An Open-Source Hierarchical Multi-fidelity Modeling Stack for Design and Analysis of Compliant Mechanisms

Abstract

This paper presents an open-source, hierarchical, eight-level multi-fidelity modeling stack as a comprehensive technical routine for the design and analysis of compliant mechanisms, utilizing the widely adopted parallelogram flexure as a representative case study. Our methodology involves the systematic implementation, integration, and cross-validation of modeling levels spanning from first-order linear beam theories and refined pseudo-rigid-body models (PRBM) with optimized characteristic radius factors, to intermediate beam constraint models (BCM), exact transcendental solutions for fixed-guided beams, numerical boundary value problem (BVP) systems, and high-fidelity 3-D solid finite element analysis (FEA). All solvers, benchmarking datasets, and interactive tools have been developed as an open-source contribution to facilitate community adoption and further research. Major results demonstrate an excellent performance spread of over eight orders of magnitude in computational runtime, ranging from sub-microsecond algebraic evaluations to solid-mesh simulations requiring nearly a minute per load case. Furthermore, we quantify the localized divergence of low-fidelity models in predicting critical second-order effects, such as parasitic rotations and nonlinear softening/stiffening behavior near buckling thresholds. Based on the summary of these benchmark test results, a practical model selection guide is concluded to assist designers in selecting optimal modeling fidelities for various flexure systems, facilitating the rapid synthesis of precision mechanisms with guaranteed accuracy across expansive workspaces.