Manufacturing Aware Multiobjective Shape Optimization of Bézier Parametrized Nonlinear Exoskeleton Flexible Links
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Metal additive manufacturing allows for lightweight, highly optimized shapes that are difficult or too expensive to produce with traditional subtractive methods \cite{Alfaify2020}, particularly in the aerospace and biomedical industries. The present work presents a design and optimization process for a flexible link of an exoskeleton \cite{Calanca2019} manufactured through metal additive manufacturing, followed by CNC machining for lightning holes. The design takes inspiration from the semi-monocoque approach used in aerospace structures. The link is effectively a multifunctional structure, providing load-bearing support while incorporating strain sensing with surface-mounted strain gauges. Two groups of beam geometries with varying spans and cross sections are defined using Bézier flange profiles and smooth spline-based control over the global shape along the span. The structural response is estimated using a simplified nonlinear continuum model based on an Euler-Bernoulli beam with von Kármán geometric nonlinearity and non-linear Vlasov torsion corrections \cite{Nayfeh2004, Lacarbonara2013}. This is set up as a boundary-value problem and is solved using a Newton-collocation method, which allows for fast evaluations within multi-objective optimization loops. A multi-objective GA/NSGA-II algorithm \cite{Deb2002} is used to generate Pareto fronts that balance mass, bending compliance (flexibility), and torsional strength, while adhering to constraints on strength, potential geometric instabilities (global and local buckling proxies), and design constraints of flexibility and high-strain areas for the sensors. Two cross-section designs are examined: (i) a reinforced, curved I-section designed to localize strain for sensing near the roots, while still maintaining load transfer ability; and (ii) a closed "squircle-like" section, adapted from super-elliptic geometry and evaluated here for structural performance. The results show that the proposed workflow produces designs that can be manufactured and meet the loading needs of the exoskeleton, while also improving the trade-off between flexibility and weight, providing clearly defined high-strain areas suitable for sensor integration.
