Biomedical Engineering Reference
In-Depth Information
θ
z
ZMP
d
x
o
Left foot
Right foot
FIGURE 8.2
Feet locations and support region.
where M
o
M
x
M
y
M
z
T
and F
o
F
x
F
y
F
z
T
. Note that the two
5
5
feet are assumed to be on the level ground.
3.
Calculate the resultant active forces at ZMP (M
zmp
, F
zmp
) using the
equilibrium condition as follows:
M
zmp
M
o
F
o
o
r
zmp
5
1
3
(8.14)
F
zmp
5
F
o
where
o
r
zmp
is the ZMP position in the global coordinate system obtained
from
Equation (8.13)
.
4.
Calculate the value and location of GRF from the equilibrium between the
resultant active forces and passive forces at the ZMP:
M
GRF
M
zmp
0
1
5
F
GRF
F
zmp
0
(8.15)
1
5
o
r
GRF
2
o
r
zmp
5
0
Next, the resultant GRF is partitioned into two feet by using a linear distance
relationship between the GRF location and feet centers as shown in
Figure 8.3
.
5.
Finally, all active forces (gravity, inertia, and external forces) and passive forces
(GRF) are applied to the multi-body human system using
Equation (8.5)
to
obtain the real joint torques that are used in the torque limit constraints and to
calculate the dynamic effort objective function.
8.4
Formulation
8.4.1
Lifting task
In this chapter, the lifting task is defined as moving a box from an initial location
to a final
location.
Figure 8.4
depicts the input parameters for the proposed
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