Modeling, analysis, and optimization of mechanical tolerances in design and manufacturing using fuzzy and interval methods

Date of Award




Degree Name

Doctor of Philosophy (Ph.D.)


Mechanical Engineering

First Committee Member

Singiresu S. Rao, Committee Chair


By applying the fuzzy and interval methods into the area of mechanical tolerance analysis, a new system of mechanical tolerance modeling method have been developed. The mathematical modeling deals with each case of mechanical tolerances, such as modeling of location tolerances and modeling of form, orientation and runout tolerances. Fuzzy and interval methods have also been used to analyze the mechanism tolerances, i.e., analysis of mechanical tolerances of a four-bar mechanism, a one-way clutch, and a remote positioner. At last, interval methods are employed in the optimal tolerance allocation of four-bar mechanisms, the one-way clutch assembly, the SCARA manipulator and the Stanford manipulator problem.The dissertation consists of four major parts: Part I Mathematical Modeling of Mechanical Tolerances; Part II Analysis of Mechanical Tolerances; Part III Optimization of Mechanical Tolerances; Part IV Conclusions and Future Work.Part I is made up of three chapters. Chapter 1 is an introduction to the fuzzy and interval methods; Chapters 2 and 3 are devoted to the mathematical modeling of mechanical tolerances. New mathematical modeling methods based on interval analysis are proposed for various kinds of mechanical tolerance, such as tolerances of location, tolerances of form, orientation, and runout. Detailed steps of application of the models are provided with practical applications in design and manufacturing.Part II is the analysis of mechanical tolerances which includes Chapter 4 and 5. Chapter 4 deals with the tolerance analysis of four-bar mechanism and the one-way clutch assembly; Chapter 5 concerns with the tolerance analysis of the remote positioner problem.Part III deals with the optimization of mechanical tolerances. Part III consists of two Chapters: Chapter 6 and Chapter 7. Chapter 6 studies the optimal tolerance allocation of four-bar mechanisms and the one-way clutch assembly; Chapter 7 presents the optimal tolerance allocation of robot joints. The SCARA manipulator and the Stanford manipulator are used as illustrative examples to minimize positional and orientation errors of the robot. In the SCARA manipulator example, total cost is modeled as the objective function. The positional and orientational errors of the SCARA manipulator are regarded as design constraints. In the Stanford manipulator example, the sum of squares of positional errors is regarded as the objective function that needs to be minimized. The effects of the upper bounds on the orientation error and the cost-tolerance constraints on the optimization results are thoroughly investigated.Part IV presents the conclusions and the future work in Chapter 8. It provides conclusions of this work, and also points out some limitations of the methods presented in this work that allow scope for further improvement.


Engineering, Mechanical

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