Efficient Design of Compliant Mechanisms Using Multi-Objective Optimization

TL;DR

This paper tackles the synthesis of compliant cross-hinge mechanisms capable of large angular strokes while approximating an ideal revolute joint. It introduces a hybrid two-stage workflow that first uses a beam-based structural model and multi-objective evolutionary optimization to map a Pareto front of kinetostatic trade-offs, then refines selected designs with high-fidelity 3D finite element analysis and Nelder-Mead scalarization. Key contributions include a centrode-based kinematic deviation measure, non-dimensionalized objectives for translational compliance and rotational stiffness, and a practical method for selecting diverse designs via pseudo-weights. The approach yields a rich set of cross-hinge geometries and demonstrates that two-stage modeling—fast exploration followed by targeted refinement—can produce robust, distributed-compliance hinges suitable for practical deployment.

Abstract

Compliant mechanisms achieve motion through elastic deformation. In this work, we address the synthesis of a compliant cross-hinge mechanism capable of large angular strokes while approximating the behavior of an ideal revolute joint. To capture the competing demands of kinematic fidelity, rotational stiffness, and resistance to parasitic motion, we formulate a multi-objective optimization problem based on kinetostatic performance measures. A hybrid design strategy is employed: an efficient beam-based structural model enables extensive exploration of a high-dimensional design space using evolutionary algorithms, followed by fine-tuning with high-fidelity three-dimensional finite element analysis. The resulting Pareto-optimal designs reveal diverse geometric configurations and performance trade-offs.

Figures (6)

• Figure 1: Different kinds of hinges: Conventional pin-hole realization and compliant mechanisms.
• Figure 2: Schematic representation and kinematic description of the shape of the cross-hinge.
• Figure 3: Approximation of the Pareto front comprising 798.0 individuals.
• Figure 4: Projections of the Pareto front onto two-dimensional subspaces spanned by pairs of objectives. Colored markers correspond to selected solutions obtained upon uniform and preferential weighting, respectively.
• Figure 5: Schematic representations of cross-hinge geometries corresponding to uniform weighting among objectives (a) and preferred weighting of one of the objectives each (b)-(d).