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