Journal Paper

Most real-world mechanical energy sources present significant dynamics in multiple degrees of freedom (DOF). As the performance of vibration-driven energy generators is highly anisotropic, and thus dependent not only on the time variation of the input mechanical excitation but also on its spatial orientation, a new era of multi-DOF generators has recently emerged to harvest energy from 6 DOF excitations. Up to date, literature reviews
analyzing the conversion of mechanical energy from vibrational sources into electrical energy using electromagnetic, triboelectric and piezoelectric generators, have not addressed multi-DOF generators and their intrinsic characteristics. Instead, they have been focused on linear and/or rotational architectures, optimized only for unidirectional vibrations. Besides, a generalized modelling approach to effectively deal with the dynamic complexity of multi-DOF generators is still lacking. This study provides a multifaceted investigation that includes a review of the major breakthroughs carried out in the scope of multi-DOF generators, and the development of a generalized dynamic modelling approach based on Lagrangian mechanics. Thorough analyses were performed encompassing several design configurations, modelling approaches, electric outcomes, and real-world applications of 35 designs of multi-DOF generators incorporating electromagnetic and triboelectric and/or piezoelectric transduction mechanisms. Both electromagnetic and hybrid generators were already engineered comprising up to fourteen rigid free bodies and twenty-four DOFs. Three modelling approaches were used to predict the electromechanical dynamics of generators: analytical, finite element, and related hybridizations. However, the complexity of the electromechanical dynamics increases significantly with the number of internal DOFs, and thus no models reach a confidence level allowing their use to accurately predict the electromechanical behavior of generators under multidimensional excitations. A generalized model is proposed from first principles, which encompasses the balance of mass, linear momentum, angular momentum, and energy and a description of magnet-magnet potential energies and magnet-coil magnetic fluxes as a function of the DOFs between bodies.