Document Type


Date of Award

Fall 1-31-2012

Degree Name

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


Biomedical Engineering

First Advisor

H. Michael Lacker

Second Advisor

Mesut Sahin

Third Advisor

Richard A. Foulds


Lagrangian dynamics and the method of superfluous coordinates are applied to predict dynamic joint reaction forces in an idealized flexible model of a branched 3-D pendulum tree system. The number of segments and joints on the tree are adjustable as is the branching tree pattern. The segments that comprise the tree are assumed to be one- dimensional rigid rods containing a discrete set of mass points that is both flexible in number and distribution on the tree. The idealized 3-D pendulum tree system is intended to provide a flexible theoretical framework to model and better understand the dynamics of human and animal movement as well as the forces associated with those movements. In particular, this work focuses on predicting the dynamic reaction forces that are produced in the simple idealized frictionless joints of the pendulum system during motion. The ability to predict dynamic joint reaction forces in this model system could prove helpful in assessing the potential effect of a posited movement technique in producing joint injury and/or pain. This thesis extends the findings of previous work on similar pendulum model systems in 2-D to model systems in 3-D.



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