Continuum-based design of selectively compliant mechanisms taking into account large deformations

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Conventional mechanisms generate the deformations necessary to perform their task through relative motions of components sliding or rolling on each other. Compliant mechanisms, on the other hand, use elastic strain, which leads to many advantages. The complexity in the mathematical formulation that arises directly from the operating principle of compliant mechanisms has hindered progress in the field to date. In conventional mechanisms, there is a clear separation between functional (desired) and undesired deformations based on the underlying physical principle. In compliant mechanisms, both desired and undesired deformations are based on elastic strain and an option for mathematical modeling, which only considers the desired part, is not available. For this reason, the synthesis of compliant mechanisms turns out to be very complex.One possible way for synthesis are continuum-based synthesis methods. Here, the mechanism is modeled as an elastic continuum and the geometry of the mechanism is freely adjustable. Currently, there are numerous continuum-based synthesis approaches, but they have some central shortcomings. Most synthesis approaches are only suitable for relatively simple tasks, while complex tasks such as shape adaptation are rarely covered. Moreover, only a limited range of transverse loads is considered in these approaches.With the idea of making the eigenproperties of the mechanism the subject of the synthesis (modal procedure), the applicant proposed a promising way to address these two shortcomings. The central advantage of this idea is the possibility of a kinematic design, i.e. a design that does not refer to specific load cases. This is otherwise only possible for conventional mechanisms, as well as with certain methods for designing compliant mechanisms (pseudo-rigid body approach), for which, however, the choice of the geometry of the mechanism is severely limited.In the course of the previous project , a new approach was elaborated that made the already existing procedures more robust. In addition, the modal procedure was extended to the case of the synthesis of mechanisms with multiple pseudo-mobility. The pseudo-mobility defines the number of scalar parameters needed to identify a single desired deformation of a compliant mechanism and can be related to the mobility of conventional mechanisms. However, the validity of the developed approach has so far been limited to geometrically linear mechanisms. The present application aims to extend it to the geometrically nonlinear case. This extension will provide a powerful tool that allows for the synthesis of complex compliant mechanisms with large deformations.