Biomedical Engineering Reference
In-Depth Information
5.2.2.2 Application of the Conservation of the Momentum Principle to Solids
If the body is completely motionless, it is said to be in static equilibrium. Then the
resultant force in a joint is obtained using the principle of static equilibrium, which
states that for a body to be in a state of static equilibrium:
The sum of all horizontal forces and sum of all horizontal moments must be
zero.
The sum of all vertical forces and sum of all vertical moments must be zero.
The sum of all torques must be zero.
Consider the reaction board shown in Figure 5.1(a) with the person in position
on the reaction board. The equation of static equilibrium for horizontal moments
about a reference axis
A
becomes
∑
MRdWxWx
=−−
=
0
(5.5)
x
2
d
d
where
R
2
is the weight scale reading,
W
is the weight of the person,
x
is the axis
A
to the CG of the person's body,
x
d
is the distance from axis
A
to the CG of the
board, and
W
d
is the weight of the board. When the person is not loaded, the board
is in static equilibrium, and horizontal moments about a reference axis
A
become
∑
MRdWx
=−
=
0
(5.6)
x
1
d
d
where
R
1
is the weight scale reading without the person. Solving (5.5) and (5.6), the
location of the CG with respect to axis
A
can be obtained as
(
)
RR
W
−
(5.7)
2
1
x
=
d
