Document Type


Date of Degree

Fall 2009

Degree Name

PhD (Doctor of Philosophy)

Degree In

Mechanical Engineering

First Advisor

Jasbir S. Arora

Second Advisor

Karim Abdel-Malek

First Committee Member

Jasbir S Arora

Second Committee Member

Karim Abdel-Malek

Third Committee Member

Salam Rahmatalla

Fourth Committee Member

Jia Lu

Fifth Committee Member

Shaoping Xiao


Mathematical modeling of human running is a challenging problem from analytical and computational points of view. Purpose of the present research is to develop and study formulations and computational procedures for simulation of natural human running. The human skeletal structure is modeled as a mechanical system that includes link lengths, mass moments of inertia, joint torques, and external forces. The model has 55 degrees of freedom, 49 for revolute joints and 6 for global translation and rotation. Denavit-Hartenberg method is used for kinematics analysis and recursive Lagrangian formulation is used for the equations of motion. The dynamic stability is achieved by satisfying the zero moment point (ZMP) condition during the ground contact phase. B-spline interpolation is used for discretization of the joint angle profiles. The joint torque square, impulse at the foot strike, and yawing moment are included in the performance measure. A minimal set of constraints is imposed in the formulation of the problem to simulate natural running motion. Normal running with arm fixed, slow jog along curves, and running with upper body motion are formulated. Simulation results are obtained for various cases and discussed. The cases are running with different foot locations, running with backpack, and running with different running speeds. Also, extreme cases are performed. Each case gives reasonable cause and effect results. Furthermore, sparsity of the formulation is studied. The results obtained with the formulation are validated with the experimental data. The proposed formulation is robust and can predict natural motion of human running.


optimization, predictive dynamics, running


xvi, 221 pages


Includes bibliographical references (pages 216-221).


Copyright 2009 Hyun-Joon Chung