Harnessing noncircular gears to achieve nonlinear passive springs

Abstract

Developing passive springs with prescribed nonlinear load-displacement features plays a crucial role in broad application areas, such as creating nonlinear energy sinks and unfolding mesh antennas. Although a few solutions, like compliant mechanisms, have been implemented to obtain nonlinear springs, the proposed new methodology can complement the existing methods in different applications. This study combines noncircular gears with a commercially available torsion spring to achieve targeted nonlinear load-displacement curves. In this design, the torsion spring stores elastic energy and multiple pairs of basic conjugate noncircular gears are used to construct a variable transmission ratio system. By adjusting the pitch lines of the basic pair, the transmission ratio can be tuned to output a prescribed load-displacement curve. The design of the pitch lines was formulated as an optimization problem and solved via the sequential quadratic programming algorithm. Experiments confirmed that exploiting noncircular gears can enable extraordinary nonlinear load-displacement, such as a U-shaped curve. The proposed approach, which is proven to be efficient and versatile, is now ready to be applied in real scenarios.