Compliant shell mechanisms utilize spatially curved thin-walled structures to transfer or transmit force, motion, or energy through elastic deformation. To design spatial mechanisms, designers need comprehensive nonlinear characterization methods, while the existing methods fall short of meaningful comparisons between rotational and translational degrees-of-freedom. This paper presents two approaches, both of which are based on the principle of virtual loads and potential energy, utilizing properties of screw theory, Plucker coordinates, and an eigen-decomposition. This leads to two unification lengths that can be used to compare and visualize all six degrees-of-freedom directions and magnitudes in a nonarbitrary, physically meaningful manner for mechanisms exhibiting geometrically nonlinear behavior.

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Compliant shell mechanisms utilize spatially curved thin-walled structures to transfer or transmit force, motion or energy through elastic deformation. To design with spatial mechanisms designers need comprehensive characterization methods, while existing methods fall short of meaningful comparisons between rotational and translational degrees of freedom. This paper presents two approaches, both of which are based on the principle of virtual loads and potential energy, utilizing properties of screw theory, Plücker coordinates and an eigen-decomposition, leading to two unification lengths that can be used to compare and visualize all six degrees of freedom directions and magnitudes of compliant mechanisms in a non-arbitrary physically meaningful manner.@en