Fig. 2: The muscle-inspired EEM actuation mechanism.

a Schematic illustration of the EEM actuation system. (i) The system is composed of a magnetized hard magnet, an elastomeric structure, and an electrical coil intertwined with soft magnets. The variable \(x\) represents the actuation displacement and \({x}_{{{{\rm{limit}}}}}\) is the physical constrained position. (ii) The EEM system relies on a delicate balance between the magnetic attractive force, \({F}_{{{{\rm{e}}}}{{{\rm{m}}}}}\) and the elastic response, \({F}_{{{{\rm{e}}}}}\), with their force-displacement curves presented in the plot. The intersection represents the initial balance position (x₀), with the system capable of reaching a displacement limit (\({x}_{{{{\rm{limit}}}}}\)) at maximum force exertion. b Force-balance modulation by adjusting the electric current for actuation. Upon applying a current signal in the coil, the force–displacement curve of \({F}_{{{{\rm{em}}}}}\) alters upwards, resulting in the system to reach a new balance position. c Force-balance modulation via designing the elastomeric structure for customizing different actuation properties. (i)–(iii) The EEM actuation system can be customized to have one, two, or even three stable states within a compact design. The elastomeric structures and force-displacement relations are presented, with the purple dot indicating their stable states. (iv) and (v) Similarly, the EEM system can be tailored with either a smooth transition property or a step transition property. The system with a step transition can produce a large energy release for enhancing dynamic performance, such as enabling a jumping motion. (vi) The contraction ratio of the EEM system can be designed to reach 60%. Source data for c are provided as a Source Data file.