Modellbasierte Entwicklung von Methoden, Algorithmen und Werkzeugen zur Analyse und Synthese nachgiebiger Mechanismen

Nachgiebige Mechanismen (NM) sind in technischen Anwendungen aufgrund ihrer Vorteile weit verbreitet. Die Berechnung des Verformungsverhaltens unter dem Einfluss äußerer Belastungen stellt aufgrund von geometrischer Nichtlinearität eine anspruchsvolle Aufgabe dar. Mit Hilfe der in dieser Arbeit beschriebenen Modellgleichungen auf Basis der nichtlinearen Balkentheorie können ebene und räumliche NM sekundenschnell numerisch berechnet werden. Dazu werden über reine Biegung hinaus, Querkraftschub und Querkontraktion im Modell berücksichtigt und Empfehlungen für die zu verwendende Theorie abgeleitet. Zudem werden Algorithmen zur Dimensionierung von NM gegeben, mit Hilfe derer die Verformungseigenschaften im Hinblick auf konkrete Zielkriterien verbessert werden können. Abschließend werden die Methoden in drei eigenständig ausführbare und frei zugängliche Softwarewerkzeuge implementiert. Durch deren Entwicklung wird ein Beitrag zum Entwurf sowie zur Analyse und Synthese von NM geleistet.

Compliant mechanisms are widely used in technical applications, especially in robotics, precision engineering, measurement and medical technology. Their deformation behavior is significantly influenced by the design of selected compliant sections, for example by systematically reducing cross-sectional dimensions. Movement of the mechanism is predominantly achieved by bending these sections. Due to geometric nonlinearity, calculating the deformation behavior under the influence of external loads is a challenging task in analyzing and synthesizing compliant mechanisms. Therefore, this work contributes to the analytical modelling and, consequently, to the analysis and synthesis process. A set of model equations is given for plane and spatial use cases. They can be used to characterize compliant mechanisms with varying cross sections, curvatures, materials, and branching points. Since we are considering arbitrary mechanisms, the equations are given in a recursive form. Due to structures of varying cross sections, shear and lateral contraction are also considered in the model in addition to pure bending. Investigations are carried out to define when to consider which effects, depending on the geometry. Based on these investigations, recommendations are given for the theory to be used.  By formulating the equations in a unified form, it is possible to customize the theory for individual sections of a compliant mechanism. Furthermore, the model is validated by example mechanisms for two- and three-dimensional application cases using the finite element method and experimental investigations. Thereby, the recommendations for the suitable theory are included. Subsequently, algorithms for dimensioning individual flexure hinges and compliant mechanisms are given. This allows for improved motion behavior with respect to specific objectives. Finally, the methods are implemented in three stand-alone executable software tools that are freely available. Through their development, a contribution is made to the design as well as the analysis and synthesis of flexure hinges and compliant mechanisms.

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