Biomedical Engineering Reference
In-Depth Information
M
GRF
F
GRF
A
d
1
ZMP
Right foot
Left foot
y
d
2
x
B
o
z
FIGURE 7.10
Partition of ground reaction forces.
Moreover, the transient value of resultant GRF is also obtained from global equilib-
rium conditions as:
M
GRF
M
zmp
0
1
5
F
GRF
1
F
zmp
0
(7.21)
5
o
r
GRF
2
o
r
zmp
5
0
In the single support phase, one foot supports the whole body and the ZMP
stays in the foot area so that GRF can be applied at the ZMP directly. However,
in the double support phase, the ZMP is located between the two supporting feet,
and the resultant GRF needs to be distributed to the two feet appropriately. This
partitioning process can be treated as a sub-optimization problem (
Dasgupta and
Nakamura, 1999
). In order to simplify this process, the GRF is distributed to the
points (A, B) of the supporting parts on each foot as shown in
Figure 7.10
, where
point A (triangle) is the left toe center and point B (triangle) is the right heel cen-
ter;
d
1
and
d
2
are the distances from the ZMP (circle) to points A and B respec-
tively. A linear relationship is used to partition GRF. The GRF value is first
linearly decomposed at the ZMP as follows:
d
2
d
1
1
d
2
d
1
1
M
GRF
1
d
2
M
GRF
F
GRF
1
d
2
F
GRF
;
5
5
(7.22)
d
1
d
1
1
d
1
d
1
1
M
GRF
2
d
2
M
GRF
F
GRF
2
d
2
F
GRF
;
5
5
Then, (M
GRF
1
, F
GRF
1
) are transferred to point A and (M
GRF
2
, F
GRF
2
) to point B
as follows:
M
A
M
GRF
1
A
d
zmp
3
F
GRF
1
5
1
(7.23)
F
A
F
GRF
1
5
M
B
5
M
GRF
2
B
d
zmp
3
F
GRF
1
2
(7.24)
F
B
F
GRF
2
5
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