Biomedical Engineering Reference
In-Depth Information
We are now ready to solve Euler's Equations (7.9) for the proximal
moments:
I x α x + (I z I y y ω z = M x = R zd l d + R zp l p + M xp M xd
M xp = 2 . 79 + 121 . 83 × 0 . 1815 + 125 . 5 × 0 . 1386 + 0 . 0138 × 3 . 312
+ ( 0 . 0138 0 . 0024 ) × 0 . 1344 × 2 . 907 = 42 . 35 N · m
I y α y + (I x I z x ω z = M y = M yp M yd
M yp = 20 . 79 0 . 0024 × 3 . 337 + ( 0 . 0138 0 . 0138 ) × 0 . 035 × 2 . 907
=
·
m
I z α z + (I y I x x ω y = M z
20 . 78 N
=− R xd l d R zp l p + M zp M zd
M zp =−
102 . 73
+
241 . 99
×
0 . 1815
+
237 . 65
×
0 . 1386
0 . 0138
×
17 . 07
+ ( 0 . 0024
0 . 0138 ) ×
0 . 035
×
0 . 1343
=−
26 . 11 N
·
m
The interpretation of these moments for the left knee is as follows as
the subject bears weight during single support. M xp is
ve ; thus, it is a
counterclockwise moment and hence an abductor moment acting at the knee
to counter the large gravitational load of the upper body acting downward
and medial of the support limb. M yp is the axial moment acting along the
long axis of the leg and reflects the action of the left hip internal rotators
actively rotating the pelvis, upper body, and right limb in a forward direction
to gain extra step length. M zp is - ve , indicating a clockwise (flexor) knee
moment in the sagittal plane that would assist in starting the knee to flex late
in stance shortly before toe-off.
The next stage of the kinetic analysis is to transform these knee moments,
M xp , M yp , and M zp (which are in the leg anatomical axis system), to the
global system so that the inverse dynamics analysis can continue for the
thigh segment. This transformation is accomplished by the [A to G] matrix
for the leg and yields a new set of distal moments, M XD , M YD , and M ZD ,for
the thigh analysis.
As
+
an
exercise,
students
may
wish
to
repeat
the
preceding
calcula-
= 5 . 89 m / s 2 , a Y
= 1 . 30 m / s 2 ,
tions for frame 5 or 7. For frame 5: a X
=− 1 . 66 m / s 2 ;
= 9 . 60 m / s 2 ,
= 1 . 94 m / s 2 ,
a Z
for
frame
7:
a X
a Y
=− . 020 m / s 2 .
a Z
For
frame
5:
M xp = 40 . 76 N · m,
M yp = 21 . 61 N · m,
M zp =− 31 . 23 N · m;
for
frame
7:
M xp = 41 . 85 N · m,
M yp = 19 . 20 N ·
m, M zp =− 19 . 80 N · m.
7.4.4 Joint Mechanical Powers
The joint mechanical power generated or absorbed at the distal and proximal
joints, P d and P p , can now be calculated using Equation (5.5) for each of
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