Date of Award

Summer 2007

Document Type


Degree Name

Master of Science in Biomedical Engineering - (M.S.)


Biomedical Engineering

First Advisor

H. Michael Lacker

Second Advisor

William Corson Hunter

Third Advisor

Richard A. Foulds

Fourth Advisor

Sergei Adamovich


Lagrangian dynamics and the method of superfluous coordinates are applied to find ground and joint reaction forces on the human body modeled as a general branched 2-D pendulum tree system with arbitrary segments and arbitrarily distributed point masses. A theoretical framework is established for predicting these constraint forces during human motion and consequently their effects on dynamics, dynamic stability, energy efficiency and the potential of these forces to produce joint injury and/or pain. Applications to human walking are initiated. During idealized phases where there is only single point contact of the stance leg with the ground such as just after heel-strike and just before toe-off, the ground reaction force is modeled as the constraint force on the root pivot joint of the tree. Treating the length of the root segment as a superfluous coordinate introduces a new degree of freedom into the equations of motion that can be used to predict human movements that occur during flight such as in jumping, running and diving. The approach of adding an explicit constraint to the pendulum tree system is used at those times when the foot or a portion of it is flat on the ground. Proof of concept for this approach is demonstrated by application to a single pendulum constrained to lie horizontally on the ground and to a double pendulum system with the same constraint imposed on its first (root) segment.