Microelectromechanical systems (MEMS) are usually fabricated using planar processing methods such as surface micromachining, bulk micromachining, or LIGA-type fabrication. If a micro mechanism is desired that has motion out of the plane of fabrication, it can be a folded mechanism in its fabricated position. The desire to design MEMS for a wide range of out-of-plane motions has led to the need for a better theoretical understanding of the design space for folded mechanisms. Thus, this paper derives the design space of arbitrary planar folded mechanisms. This results in the definition of the orientation set measures equality condition (OSMEC) which can be used in constructing adjacency set patches and joining them to construct the design space. The results can be used to explore different properties of the mechanisms in the design space. One such property, the mechanisms’ folded length, is given as an example. Although MEMS provide the primary motivation for the work, the results are general and apply to other areas of application.

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