Graduation Year


Document Type




Degree Name

Doctor of Philosophy (Ph.D.)

Degree Granting Department

Mechanical Engineering

Major Professor

Craig Lusk, Ph.D.

Co-Major Professor

Alex Volinsky, Ph.D.

Committee Member

Yu Sun, Ph.D.

Committee Member

Kyle Reed, Ph.D.

Committee Member

Mark Weston, M.Arch.


Compliant Mechanisms, Heavy Beams, Kinematics, Large Deflections, Phase Space


This dissertation describes the development and effectiveness of a mathematical model used to predict the behavior of cantilever beams whose loading conditions include parallel combinations of evenly distributed loads and endpoint forces. The large deflection of cantilever beams has been widely studied. A number of models and mathematical techniques have been utilized in predicting the endpoint path coordinates and load-deflection relationships of such beams. The Pseudo-Rigid-Body Model (PRBM) is one such method which replaces the elastic beam with rigid links of a parameterized pivot location and torsional spring stiffness. In this paper, the PRBM method is extended to include cases of a constant distributed load combined with a parallel endpoint force. The phase space of the governing differential equations is used to store information relevant to the characterization of the PRBM parameters. Correction factors are also given to decrease the error in the load-deflection relationship and extend the angular range of the model, thereby further aiding compliant mechanism design. The calculations suggest a simple way of representing the effective torque caused by a distributed load in a PRBM as a function of easily calculated model parameters.