Biomedical Engineering Reference
In-Depth Information
F
1
x
3
x
1
e
y
e
x
x
2
F
3
x
P
P
F
2
Figure 2.22
Forces and moment.
while the points of application are, respectively:
x
1
=
2
e
x
+
2
e
y
x
2
=
e
x
−
e
y
3
2
x
3
=−
4
e
x
+
2
e
y
.
The point P has location:
x
P
=−
2
e
x
−
2
e
y
.
The resulting moment of the forces with respect to the point P follows from
M
×
F
1
+
×
F
2
+
×
F
3
,
=
(
x
1
−
x
P
)
(
x
2
−
x
P
)
(
x
3
−
x
P
)
hence
M
=
(4
e
x
+
4
e
y
)
×
(3
e
x
+
e
y
)
+
5
e
x
×
(4
e
x
−
e
y
)
+
(
−
2
e
x
+
4
e
y
)
×
(
−
2
e
x
−
3
e
y
)
=−
8
e
z
−
5
e
z
+
14
e
z
=
e
z
.
2.12
Drawing convention of moments in three dimensions
An arrow drawn with two arrowheads, and identified by a scalar, rather than a
vector symbol, denotes a moment vector following the right-handed or corkscrew
rule. For example the moment vectors drawn in Fig.
2.23
and identified by the
scalars
M
1
,
M
2
and
M
3
, respectively, correspond to the moment vectors:
