Biomedical Engineering Reference
In-Depth Information
M
y
p
z
6
Rotation
z
5
(
q
6
,
t
6
)
(
q
5
,
t
5
)
Rotation
M
x
p
O'
(
q
4
,
t
4
)
Pelvis
z
4
M
p
z
y
Rotation
x
(
q
3
,
t
3
)
Translation
o
z
1
z
3
z
z
2
(
q
1
,
t
1
)
Translation
(
q
2
,
t
2
)
Translation
FIGURE 7.8
Global DOFs in virtual branch.
7.7.2
Global forces at origin
After obtaining the global forces at the pelvis in the global Cartesian coordinates
we can transfer the resultant active force from the pelvis to the origin using the
equilibrium conditions. Thus, the resultant active forces (M
o
, F
o
) at the origin are
obtained as follows:
M
o
M
p
o
r
p
3
F
p
5
1
(7.16)
F
o
F
p
5
where M
o
T
;
o
r
p
is the pelvis posi-
tion vector in the global coordinate system, as depicted in
Figure 7.9
.
5
½
M
x
M
y
M
z
T
and F
o
5
½
F
x
F
y
F
z
7.7.3
ZMP calculation
Next, the resultant active forces are further transferred from the origin to the
ZMP by using the equilibrium conditions; i.e., (M
zmp
, F
zmp
) are obtained using
the equation:
0
@
1
A
5
0
@
1
A
1
0
@
1
A
3
0
@
1
A
M
zmp
x
M
zmp
y
M
zmp
z
M
x
M
y
M
z
F
x
F
y
F
z
x
zmp
y
zmp
z
zmp
(7.17)
F
zmp
F
o
5
where
o
r
zmp
5
½ x
zmp
T
is the ZMP position vector in the global coor-
dinates. Since ZMP is set on the level ground and tangential moments are zero
due to its definition, we have:
y
zmp
z
zmp
M
zmp
x
M
zmp
z
y
zmp
5
0
;
0
;
0
(7.18)
5
5
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