Biomedical Engineering Reference
In-Depth Information
F
e
z
Q
d
P
x
P
x
Q
e
y
e
x
Figure 2.16
A point in space identified by its position vector
x
.
y
F
y
F
Q
F
x
d
d
y
P
d
x
e
y
x
e
z
e
x
Figure 2.17
The moment of a force acting at point Q with respect to point P.
distance of the forces, i.e.
d
x
e
x
is perpendicular to
F
y
e
y
and
d
y
e
y
is perpendicular to
F
x
e
x
.
M
1
M
2
•
The directions of the composing moments
e
z
follow
from the corkscrew rule. To apply this corkscrew rule correctly, place the tails of the
two vectors (e.g.
d
x
e
x
and
F
y
e
y
) at the same location in space, see Fig.
2.18
.Inthe
case of the combination
d
x
=
d
x
F
y
e
z
and
=−
d
y
F
x
e
y
, the rotation of the arm to the force is a coun-
terclockwise movement, leading to a vector that points out of the plane, i.e. in positive
e
x
and
F
y
e
z
-direction. In the case of the combination
d
y
e
x
, rotating the arm to the force
is a clockwise movement resulting in a moment vector that points into the plane, i.e. in
negative
e
y
and
F
x
e
z
-direction.
In the definition of the moment vector the location of the force vector along the
line-of-action is not relevant since only the magnitude of the force, the direction
and the distance of the point P to the line-of-action are of interest. This is illus-
trated in Fig.
2.19
. We can decompose the vector
d
pointing from the point P to
Q in a vector
d
n
, perpendicular to the line of action of the force
F
, and a vector
