Biomedical Engineering Reference
In-Depth Information
The field of biomechanics applies physical principles to living systems using the language
of mathematics. Hemodynamics studies the human cardiovascular system, which comprises
a complex pump moving complex fluid around an extensive network of complex pipes. In
developing hemodynamic principles, experiments and analysis go hand-in-hand, ensuring
the validity of principles with experiments and with analysis clarifying, modifying, and often
preceding experiments. In this fashion, interpretations of cardiovascular health are further
defined.
4.8 EXERCISES
1. Write and evaluate all the vector expressions of Eqs. (4.1) through (4.14) using MATLAB.
2. The measurement error associated with the pointer marker data presented in Example
Problem 4.2 is
5 mm in all three coordinate directions. Given the geometry of the
pointer in the example problem, what is the measurement error associated with the pointer
tip, point T? If you wanted to minimize the measurement error at point T, how would you
design the pointer with respect to the distances between markers A and B, and between
marker B and the pointer tip T?
3. Repeat Example Problem 4.3 using a
0
:
rotation sequence.
4. Write the free-body diagrams for each of the three orientations of the humerus in Figure 3.36.
For a particular load and fixed position, write and solve the equations of static equilibrium.
5. The force plate in Figure 4.11 is 70 cm wide in the
-
-
z
x
y
x
-direction and 80 cm long in the
y
-direction. At a particular instant of the gait cycle each transducer reads
F 1
¼
150 N,
210 N. Compute the resultant force and its location.
6. Solve Example Problem 4.8 for forearm orientations angled y from the horizontal position.
Let y vary from 0
F 2 ¼
180 N,
F 3 ¼
220 N, and
F 4 ¼
to 70 down from the horizontal in 5
increments. Using MATLAB, plot
F B for static equilibrium as a function of y. By how much
does this force vary over this range?
7. Repeat Problem 6, this time plotting forces
the required biceps muscle force
F C over the same range of angles y.
8. Considering the previous problem, explain why Nautilus weight machines at the gym use
asymmetric pulleys.
9. Solve Example Problem 4.7 using the moment of inertia of the thigh with respect to the knee.
10. For your own body, compute the mass moment of inertia of the body segments: Forearm,
Total Arm, Thigh, Foot, and Trunk in Table 4.1 with respect to their centers of mass.
11. Repeat Example Problem 4.9 using a cobalt alloy rod with circular cross-sectional diameter of
10 mm.
12. Write the Simulink models of the three-element Kelvin viscoelastic description and perform
the creep and stress relaxation tests, the results of which appear in Figures 4.26 and 4.27.
13. Use the three-element Kelvin model to describe the stress relaxation of a biomaterial of your
choice. Using a stress response curve from the literature, find the model spring constants
F A ,
F B , and
K 1
K 2 , and the viscous damping coefficient b.
14. Write and solve the kinematic equations defining an anatomically referenced coordinate
system for the pelvis,
and
, using MATLAB.
15. Using the kinetic data of Section 4.6.3, compute the instantaneous ankle power of the 25.2 kg
patient using MATLAB.
f
e pa g
Continued
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