Spring based on flat permanent magnets: design, analysis and use in variable stiffness actuator

Modern robot applications benefit from including variable stiffness actuators (VSA) in the kinematic chain. In this paper, we focus on VSA utilizing a magnetic spring made of two coaxial rings divided into alternately magnetized sections. The torque generated between the rings is opposite to the angular deflection from equilibrium and its value increases as the deflection grows - within a specific range of angles that we call a stable range. Beyond the stable range, the spring exhibits negative stiffness what causes problems with prediction and control. In order to avoid it, it is convenient to operate within a narrower range of angles that we call a safe range. The magnetic springs proposed so far utilize few pairs of arc magnets, and their safe ranges are significantly smaller than the stable ones. In order to broaden the safe range, we propose a different design of the magnetic spring, which is composed of flat magnets, as well as a new arrangement of VSA (called ATTRACTOR) utilizing the proposed spring. Correctness and usability of the concept are verified in FEM analyses and experiments performed on constructed VSA, which led to formulating models of the magnetic spring. The results show that choosing flat magnets over arc ones enables shaping spring characteristics in a way that broadens the safe range. An additional benefit is lowered cost, and the main disadvantage is a reduced maximal torque that the spring is capable of transmitting. The whole VSA can be perceived as promising construction for further development, miniaturization and possible application in modern robotic mechanisms.