Biomedical Engineering Reference
In-Depth Information
Example 2.8
Resulting moment using scalar notation. Following the drawing convention of
Section
2.2
, the force vectors in Fig.
2.21
are given by
F
1
=
F
1
e
x
F
2
=−
F
2
e
x
F
3
=
F
3
e
x
.
Similarly,
d
1
=
3
e
x
+
4
e
y
d
2
=−
2
e
x
−
2
e
y
d
3
=
2
e
x
−
5
e
y
.
Each of the force vectors
F
i
generates a moment vector with respect to the point P:
M
i
=
d
i
×
F
i
.
Clearly, given the fact that all force vectors are in the plane spanned by the
e
x
and
e
y
vectors, the moment vectors are all in the
e
z
direction:
M
i
=
M
i
e
z
.
Either using the formal definition of the moment vector or the drawing convention
for two-dimensional problems as given above, it follows that
M
1
=−
4
F
1
M
2
=−
2
F
2
M
3
=
5
F
3
.
The force vectors
F
1
and
F
2
produce a clockwise, hence negative, moment, while
F
3
produces a counterclockwise, hence positive, moment. The resulting moment
with respect to point P equals
M
=
M
1
+
M
2
+
M
3
=−
4
F
1
−
2
F
2
+
5
F
3
.
Example 2.9
Resulting moment using vector notation. Consider the forces as depicted in
Fig.
2.22
. The forces are given by
F
1
=
3
e
x
+
e
y
F
2
=
4
e
x
−
e
y
F
3
=−
2
e
x
−
3
e
y
,
