Multi-domain multi-objective optimization of mechanisms: a general method with two case studies

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Multi-domain multi-objective optimization of mechanisms: a general method with two case studies

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While the design of mechanisms is a well-studied field, current optimization techniques generally focus on the kinematics and dynamics and relegate other aspects of the analysis to separate stages of the overall design process, resulting in a loss of optimality when the entire multi-domain system is considered. This thesis presents a general method by which a mechanism optimization problem may be efficiently formulated and solved, considering multiple competing design objectives across multiple analysis domains. Two case studies illustrate the practical application of this general method. The first is the kinematic-structural optimization of a hydraulic rescue spreader ("jaws of life"). The second is the kinematic-dynamic-thermodynamic optimization of a novel six-bar linkage for an internal combustion engine. A variety of powerful general-purpose multi-objective algorithms are available from the literature. In particular, genetic algorithms are well-suited to multi-objective problems, and the NSGA-II algorithm from this category is employed here. Three strategies are presented to formulate multi-domain mechanism optimizations in a way that can be solved efficiently by a multi-objective genetic algorithm and is free of explicit constraint functions even for complex problems. First, it is shown that the use of non-traditional design variables, such as angles and adaptive interpolations, can result in smaller design spaces to be searched and can guarantee that all optima lie within the selected range of a given design variable. It is also shown that traditional precision-position synthesis techniques can in some cases be employed in a preliminary analysis to reduce the dimension of the design space. Finally, a nested optimization structure is proposed in which kinematic design variables and objectives are optimized in an outer loop, with the non-kinematic problem being optimized in an inner loop at every outer loop iteration, improving the efficiency and stability of the optimization process. These techniques were applied to the hydraulic rescue spreader problem in order to design a six-bar mechanism that could exert a 10,000 pound force through a pair of jaws over a 24 inch spreading distance while maintaining performance-critical kinematic behavior and remaining light and compact enough to be a handheld tool. The structural stresses in each part of the linkage were modeled, using a combination of analytical methods and finite element analysis. The final optimization result was superior to a similar commercially available model with respect to all four kinematic and structural objectives. Having successfully optimized a low-speed mechanism with a structural motivation, the method was also applied to a high-speed mechanism with a thermodynamic motivation. A Stephenson-III six-bar linkage was developed in order to optimize the motion of the piston in an internal combustion engine and achieve a cylinder volume as a function of time most conducive to efficient combustion. A number of mechanical objectives relating to balancing and mechanism size were used in order to find a solution capable of practical implementation. A slight increase in thermal efficiency over a purely sinusoidal piston motion was obtained, along with satisfactory values of the mechanical objectives.


University of Minnesota M.S. thesis. October 2013. Major:Mechanical Engineering. Advisor: James D. Van de Ven. 1 computer file (PDF); viii, 292 pages, appendices A-C.

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