Degree Type


Date of Award


Degree Name

Doctor of Philosophy


Mechanical Engineering

First Advisor

D. R. Flugrad, Jr.

Second Advisor

J. E. Bernard


In the synthesis of high-speed cam profiles, we must compensate for the elastic deflections induced by large inertial effects generated during operation. Thus, differential equations with kinematic constraints need to be solved. The governing dynamic equations are in homogeneous, periodic, linear, ordinary differential equations which possess multiple unstable and high vibrational regions at various operating speed zones. These regions are found to be intrinsically determined by the changing geometry of the follower linkage during operation;This dissertation considers two types of cam driven linkages. Parts I and II consider a cam driving a lumped inertia through a massless elastic slider-crank follower linkage with concentrated masses located at two of the joints. The output shaft and the links are subject to torsional and axial deflection, respectively. Part III considers a cam driving a lumped mass through an elastic slider-crank follower linkage with a curved beam coupler. The coupler is modeled using finite element techniques, and the output shaft is subject to torsion only;In both Parts I and III an iterative procedure, taking the elasticity, damping, and changing geometry of the linkage into account, is developed for synthesizing the cam profile to produce a desired output motion at a given design speed. The response improves as iteration proceeds. The number of iteration is limited by the numerical truncation because the value of a parameter decreases at each iteration. The iterative procedure lowers all the high amplitude vibrations in Part I and some of the high amplitude vibrations in Part III;In Part II the location of a single dominant pair of complex characteristic multipliers on the complex plane is used to explain the formation of high amplitude vibrations at certain speeds. These multipliers, which are eigenvalues of the discrete transition matrix for a complete cycle of operation, also predict the effects of inaccurate damping ratio estimates;For either type of linkage considered, design speeds should not be chosen close to the intrinsically high vibration speeds which can be found through simulation of the initial trial design.



Digital Repository @ Iowa State University,

Copyright Owner

Hsin-Ting Jonathan Liu



Proquest ID


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File Size

187 pages