Biomedical Engineering Reference
In-Depth Information
(c) Calculate the location of the center of mass of the forearm along its
long axis and give its distance from the elbow axis. Compare that
with the center of mass as determined from Table 4.1. Answer: COM
=
10.34 cm from the elbow; from Table 4.1, COM
=
10.32 cm from
the elbow.
(d) Calculate the moment of inertia of the forearm about the elbow axis.
Then calculate its radius of gyration about the elbow and compare
it with the value calculated from Table 4.1 Answer: I p =
0 . 0201 kg
·
m 2 ; radius of gyration
=
12.27 cm; radius of gyration from Table 4.1
12.62 cm.
2. (a) From data listed in Table A.3 in Appendix A, calculate the center
of mass of the lower limb for frame 70. Answer: x
=
=
1 . 755 m; y
=
0 . 522 m.
(b) Using your data of stride length (Problem 2(f) in Section 3.8) and a
stride time of 68 frames, create an estimate (assuming symmetrical
gait) of the coordinates of the left half of the body for frame 30.
From the segment centers of mass (Table A.4), calculate the center
of mass of the right half of the body (foot
1 / 2HAT),
and of the left half of the body (using segment data suitably shifted in
time and space). Average the two centers of mass to get the center of
mass of the total body for frame 30. Answer: x 1 . 025 m, y
+
leg
+
high
+
0 . 904 m.
3. (a) Calculate the moment of inertia of the HAT about its center of mass
for the subject described in Appendix A. Answer: I 0 =
=
m 2 .
(b) Assuming that the subject is standing erect with the two feet together,
calculate the moment of inertia of HAT about the hip joint, the
knee joint, and the ankle joint. What does the relative size of these
moments of inertia tell us about the relative magnitude of the joint
moments required to control the inertial load of HAT. Answer: I h =
5 . 09 kg
1 . 96 kg
·
m 2 .
(c) Assuming that the center of mass of the head is 1.65 m from the
ankle, what percentage does it contribute to the moment of inertia
of HAT about the ankle? Answer: I head about ankle
m 2 , I k
m 2 , I a =
·
=
15 . 78 kg
·
42 . 31 kg
·
m 2 ,
=
12 . 50 kg
·
which is 29.6% of I hat about the ankle.
4. (a) Calculate the moment of inertia of the lower limb of the subject
in Appendix A about the hip joint. Assume that the knee is not
flexed and the foot is a point mass located 6 cm distal to the ankle.
Answer:I lower limb about hip
m 2 .
(b) Calculate the increase in the moment of inertia as calculated in (a)
when a ski boot is worn. The mass of the ski boot is 1.8 kg, and
assume it to be a point mass located 1 cm distal to the ankle. Answer:
I boot about hip = 1 . 01 kg · m 2 .
=
1 . 39 kg
·
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