In this paper, we extend the principles of the freedom and constraint topologies (FACT) synthesis approach such that designers can analyze and synthesize serial flexure elements—not to be confused with serial flexure systems. Unlike serial systems, serial elements do not possess intermediate rigid bodies within their geometry and thus avoid the negative effects of unnecessary mass and underconstrained bodies that generate uncontrolled vibrations. Furthermore, in comparison with other common parallel flexure elements such as wire, blade, and living hinge flexures, serial elements can be used within flexure systems to achieve (i) a larger variety of kinematics, (ii) more dynamic and elastomechanic versatility, and (iii) greater ranges of motion. Here, we utilize the principles of FACT to intuitively guide designers in visualizing a multiplicity of serial flexure element geometries that can achieve any desired set of degrees of freedom (DOFs). Using this approach, designers can rapidly generate a host of new serial flexure elements for synthesizing advanced flexure systems. Thirty seven serial flexure elements are provided as examples, and three flexure systems that consist of some of these elements are synthesized as case studies.

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