Graduation Year


Document Type




Degree Name

Doctor of Philosophy (Ph.D.)


Mechanical Engineering

Degree Granting Department

Mechanical Engineering

Major Professor

Craig P. Lusk, Ph.D.

Committee Member

Fernando Burgos, Ph.D.

Committee Member

Nathan Crane, Ph.D.

Committee Member

Delcie Durham, Ph.D.

Committee Member

Jing Wang, Ph.D.


Axisymmetric deflections, Cantilever beams, Kinematics, Large-deflections, Three-dimensional deflections


The objective of the dissertation is to develop and describe kinematic models (Pseudo-Rigid-Body Models) for approximating large-deflection of spatial (3D) cantilever beams that undergo multiple bending motions thru end-moment loading. Those models enable efficient design of compliant mechanisms, because they simply and accurately represent the bending and stiffness of compliant beams.

To accomplish this goal, the approach can be divided into three stages: development of the governing equations of a flexible cantilever beam, development of a PRBM for axisymmetric cantilever beams and the development of spatial PRBMs for rectangular cross-section beam with multiple end moments.

The governing equations of a cantilever beam that undergoes large deflection due to force and moment loading, contains the curvature, location and rotation of the beam. The results where validated with Ansys, which showed to have a Pearson's correlation factor higher than 0.91.

The resulting deflections, curvatures and angles were used to develop a spatial pseudo-rigid-body model for the cantilever beam. The spatial pseudo-rigid-body model consists of two links connected thru a spherical joint. For an axisymmetric beam, the PRB parameters are comparable with existing planar PRBMs. For the rectangular PRBM, the parameters depend on the aspect ratio of the beam (the ratio of the beam width over the height of the cross-section). Tables with the parameters as a function of the aspect ratio are included in this work.