Graduation Year


Document Type




Degree Name

MS in Mechanical Engineering (M.S.M.E.)

Degree Granting Department

Mechanical Engineering

Major Professor

Kyle B. Reed, Ph.D.

Committee Member

Rajiv Dubey, Ph.D.

Committee Member

Seok Hun Kim, Ph.D.


Gait Symmetry, Uncoupled Synchronization, Gait Modeling, Passive Dynamic Walkers, Nonlinear Systems


The ubiquitous nature of symmetry lends itself to be taken for granted, however the breath of research on symmetry encompasses several disciplines. In engineering, studies centered on symmetry often address issues in dynamic systems theory, robotics, and gait rehabilitation. This thesis presents findings on two specific topics dealing with passively induced symmetry; dissimilar rotating systems and human gait. Past studies on passive symmetry in dynamic systems often incorporate physical coupling or a controller. This thesis presents a technique to passively induce symmetry between two dissimilar systems that are not physically connected. This work also presents a human gait study consisting of several elements that merge to provide a unique look at how walking symmetry and altered physical parameters (leg length and added weight) of the lower limbs are related.

One aspect of this thesis shows the successful development of a general method to induce synchronization between any two dissimilar, uncoupled, rotating systems given the same degrees of freedom, initial angular dynamics, and applied torque. This method is validated with a simulation and subsequent comparison with two physical experiments. The results are in agreement, with slight variations due to the friction and damping of the physical systems. This is further expanded to include the induced symmetry of two systems that experience an external collision. Due to the highly non-linear nature of such systems, an analytical solution was not found; instead a numerical solution is presented that resulted in partial symmetry between systems.

The gait study demonstrated that weighted walking and altered leg length have both independent and combined spatio-temporal effects on lower limb symmetry. While altered leg length alone resulted in higher gait asymmetry, the combination of the two physical changes increases this asymmetry to affect the same limb. This study also showed that cognitive and physically distracted walking does not have an added effect to the gait symmetry with passive physical changes. In addition, this study was able to demonstrate that the arm swinging that occurs during natural walking does not significantly alter spatial or temporal gait parameters.