Large-stroke flexure mechanisms inherently lose stiffness in supporting directions when deflected. A systematic approach to synthesize such hinges is currently lacking. In this paper, a new building block-based spatial topology synthesis method is presented for optimizing large-stroke flexure hinges. This method consists of a layout variation strategy based on a building block approach combined with a shape optimization to obtain the optimal design tuned for a specific application. A derivative-free shape optimization method is adapted to include multiple system boundaries and constraints to optimize high complexity flexure mechanisms in a broad solution space. To obtain the optimal layout, three predefined three-dimensional (3D) “building blocks” are proposed, which are consecutively combined to find the best layout with respect to specific design criteria. More specifically, this new method is used to optimize a flexure hinge aimed at maximizing the frequency of the first unwanted vibration mode. The optimized topology shows an increase in frequency of a factor ten with respect to the customary three flexure cross hinge (TFCH), which represents a huge improvement in performance. The numerically predicted natural frequencies and mode shapes have been verified experimentally.
Flexure hinges inherently lose stiffness in supporting directions when deflected. In this paper a method is presented for optimizing the geometry of flexure hinges, which aims at maximizing supporting stiffnesses. In addition, the new ∞-flexure hinge design is presented. The considered hinges are subjected to a load and deflected an angle of up to ±20 deg. The measure of performance is defined by the first unwanted natural frequency, which is closely related to the supporting stiffnesses. During the optimization, constraints are applied to the actuation moment and the maximum occurring stress. Evaluations of a curved hinge flexure, cross revolute hinge, butterfly flexure hinge, two cross flexure hinge types, and the new ∞-flexure hinge are presented. Each of these hinge types is described by a parameterized geometric model. A flexible multibody modeling approach is used for efficient modeling while it accounts for the nonlinear geometric behavior of the stiffnesses. The numerical efficiency of this model is very beneficial for the design optimization. The obtained optimal hinge designs are validated with a finite element model and show good agreement. The optimizations show that a significant increase in supporting stiffness, with respect to the conventional cross flexure hinge, can be achieved with the ∞-flexure hinge.
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