Date of Award

Fall 2009

Document Type


Degree Name

Doctor of Philosophy in Mechanical Engineering - (Ph.D.)


Mechanical and Industrial Engineering

First Advisor

R. S. Sodhi

Second Advisor

Bernard Koplik

Third Advisor

Chao Zhu

Fourth Advisor

Zhiming Ji

Fifth Advisor

Kevin Russell


Adjustable mechanisms provide degrees of flexibility while retaining desirable features of one degree of freedom close-loop mechanisms, such as simplicity, stability, and high speed capabilities. By adjusting linkage parameters, additional phases of motions can be achieved using the same hardware. However, an adjustment to the mechanism adds only one or two additional design positions and divides desired positions into "phases", each of which contains only a few positions usually insufficient for industrial applications.

In order to extend the design position limitation of adjustable mechanisms, an optimal synthesis method based on link length structural error is developed and applied to kinematic synthesis of adjustable planar mechanisms in this research. Designed with this method, adjustable mechanisms can achieve phases of many design positions with a minimized error. The conveniently-calculated link length structural error effectively reflects the overall difference between generated and desired motions without directly comparing them; and its compact fourth-order polynomial form facilitates the gradient- based optimization process.

Link length structural error based optimal synthesis methods are developed for adjustable planar four-bar mechanisms for three typical synthesis tasks. For multi-phase approximate motion generation, standard optimization model is established based on adjustable optimal dyads considering all types of adjustments. For multi-phase continuous path generation, a proper driving dyad is firstly found by an optimization procedure using the full rotation requirement. The driven dyad is then found using the optimization technique for motion generation after calculating all coupler angles. For multi-phase function generation, the coupler length is chosen to carry the structural error and adjustments to the coupler and the side-link lengths are considered.

Numerical synthesis examples have demonstrated that the developed method is effective and efficient for multi-phase motion, path, and function generation of planar four-bar linkages with a large number of specified positions in each phase.