Topology optimization of beam-based flexural pivots with arbitrary centers of rotation

Abstract In self-reconfigurable structures, the mechanical design of the joints is one of the most challenging tasks. Within this context, flexural pivots are widely adopted as compliant mechanisms due to their ideal design for achieving low rotational stiffness and high off-axis stiffness. To maximize performance, they are often optimized for specific application requirements. However, designing flexural pivots for self-reconfigurable structures with an arbitrary center of rotation remains a significant challenge. To address this, we propose an approach for optimizing the topology of beam-based flexural pivots undergoing large deflections, aiming to achieve an optimal configuration with an arbitrary center of rotation. To this end, both the stiffness-based objective function and the strain energy-based objective function are introduced. For the implementation, a geometrically exact beam element is utilized to establish a dual-layer ground structure for optimization. A genetic algorithm is employed to identify optimal configurations for flexural pivots, including traditional notch hinges and cross-spring pivots. Additionally, the influence of different objective functions and their corresponding parameters on the optimized topology is examined and verified. Ultimately, this approach yields optimal topologies in three representative examples with different centers of rotation, establishing a foundation for the design of compliant mechanisms with user-defined rotational behavior.