A-posteriori adjustment of the stiffness of compliant mechanisms considering geometrical nonlinearities

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Compliant mechanisms use elastic strains in the material to generate the deformations necessary for their task. This differentiates them from conventional mechanisms, which are, based, instead, on finite relative movement of sliding or rolling interfaces. In contrast to its conventional alternative, a compliant mechanism requires a defined amount of mechanical work to generate functional deformations, which is stored as strain energy in the elastically deformed, compliant areas of the mechanism. This implies that the compliant mechanism produces restoring forces, which are undesirable for certain applications. This proposal deals with modifying the stiffness of flexible mechanisms (and thus their tendency to produce restoring forces) through the targeted use of preload forces. This is a follow-up application to the project "A posteriori adjustment of the stiffness of compliant mechanisms“. Three limitations of the method that was developed in the previous project are to be removed by the follow-up project: a) the method is restricted to linear behavior. b) the optimization formulation leads to a simplified solution; However, it is unfavorable for use in practical cases, since it may provide optimal solutions with a large number of preload forces. c) the method only deals with preload forces that remain constant even when the mechanism is loaded by external forces. This is also quite unrealistic. If the preload is implemented using passive elements, the possibility of changing the preload force with the load on the mechanism (with a linear, progressive or degressive characteristic) must be taken into account. The work program consists of four main work packages (HAP), which, in turn, are subdivided into work packages (AP). First, an appropriately parameterized analysis module, capable of calculating flexible mechanisms with distributed compliance, idealized as beam trusses, under consideration of large deformations is provided as first step of the HAP 1. Further steps progressively update the analysis module with the properties necessary for the purposes of the project, such as a modal projection to reduce the kinematics to one kinematic degree of freedom (ideally selective behavior), the introduction of a scalar coordinate to label the single deformations (deformation coordinate) and the option of integrating preload elements with a general quadratic characteristic. After that, the method from the previous project is gradually adapted to the geometrically non-linear case. The project is completed by the investigation of discrete optimization methods, a plausibility analysis of the assumption of ideally selective behavior, an analysis of the non-linear character and the realization and testing of a demonstrator.