Impedance matching in an elastic actuator

We optimize the performance of an elastic actuator consisting of an active core in a host which performs mechanical work on a load. The system, initially with localized elastic energy in the active component, relaxes and distributes energy to the rest of the system. Using the linearized Mooney-Rivlin hyperelastic model in a cylindrical geometry and assuming viscous relaxation, we show that the value of Young's modulus of the impedance matching host which maximizes the energy transfer from the active component to the load is the geometric mean of Young's moduli of the active component and the elastic load. This is similar to the classic results for impedance matching for maximizing the transmittance of light propagating through dielectric media. We consider energy transfer from an elastic actuator to an elastic load, and show that the energy transfer can be optimized by tuning Young's modulus of the impedance matching host material.