The study of the forces that bring about the movements discussed above is called kinetics. Because kinetics provides insights into the cause of the observed motion, it is essential to the proper interpretation of human movement processes. Forces and loads are not visually observable; they must be either measured with instrumentation or calculated from kinematics data. Kinetic quantities studied include such parameters as the forces produced by muscles; reaction loads between body parts as well as their interactions with external surfaces; the load transmitted through the joints; the power transferred between body segments; and the mechanical energy of body segments. Inherent to such studies are the functional demands imposed on the
body. The structure and stability of each extremity and its joints reflect different systems and functional demands. The functional demands on the upper extremity are quite different from those on either the upper and lower axial skeleton or those on the lower extremity. Depending on which joint and/or structure is addressed, different types and degrees of rotational motion are allowed and are functional. How much structural strength is needed versus how much movement is allowed in each area dictates the nature of the material, size, shape, and infrastructure of the joint system established to perform a given movement.
3.1 Equations of motion
The kinetics deal with the effects of forces on the motion of a body. When the motion is known, the problem is then to find the force system acting on the body. There are joint forces and joint moments. With all the kinematic quantities known, it is possible to find the joint forces and moments from the resulting force system that acts on each element. This is done by solving a system of simultaneous equations at successive time intervals. Since muscles are an unknown force system, the resolved muscle force and the real joint force are treated as totally unknown joint forces in the analysis. The three equations of motion for linear motions are
x F=ma
∑
∑
F=may∑
F=mazThe three equations of motion for rotation are
(
)
(
)
(
2 2)
(
)
x xx x yy zz y z xy y x z yz y z xx z x y M =I α − I −I ω ω −I α −ω ω −I ω −ω −I α ω ω+∑
(
)
(
)
(
2 2)
(
)
y yy y zz xx z x yz z y x xx z x xy x y z M =I α − I −I ω ω −I α ω ω− −I ω −ω −I α +ω ω∑
(
)
(
)
(
2 2)
(
)
z zz z xx yy x y zx x z y xy x y yz y z x M =I α − I −I ω ω −I α −ω ω −I ω −ω −I α +ω ω∑
where M is the moment, I is the mass moment of inertia, α the angular acceleration, and ω is the angular velocity. The moment equations can be simplified if the axes of the reference frames coincide with the principal axes, with the origin at the center of gravity. These equations, called Euler equations, are
(
)
x x x y z y z M =I α − I −I ω ω∑
(
)
y y y z x z x M =I α − I −I ω ω∑
(
)
z z z x y x y M =Iα − I −I ω ω∑
Continuity conditions are derived based on the fact that equal and opposite forces and moments occur at the joint between the two segments.
The anthropometric data for the mass, the center of gravity, the moment of inertia, and so on for the different parts of the human body are available in the literature (23, 24).
3.2 Motion and forces on diarthroidal joints
In vivo experimental measurements on the relative motions between articulating surfaces of a joint, which correspond to daily activities, are limited. Most quantitative information is obtained from gait studies that do not provide the accuracy and precision for the detailed information required for lubrication studies. However, even simple calculations show that translational speeds between two articulating surfaces can range from approximately 0.06 m/s between the femoral head surface and the acetabulum surface during normal walking, to approximately 0.6 m/s between the humeral head surface and the glenoid surface of the shoulder when a baseball pitcher throws a fastball. Cartilage to cartilage contact or fluid-film layers, or a mixture of both are normally the contact mechanisms at the joint. During a normal walking cycle, the human hip, knee, and ankle joints can be subjected to loads on the order of 6 times body weight, with these peak loads occurring just after heel-strike and just before toe-off. The average load on the joint is approximately 3 to 5 times body weight, which lasts as long as 60% of the walking cycle. During the swing phase of walking, only light loads are carried. During this phase, the articular surfaces move rapidly over each other. In addition, extremely high forces occur across the joints in the leg during jumping. Descending stairs can load the knee with up to 10 times body weight, suggesting that the load on the joint surface is dependent on the task performed, that is, the loading sites change drastically as the articulating surfaces move relative to each other.