Compliant mechanisms are rapidly gaining importance, yet their design remains challenging. A great variety of methods are being developed as it is reported in a growing stream of publications. However, so far no review of this body of literature is available. This paper provides a comprehensive and conceptual overview of the main notions behind the most relevant design methods for compliant mechanisms. Rigid-Body-Replacement methods including the Pseudo-Rigid-Body model and the FACT approach are covered, as well as Building Block approaches. In addition an introduction and explanation on Topology Optimization and Shape Optimization is provided, including their most common parameterizations and formulations. This work aims to serve as an introduction into compliant mechanism design methods and as a reference work for more experienced scholars and professionals. It is intended to be a starting point for the exploration of the literature, as well as a guide to specific papers about a particular design problem one may have. For this reason, the paper presents the methods in a wide perspective, emphasizing the conceptual ideas behind every method and refers to literature for details and advanced features.

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