Modeling of a nonlinear coupled compliant mechanism via developed kinematics-integrated neural network algorithm

Abstract

A precise motion control for compliant mechanisms hinges on an accurate kinematics model, particularly when dealing with intricate nonlinear coupled mechanisms. The motivation driving this research lies in leveraging existing knowledge to direct traditional neural networks (NN) in acquiring a nonlinear kinematics model (grey box), even with a limited dataset. Within this study, the 3-RRR (Revolute-Revolute-Revolute) flexure mechanism was selected due to its inherent nonlinear multi-input multi-output (MIMO) configuration. In relation to this type of flexure mechanism, the convolutional modeling approach based on compliance matrix theory aptly captures the relationship between inputs and outputs. Nonetheless, its linearity poses challenges in achieving utmost precision. In contrast, the NN modeling technique (black box) excels in accurately fitting kinematics models, yet its reliance on extensive data samples hinders practical engineering applications. To achieve a finely-tuned nonlinear kinematic model with a minimal dataset, theoretical prior knowledge serves as a guiding force for the NN to discern the intricate kinematic correlations within the 3-RRR nanopositioner. In-depth, the grey-box network’s training process is steered by a refined learning rate, tailored through convolutional modeling theory (adaptive learning rate). Ultimately, the validation outcomes underscore a substantial enhancement in modeling accuracy.