Biomedical Engineering Reference
In-Depth Information
Thus, knowing the weight scale readings and the weight of the person, the CG
of that person in the supine position can be determined. However, the CG changes
with every posture of the body motion and the reaction board cannot be applied.
For an object in motion (i.e., dynamics conditions), the sum of the external
forces is equal to the mass of the object times its acceleration (i.e., Newton's second
law). To emphasize the importance of the kinematics in a dynamics problem, it is
essential to draw both the free body diagram and the kinetic diagram (sometimes
referred to as the Hibbeler diagram). The combination of a free-body diagram and
a kinetic diagram is a pictorial representation of Newton's second law. Then the
equations of motion associated with the object of interest are written directly us-
ing these diagrams by considering the appropriate components. Steps involved in
constructing a free body diagram and a kinetic diagram are as follows:
1. Identify and isolate the object or group of objects to focus on as the body.
2. Sketch the body “free” of its surroundings. The body could be represented
by a single point located at the body's center of mass.
3. Draw the magnitude and the direction of those forces acting directly on
the body.
4. Except for rotational problems, the forces can be sketched as though they
were acting through a single point at the center of mass of the body. It is
useful to draw the force vectors with their tails at the center of mass.
5. Do not include any forces that the body exerts on its surroundings; they do
not act on the body. However, there is always an equal reaction force
acting on the body.
6. For a compound body, do not include any internal forces acting between
the body's subparts, since these internal forces come in action-reaction
pairs that cancel each other out.
7. Choose a convenient coordinate system and sketch it on the free-body
diagram.
8. Place the mass times acceleration vector for that body on the kinetic diagram,
which is not for statics problems.
EXAMPLE 5.2
A physical therapist is applying cervical traction to a patient. The traction force is devel-
oped by the therapist leaning backwards while maintaining straight arms, and the system
is in static equilibrium. The therapist's height is 1.6m, the therapist's mass is 60 kg, and
the therapist's body proportions from the feet are as follows: the level of the glenohumeral
joint (~shoulder height)
=
85% of the total body height; the level of center of mass
=
59%
of the total body height; and the level of the hip joint
=
52% of the total body height. Find
the amount of traction force.
Solution: This problem is solved by setting up a moment equation about the heel.
Draw the free body diagram as shown in the figure.
