lists:
LRS
(
1
)
=
[1,
q
2
], LRS
(
2
)
=
[3,
q
3
], LRS
(
3
)
=
[5,
q
4
]
pt (
1
)
=
[0,
q
1
,0],
pt (
2
)
=
[1,
r
1
,0],
pt (
3
)
=
[1,
l
1
,0],
pt (
4
)
=
[2,
r
2
,0]
pt (
5
)
=
[2,
l
2
,0]
pt (
6
)
=
[3,
r
3
,0]
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