Biomedical Engineering Reference
In-Depth Information
Using Table 4.1, and neglecting the weight of the thigh, the weight of the foot and leg is 0.061
multiplied by total body weight, yielding
mg
j
¼ð
0
:
061
Þð
150 j lb
Þ¼
9
:
2 j lb
Summing the
x
components gives
T T
cos 30 þ T
cos 40 þ F femur cos 20 ¼
0
Summing the
y
components gives
T
sin 30 þ T
sin 40 F femur sin 20 mg ¼
0
The last two expressions may be solved simultaneously, giving both
T
, which is equal to the
required externally applied weight, and the axial tensile force,
F femur
T ¼
12
:
4lb
F femur ¼
14
:
5lb
EXAMPLE PROBLEM 4.6
The force plate depicted in Figure 4.11 has four sensors, one at each corner, that read the
vertical forces
F 1 ,
F 2 ,
F 3 , and
F 4 . If the plate is square with side of length
l
and forces
F 1 F 4
are known, write two expressions that will give the
x
and
y
locations of the resultant force
R
.
Solution
The resultant magnitude
R
can be computed from the sum of forces in the
z
-direction:
P F z ¼
0
F 1 þ F 2 þ F 3 þ F 4 R ¼
0
R ¼ F 1 þ F 2 þ F 3 þ F 4
z
R
y
F4
F3
F1
F2
x
FIGURE 4.11
A square force plate with sides of length
l
is loaded with resultant force
R
and detects the
vertical forces at each corner,
F 1
F
4 .
The force plate remains horizontal, so the sum of the moments about the
x
and
y
axes must
each be zero. Taking moments about the
x
-axis,
X
M x ¼
0
F 2 l þ F 3 l Ry ¼
0
y ¼ ð F 2 þ F 3 Þ l
R
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