Page 220 - Biomedical Engineering and Design Handbook Volume 1, Fundamentals

BIODYNAMICS: A LAGRANGIAN APPROACH 197

By solving for the moment created by the muscles at the elbow, an estimation of the effort
required during a forearm movement activity can be determined.
In order to yield estimates for each term within the equations of motion for a biodynamic system,
an experimental approach involving the simultaneous collection of information from several
modalities would be required. More specifically, systems such as optoelectronic motion capture
(to track anatomical positioning) and sensors such as accelerometers (to measure acceleration or
vibration), inclinometers (to measure displacement or position), load cells or force sensitive resistors
(to measure applied load or grip forces), and electrogoniometers (to measure anatomic angles)
should be considered. The selection of modalities, and their respective sensors, will depend upon the
nature of the terms given in the equations of motion. In addition, estimates of anthropometric quan-
tities involving mass, segment length, location of the center of mass, and the mass moment of inertia
of each body segment are also required. It should be understood that these modalities might be
costly to purchase and operate, and can generate large volumes of data that must be analyzed and
modeled properly in order to yield practical estimates for each desired term. The results for each
term can then be substituted into the equation of motion to model the dynamic behavior of the
system. This approach to modeling the biodynamics of the human musculoskeletal system has
proved to be extremely valuable for investigating human motion characteristics in settings of normal
biomechanical function and in settings of disease (Peterson, 1999).
This chapter presents a straightforward approach to developing dynamic analytical models of
multirigid body systems that are analogous to actual anatomic systems. These models can yield over-
all body motion and joint forces from estimated joint angles and applied loads, and even begin to
structure dynamic correlations such as those between body segment orientations and body segment
kinematics and/or kinetics. The applications of these equations to clinical or experimental scenarios
will vary tremendously. It is left to the reader to utilize this approach, with the strong suggestion of
reviewing the current literature to identify relevant correlations significant to their applications.
Listing and discussing correlations typically used would be extensive and beyond the scope of this
chapter.

8.2 THE SIGNIFICANCE OF DYNAMICS

The theory and applications of engineering mechanics is not strictly limited to nonliving systems.
The principles of statics and dynamics, the two fundamental components within the study of
engineering mechanics, can be applied to any biological system. They have proved to be equally
effective in yielding a relatively accurate model of the mechanical state of both intrinsic and extrinsic
biological structures (Peterson, 1999). In fact, nearly all of the dynamic phenomena observed within
living and nonliving systems can be modeled by using the principles of rigid body kinematics and
dynamics. Most machines and mechanisms involve multibody systems where coupled dynamics
exist between two or more rigid bodies. Mechanized manipulating devices, such as a robotic arma-
ture, are mechanically analogous to the human musculoskeletal system, which is an obvious multi-
body system. Consequently, the equations of motion governing the movement of the armature will
closely resemble the equations derived for the movement of an extremity (i.e., arm or leg).
Careful steps must be taken in structuring the theoretical approach, particularly in identifying the
initial assumptions required to solve the equations of motion. By varying any of the initial assump-
tions (and the justification for making them), the accuracy of the model is directly affected. For
example, modeling a human shoulder joint as a mechanical ball and socket neglects the shoulder’s
ability to translate and thus prohibits any terms describing lateral motion exhibited by the joint.
Therefore, any such assumption or constraint should be clearly defined on the basis of the desired
approach or theoretical starting point for describing the dynamics of the system. Elasticity is another
example of such a constraint, and is present to some degree within nearly all of the dynamics of a
biological system. Ideally, elasticity should not be avoided and will have direct implications on deter-
mining the resulting dynamic state of the system.