Biomedical Engineering Reference
In-Depth Information
where the distance vector
d
is given by
d
=
b
e
x
+
a
e
y
,
hence
d
×
P
=
(
be
x
+
ae
y
)
×
(
−
Pe
z
)
=
bPe
y
−
aPe
x
.
Consequently
M
x
−
aP
=
0,
M
y
+
bP
=
0,
M
z
=
0.
Example 3.7
Consider the man sketched in Fig.
3.9
who is lifting a weight. We would like to
compute the force
F
M
in the muscle connecting the upper arm to the shoulder. A
basis
{
e
x
,
e
y
}
is introduced with the origin in the joint, point J. The basis vector
e
x
has the direction of the arm, while basis vector
e
y
is perpendicular to the arm (see
W
W
0
=−
figure). The forces
e
y
due to the lifted weight are both supposed to be known. The reaction force in the
joint
F
J
and the force in the muscle
F
M
are both unknown. However, the direction
of the force in the muscle is known since this force is oriented with respect to the
arm at an angle
θ
. Consequently
=−
W
e
y
, due to the weight of the arm, and
W
0
F
J
=
F
J
x
e
x
+
F
J
y
e
y
,
F
M
e
y
A
C
B
θ
F
J
e
x
J
W
W
0
a
b
c
Figure 3.9
Lifting a weight.
