Page 218 - Biomedical Engineering and Design Handbook Volume 1, Fundamentals

CHAPTER 8

BIODYNAMICS: A LAGRANGIAN

APPROACH

Donald R. Peterson
University of Connecticut School of Medicine, Farmington,
Connecticut
Ronald S. Adrezin
University of Hartford, West Hartford, Connecticut

8.1 MOTIVATION 195 8.5 INTRODUCTION TO THE KINEMATICS
8.2 THE SIGNIFICANCE OF DYNAMICS 197 TABLE METHOD 210
8.3 THE BIODYNAMIC SIGNIFICANCE OF 8.6 BRIEF DISCUSSION 218
THE EQUATIONS OF MOTION 198 8.7 IN CLOSING 219
8.4 THE LAGRANGIAN (AN ENERGY REFERENCES 219
METHOD) APPROACH 198

8.1 MOTIVATION

Athletic performance, work environment interaction, and medical sciences involving rehabilitation,
orthotics, prosthetics, and surgery rely heavily on the analysis of human performance. Analyzing
human motion allows for a better understanding of the anatomical and physiological processes
involved in performing a specific task, and is an essential tool for accurately modeling intrinsic and
extrinsic biodynamic behaviors (Peterson, 1999). Analytical dynamic models (equations of motion)
of human movement can assist the researcher in identifying key forces, movements, and movement
patterns to measure, providing a base or fundamental model from which an experimental approach
can be determined and the efficacy of initially obtained data can be evaluated. At times, the funda-
mental model may be all that is available if laboratory or field-based measurements prove to be costly
and impractical. Finally, it permits the engineer to alter various assumptions and/or constraints of the
problem and compare the respective solutions, ultimately gaining an overall appreciation for the
nature of the dynamic system.
As an example, consider the motion of an arm-forearm system illustrated in Fig. 8.1. The
corresponding equation of motion for the elbow joint (point C), or a two-link, multibody system
is given in Eq. (8.1).

Iθ + mgl cos θ + M Applied = M Elbow (8.1)

195