Realizing nonlinear springs through noncircular planetary gears

•Noncircular planetary gear trains can implement compact nonlinear springs.•Planetary motion is adopted to save space and realize rotational range scaling.•A solution for noncircular pitch lines is formulated as an optimization problem.•Prescribed nonlinear torque-angle curves are obtained and experimentally verified. Nonlinear springs are beneficial for various mechanisms because of their tailored load-displacement relationships. These can be achieved by utilizing variable transmission ratio mechanisms, such as linkages, convex cams and noncircular gears, to adjust a linear spring’s load-displacement curve to be nonlinear. However, obtaining a target nonlinear feature that has a simple structure and compact space remains a significant challenge. This study develops a set of noncircular planetary gears consisting of an external pair and an internal pair with variable pitch lines, to realize a specific variable transmission ratio mechanism. The pitch lines were formulated as an optimization problem and solved with a sequential quadratic programming algorithm. The experimental results confirm that the proposed mechanism is capable of realizing targeted nonlinear curves to meet a specified design purpose. Moreover, the proposed method fully utilizes the compact and simple structure of planetary gears, meaning it has strong potential in practical applications.