Because it is difficult to select in advance an appropriate linkage for converting an input motion to a desired output motion, a linkage synthesis method that does not require any baseline linkage would be preferred. To this end, an optimization-based linkage synthesis method that employs a spring-connected rigid block model has recently been suggested and applied for open-path problems. The objective of this study is to expand the method for the synthesis of more complex linkage mechanisms such as closed-loop linkages. Because the direct application of the method originally developed for open-path problems causes several numerical difficulties for closed-loop problems, an alternative optimization-based synthesis formulation is proposed in this investigation. The effectiveness of the suggested formulation is verified through several case studies including the synthesis of mechanisms generating closed paths.

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