36 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | FEBRUARY 2012 1556-603X/12/$31.00©2012IEEE Chiu-Hung Chen,Tung-Kuan Liu, and I-Ming Huang National Kaohsiung First University of Science and Technology, TAIWAN Jyh-Horng Chou National Kaohsiung First University of Science and Technology, TAIWAN and National Kaohsiung University of Applied Sciences, TAIWAN Abstract – The purpose of this paper is to develop a new approach to evolutionary synthesis for applications involved in the design of collision-free linkage mechanisms. We first analyze the kinematical position, velocity, and acceleration equations for mechanisms in question and utilize the inferred equations to formulate practical colli- sion-free requirements into geometrical constraints and convert manufacturing criteria into multiple objectives. In order to explore precise and widespread design solutions, we develop an improved version of the method of inequality-based multiobjective genetic algorithms (MMGA) by employing a Euclidean-distance-based diversity method, to serve as a global explorer. Several case studies are used to verify the correctness and effectiveness of the proposed approach, and the results have been successfully applied to the design of a commercial-use ladle mechanism, which has been hindered by obstacles from related peripheral equipment. I. Introduction collision-free requirement is a particular challenge in the design of planar link- age mechanisms, especially when the linkage synthesis needs to simultaneously meet various geometrical constraints and manufacturing criteria such as error- free positioning, collision-free movement, efficient performance, and low acceleration. For example, in metal-mold-die-casting systems (http://www.techbasecorp. com/), a six-bar ladle mechanism must be designed such that it takes over the job of colli- sion-free transferring. Many previous studies have investigated linkage synthesis problems, and various techniques have been developed to aid the design work. Among these, graphical and analytical methods are the best-known and most-studied techniques reported [1, 2]; however, they are limited to a finite Multiobjective Synthesis of Six-Bar Mechanisms Under Manufacturing and Collision-Free Constraints Digital Object Identifier 10.1109/MCI.2011.2176996 Date of publication: 17 January 2012 A