Page 242 - Biomedical Engineering and Design Handbook Volume 1, Fundamentals

BIODYNAMICS: A LAGRANGIAN APPROACH 219

8.7 IN CLOSING

This chapter is presented as an introduction to the use of the Lagrangian approach to biodynamically
model human mechanics. Several important aspects of dynamics are briefly introduced and discussed,
and may require a review of the literature for more detailed explanations and additional examples.
Assumptions were made within each example to simplify the solution and provide a clear presentation
of the material.
Further applications may consider dynamic systems that involve adding two or more viscoelastic
or elastic bodies to the single-body pendulum examples. As a result, solutions defining the
dynamic behavior of a multisegment pendulum problem would be determined. Combinations of
viscoelastic and elastic segments may also be linked together, but may add to the complexity of the
solutions because of the elasticity variations between segments. Other applications may include various
combinations of spring and dashpot systems, such as a Maxwell model or a Kelvin body, to further
study the effects of viscoelasticity on a dynamic system.
The multisegment extremity model demonstrated the ability to subsequently add segments to a
base model and determine the equations of motion with each addition. These models were derived
with the assumption that the links between segments were revolute joints. Further modifications of
this example may involve combinations of revolute and ball-and-socket joints to more accurately
model an actual biodynamic system. The final example (Tables 8.5, 8.6, 8.7, and 8.8) begins to solve
a system that assumes all links to be of a ball-and-socket type. If one those links is assumed to be a
revolute joint (e.g., point C, the elbow), then the appropriate angles ψ and angular velocities ψ for
the adjoining segments would be negligible on the basis of the constraints of a revolute joint.

REFERENCES

Allard, P., Cappozzo, A., Lundberg, A., and Vaughan, C. L., Three-dimensional Analysis of Human Locomotion,
John Wiley and Sons, New York, 1997.
Baruh, H., Analytical Dynamics, McGraw-Hill, New York, 1999.
Benaroya, H., Mechanical Vibration: Analysis, Uncertainties, and Control, Prentice Hall, Englewood Cliffs,
N. J., 1998.
Harrison, H. R., and Nettleton, T., Advanced Engineering Dynamics, John Wiley and Sons, New York, 1997.
Lanczos, C., The Variational Principles of Mechanics, Dover, New York, 1970.
Meirovitch, L., Methods of Analytical Dynamics, McGraw-Hill, New York, 1970.
Moon, F. C., Applied Dynamics with Applications to Multibody and Mechatronic Systems, John Wiley and Sons,
New York, 1998.
Peterson, D. R., “A Method for Quantifying the Biodynamics of Abnormal Distal Upper Extremity Function:
Application to Computer Keyboard Typing,” Ph.D. Dissertation, University of Connecticut, 1999.
Wells, D. A., Theory and Problems of Lagrangian Dynamics, McGraw-Hill, New York, 1967.