Generalized model of mechanical motion rectifiers

Abstract

This study introduces a new dynamical model for single-input single-output (SISO) mechanical motion rectifiers (MMRs), utilized in various applications such as wave energy converters, energy harvesting devices, and continuously variable transmissions. Existing models have limitations that affect their accuracy in representing the system’s dynamical response and restrict the applicability of control strategies. These limitations are addressed by introducing rigorous velocity and torque constraints to derive a novel disengagement condition, four new coupling modes, and the unidirectional power transmission constraint. These features are integrated into a concise set of generalized motion equations capable of handling arbitrary output torques. The resulting model provides a more precise dynamical description and serves as a unified modeling approach for SISO MMR-based devices. Leveraging its distinctive features, a comprehensive friction model for MMRs is obtained, and a simple method to activate the introduced coupling modes by controlling the output torque is provided. An algorithm to numerically implement the model is presented. The model’s capabilities are verified through numerical simulation and experimentally validated using an MMR prototype, demonstrating its accuracy in replicating the system’s nonlinear dynamical response.