Simulation of spatial constant velocity transmission using equivalent RL approximation circuits

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Abstract

In engineering, numerous systems are either inaccessible or prohibitively expensive to evaluate using their original physical models. In such cases, equivalent models serve as viable alternatives. This approach requires a rigorous mathematical foundation to ensure that conclusions drawn from the equivalent model remain valid for the original system. From a modeling perspective, while machine learning (ML) models can approximate highly complex laws with significant precision, they often lack the ability to explain the underlying physical mechanisms, thus being categorized as "black boxes." The latest global trend in machine learning involves integrating physical relationships into model training (Physics-Informed Machine Learning). This integration offers dual benefits: the data-driven accuracy of ML and the interpretability of physical models. This paper presents the mathematical foundations for approximating the kinematic atlas of a mechanical object using an equivalent RL circuit as a surrogate model. Achieving high approximation accuracy enables the potential to represent various kinematic atlases through electrical circuits. This paves the way for circuit-based simulation research across diverse domains, combining both precision and the transparency of "grey-box" modeling. This methodology represents a highly promising research direction in modern engineering, offering a robust alternative to conventional black-box approaches.