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Compliant mechanisms are widely used in technical applications, especially in robotics, precision engineering, measurement and medical technology. Their deformation behavior is signifcantly infuenced 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 infuence 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 defne when to consider which efects, depending on the geometry. Based on these investigations, recommendations are given for the theory to be used. By formulating the equations in a unifed 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 threedimensional application cases using the fnite element method and experimental investigations. Thereby, the recommendations for the suitable theory are included. Subsequently, algorithms for dimensioning individual fexure hinges and compliant mechanisms are given. This allows for improved motion behavior with respect to specifc 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 fexure hinges and compliant mechanisms. [ABSTRACT FROM AUTHOR]