The primary compliance vector (PCV) captures the dominant kinematic behavior of a compliant mechanism. Its trajectory describes large deformation mechanism behavior and can be integrated in an optimization objective in detailed compliant mechanism design. This paper presents a general framework for the optimization of the PCV path, the mechanism trajectory of lowest energy, using a unified stiffness characterization and piecewise curve representation. We present a meaningful objective formulation for the PCV path that evaluates path shape, location, orientation, and length independently and apply the framework to two design examples. The framework is useful for design of planar and shell compliant mechanisms that traverse a specified mechanism trajectory and that are insensitive to load perturbations.

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Compliant shell mechanisms utilize thin-walled structures to achieve motion and force generation. Shell mechanisms, because of their thin-walled nature and spatial geometry, are building blocks for spatial mechanism applications. In spatial compliant mechanism design, the ratio of compliance is the representation of the kinetostatics involved. Using shell mechanisms in concept design, however, can prove difficult without a uniform characterization method. In this article, we make use of compliance ellipsoids to achieve characterization of the ratio of compliance for shell mechanisms. Ten promising shells are presented with the kinetostatic characteristics, combined with a uniform method of determining the kinetostatic characteristics for other unknown shells. Finally, we show how shells are indeed a valid alternative in the spatial mechanism design, compared to conventional flexure mechanisms.

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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 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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The primary compliance vector captures the predominant kinematic degree of freedom of a mechanism. Its displacement describes large deformation mechanism behavior and can be an optimization objective in detailed compliant mechanism design. This paper presents a general framework for the optimization of the PCV path of compliant mechanisms using unified stiffness characterization, Fourier descriptors, and surrogate-based optimization. We found a meaningful objective formulation that evaluates PCV path shape independently. Furthermore, we reason that design variables should effect mechanism shape. Lastly, we apply the framework to a design example.@en

Spatial compliant mechanism are challenging to design owing to their complex spatial kinetic and kinematic behavior. There are many synthesis methods to design compliant mechanisms, but they are often presented for planar mechanisms or have other limitations such as lack of designer input possibilities. In this paper a method based on the compliance ellipsoid is presented to create compliant mechanism topologies for spatial design cases. The result of this synthesis method is a qualitative concept which fundamentally creates the desired kinetic and kinematic profile. This concept can then be further refined using a large deformation eigentwist analysis, presented here. Lastly, these tools are used in a design example to show its potential.

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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

In this paper a first iteration of a new scoliosis brace design and correction strategy is presented using compliant shell mechanisms to create both motion and correction. The motion profile of the human spine was found using a segmented motion capture approach. The brace was designed for a case study using a conceptual ellipsoid design approach. The force controlled correction profile was re-invented using a two fold zero and positive stiffness profile. These force generators were built and validated to prove their zero stiffness characteristic. The kinematic part of the brace was detail designed with the correct order of magnitude and validated through their force-deflection characteristic. The end result was a first iteration of a new brace validated and analysed on some critical components which can form the basis for a future biomechanical study.

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