Biomedical Engineering Reference
In-Depth Information
R
yp
M
xp
R
xp
M
yp
a
y
M
zp
y
R
zp
x
,
x
x
y
,
I
p
y
a
x
a
z
z
,
Y
z
R
zd
z
M
zd
I
d
R
xd
M
yd
M
xd
X
R
yd
Z
Figure 7.3
3D free-body diagram for solution of the inverse dynamics equations.
Known are the distal reaction forces and moments, the COM linear accelerations, and
the segment's angular velocities and accelerations. Using the kinetic Equations (7.8)
and (7.9), we calculate the proximal reaction forces and moments.
of the segment with their origin at the COM of the segment. Thus, the
x
z
axes of the segment in Figure 7.3 satisfy those conditions. The angular veloc-
ity of the segment in its coordinate system is
ω
. The rotational equations of
motion are:
−
y
−
I
x
α
x
+
(I
z
−
I
y
)ω
y
ω
z
=
M
x
=
R
zd
l
d
+
R
zp
l
p
+
M
xp
−
M
xd
(7.9
a
)
I
y
α
y
+
(I
x
−
I
z
)ω
x
ω
z
=
M
y
=
M
yp
−
M
yd
(7.9
b
)
I
z
α
z
+
(I
y
−
I
x
)ω
x
ω
y
=
M
z
=−
R
xd
l
d
−
R
xp
l
p
+
M
zp
−
M
zd
(7.9
c
)
where
I
x
,
I
y
,
I
z
=
moments of inertia about
x
−
y
−
z
axes
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