In this paper we introduce the principles necessary to analyze and design serial flexure elements, which may be used to synthesize advanced compliant mechanisms (CMs). The most commonly used flexure elements (e.g., wire, blade, or living hinge flexures) are often parallel and thus impose constraining forces directly through all parts of their geometry to the rigid bodies that they join within the CM. Serial flexure elements, on the other hand, constrain rigid bodies with a larger variety of forces and moments and thus enable CMs to achieve (i) more degrees of freedom (DOFs), (ii) larger dynamic and elastomechanic versatility, and (iii) greater ranges of motion than parallel elements. In this paper, we extend the principles of the Freedom and Constraint Topologies (FACT) synthesis approach such that it enables the synthesis of CMs that are not only constrained by parallel flexure elements, but also by serial elements. FACT utilizes geometric shapes to intuitively guide designers in visualizing compliant element geometries that achieve any desired set of DOFs. In this way, designers can rapidly generate a host of new serial flexure elements for various CM applications. Such elements are provided here as case studies.

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