Universal Custom Complex Magnetic Spring Design Methodology

A design methodology is presented for creating custom complex magnetic springs through the design of force-displacement curves. This methodology results in a magnet configuration, which will produce a desired force-displacement relationship. Initially, the problem is formulated and solved as a system of linear equations. Then, given the limited likelihood of a single solution being feasibly manufactured, key parameters of the solution are extracted and varied to create a family of solutions. Finally, these solutions are refined using numerical optimization. Given the properties of magnets, this methodology can create any well-defined function of force versus displacement and is model-independent. To demonstrate this flexibility, a number of example magnetic springs are designed; one of which, designed for use in a jumping-gliding robot's shape memory alloy actuated clutch, is manufactured and experimentally characterized. Due to the scaling of magnetic forces, the displacement region which these magnetic springs are most applicable is that of millimeters and below. However, this region is well situated for miniature robots and smart material actuators, where a tailored magnetic spring, designed to compliment a component, can enhance its performance while adding new functionality. The methodology is also expendable to variable interactions and multi-dimensional magnetic field design.