Date of Award

Summer 1997

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical & Aerospace Engineering


Engineering Mechanics

Committee Director

Sebastian Bawab

Committee Member

Han Bao

Committee Member

Gene J.-W. Hou

Committee Member

Jen-Kuang Huang


Theory to rectify circuit defects in rocker-crank and double-rocker at the synthesis level is described based on the angular joint displacements. It complements the crank-rocker and double-crank circuit rectification to complete the circuit rectification of four-bar linkages. The procedure utilizes the algebraic method where special points followed by a line construction procedure are employed to validate the range of the critical angle that can identify the circuit defects as a function of the design positions prior to the completion of the linkage.

A complete procedure of the rectified synthesis of the coupler-driven Watt I six-bar linkage to pass through the pre-defined four design positions is presented. This is done by de-coupling the six-bar mechanism as a coupler-driven and crank-driven four-bar linkages with common links. The vector component mechanism modeling method is applied to these linkages where the dyad and triad synthesis approaches are adopted in conjunction with the vector-algebraic method to find the solutions. The linkage with the coupler-driver is initially synthesized and rectified, then followed by the crank-driven four-bar linkage. The six-bar linkage is thus insured to assemble free of circuit, branch, and order defects. Optimization techniques are used to render the best solution linkages according to the specified design criteria. The process is coded and added to a mechanism design platform--RECSYN that allows a designer to synthesize coupler-driven Watt I linkages and the new circuit rectification theory is also applied in the program.

A methodology to determine the optimum link length tolerance and joint clearance distributions in four-bar linkages for motion generation with specified structural error in order to manufacture the linkages is proposed. A stochastic model incorporated with tolerances and clearances for four-bar motion generation is proposed. The statistical characteristics of the random variables in the model are discussed. The mechanical error of four-bar motion generation as a function of statistical properties of random variables is defined. The tolerances and clearances are obtained as a result of solving an optimization problem with the objective function of link length tolerances and joint clearances and structural error as constraints. A FORTRAN code is written based on the proposed theory and ADS is employed as an optimization design tool. With this program, optimum link length tolerance and joint clearance distribution can be computed when the user input the required linkage information and structural errors. Examples of assigning tolerance and clearance for four-bar motion generation are presented to demonstrate the application of the method.