Biomedical Engineering Reference
In-Depth Information
ω
x
,
ω
y
, and
ω
z
=
components of angular velocity
ω
about
x
−
y
−
z
axes
α
x
,
α
y
,
α
z
=
components of angular acceleration
about
x
−
y
−
z
axes
M
xd
,
M
yd
,
M
zd
=
previously transformed distal moments
(not shown in Figure 7.3) about
x
−
y
−
z
axes
R
xd
,
R
xp
,
R
yd
,
R
yp
,
R
zd
,
R
zp
=
previously transformed joint reaction
forces about
x
−
y
−
z
axes
l
p
,
l
d
=
distances from COM to proximal and
distal joints
The unknowns in these three equations are the three moments (
M
xp
,
M
yp
and
M
zp
) about the proximal
x
,
y
,
z
axes. Note that Equations (7.9) are in the
same form as the 2D Equation (4.3) with the additional term
(I
1
−
I
2
)ω
1
ω
2
to account for the interaction of the angular velocities in the other two axes.
Also note that the moments about the
y
axis (long axis of the segment) does
not involve the proximal and distal reaction forces because these forces have
zero moment arms about that axis.
7.4.3 Example of a Kinetic Data Set
The set of kinematic and kinetic data shown in Tables 7.3 and 7.4 is taken
from stance phase of walking, and we will confine our analysis to the leg
segment (see Figure 7.3). The following anthropometric measures apply:
m
=
TABLE 7.3
Ankle Reaction Forces (N) and Moments (N
·
m) in GRS
Frame
R
XD
R
YD
R
ZD
M
XD
M
YD
M
ZD
4
−
86.55
−
766.65
−
13.81
10.16
6.74
−
97.55
5
−
102.71
−
790.27
−
12.12
11.94
4.65
−
102.50
−
119.04
−
791.44
−
12.03
−
103.85
6
14.29
2.11
−
134.33
−
763.38
−
10.26
−
0.49
−
101.32
7
16.13
8
−
146.37
−
704.00
−
5.26
16.64
−
2.88
−
94.59
TABLE 7.4
Leg Angular Displacements (rad) and Velocities (rad/s)
θ
1
θ
2
θ
3
Frame
θ
1
θ
2
θ
3
−
−
−
−
−
4
0.14246
0.02646
0.37248
0.1752
0.2459
2.358
5
−
0.14512
−
0.02362
−
0.41396
−
0.1607
0.0434
−
2.641
6
−
0.14781
−
0.02501
−
0.46053
−
0.0911
−
0.1048
−
2.909
7
−
0.14815
−
0.02705
−
0.51094
−
0.1139
−
0.0923
−
3.209
8
−
0.15161
−
0.02809
−
0.56749
−
0.1109
0.2175
−
3.472
Search WWH ::
Custom Search