Lubrication of Joints - Biofluidmechanics: An Introduction to Fluid Mechanics Macrocirculation and Microcirculation - page 303

traditional engineering statics, dynamics, or solid mechanics course sequence. To start this
discussion, we will first restrict ourselves to the standard statics/dynamics assumption
that there are no changes in the orientation of the molecules within the joint (i.e., there are
no deformations that alter that chemical bonding arrangement). When this assumption is
made, the governing equations become

X -

5 m -

ð 11 : 4 Þ

and:

X -

-

Þ
where - is the forces acting on a body, m is the mass of the body, - is the acceleration of
the body, - is the moments acting on a body, I is the mass moment of inertia of the body,
and

5 I α

ð :

11 5

- is the angular acceleration of the body (remember that the moments and the mass
moment of inertia were typically calculated about the bodies center of mass). If you recall
your course in statics, - and

α

- were always assumed to be zero, allowing you to simplify
Equations 11.4 and 11.5 to the summation of the forces is equal to zero and the summation
of the moments is equal to zero, respectively. In dynamics, we generally include the accel-
eration (both linear and angular) of the body. Recall from either class that these equations
could be broken up into component form (Cartesian directions). Using Equations 11.4 and
11.5 , one can calculate the forces required to maintain a joint in place during normal physi-
cal activities.

α

Example
Calculate the force on the shoulder joint for an athlete who is holding a weight with the arm
perfectly horizontal (see Figure 11.3 ). To calculate the reaction forces within the shoulder joint,
consider that the weight of the arm is equal to 10 lbf and is located at a distance 1 ft from the
shoulder joint. The weight that the athlete is holding is equal to 40 lbf, and it is held at a distance
of 2.1 ft from the shoulder joint. To simplify the problem, let us consider that the deltoid muscle
is the primary muscle holding the arm in place and that it attaches to the humerus at a distance
of 0.45 ft from the shoulder joint at an angle of 17 .

Solution
First, let us draw a free-body diagram of the arm.
In Figure 11.4 ,W A is the weight of the arm, W is the weight that is being held, F D is the force
of the deltoid muscle, and F S is the force exerted by the shoulder joint.

FIGURE 11.3

Diagram of a shoulder joint for the
in-text example. Adapted from Ozkaya and Nordin
(1999).