compliant mechanism design

To address the conflicting challenges of low kinematic fidelity, insufficient rotational stiffness, and significant parasitic motion in large-angle (±15°) flexible crossed-hinge mechanisms, this paper proposes a static-dynamic-driven multi-objective optimization design methodology. We innovatively integrate rapid Euler–Bernoulli beam modeling with high-fidelity 3D ANSYS finite-element refinement to establish an interpretable hybrid modeling framework. Coupled with the NSGA-II algorithm, this approach efficiently explores the high-dimensional design parameter space and yields a Pareto-optimal solution set. The optimized configuration achieves motion error <0.5° over ±15° rotation, enhances rotational stiffness by 3.2×, and suppresses parasitic displacement by 87%, substantially outperforming conventional designs. This work provides both theoretical foundations and an engineering paradigm for high-performance compliant mechanisms.

Multi-degree-of-freedom (MDOF) compliant mechanisms are prone to fatigue, buckling, and yielding failures under complex, uncertain loads; conventional single-DOF stacked hard stops—designed for safety—severely constrain operational workspace. Method: This paper proposes a compact hard-stop design integrating coupled-motion limiting, introducing the first holistic framework for synthesizing MDOF-coupled limiting surfaces. Leveraging contact-surface geometry optimization, the method incorporates elastic boundary-constrained modeling, high-fidelity numerical simulation, and experimental validation to precisely tailor limiting surface topography. Contribution/Results: Validated on an orthopedic implant hinge mechanism, the design reliably suppresses yielding, buckling, and fatigue simultaneously while increasing workspace by 37%. It resolves the intrinsic trade-off between rigid motion limiting and large workspace, thereby significantly expanding the applicability of compliant mechanisms in high-reliability domains.

Large-scale mechanical systems face significant challenges in parametric design—including geometric constraint handling, variable loading conditions, performance deviations, over-specification, and cost-performance trade-offs. To address these, this paper proposes a modular mechanism design optimization framework based on Kriging surrogate modeling. Departing from conventional predefined design schemes, the method uniquely integrates geometry-constrained kinematic parameter optimization with manufacturability-aware cost modeling. It employs NSGA-II for multi-objective optimization to dynamically cluster components, enable customized grouping, and embed cost sensitivity analysis with decision support. The framework significantly improves motion performance consistency and component interchangeability while reducing over-specification rates. In validation on representative industrial systems, it achieves an average 12.7% reduction in manufacturing cost and a 9.4% decrease in carbon footprint.

This work proposes a novel topology optimization framework that integrates the implicit Material Point Method (MPM) to address numerical instabilities arising from mesh distortion and large rotations in large-deformation problems. For the first time, MPM is incorporated into topology optimization within an end-to-end differentiable pipeline, leveraging automatic differentiation and hyperelastic constitutive models to enable stable and efficient quasi-static optimization of structures undergoing finite deformations. The approach naturally supports both single- and multi-material designs and demonstrates robust performance on complex geometries, including soft robotic grippers. By circumventing the limitations of traditional finite element–based methods, the proposed framework significantly enhances the robustness and applicability of topology optimization in highly nonlinear deformation regimes.

To address assembly failures in high-precision connector mating caused by geometric deviations of workpieces, this paper proposes a simulation-driven design methodology for underactuated robotic fingers. Departing from conventional paradigms reliant on time-consuming hardware iterations or oversimplified planar contact models, our approach employs high-fidelity multibody dynamics simulation to jointly model nonlinear contact mechanics and frictional behavior. We formulate task success rate as the objective function and systematically optimize both the geometric configuration and spatial stiffness distribution of the finger. Experimental validation on the NIST Standard Task Board demonstrates that the designed finger tolerates misalignment up to 8.6 mm—improving error tolerance by 2.29×—and significantly enhances insertion success rate and operational robustness under dynamic contact conditions on a real robotic platform. The core contribution is a task-performance-oriented optimization framework for compliant mechanisms, overcoming the empirical dependency bottleneck in adaptability design for complex, multi-point contact scenarios.

Traditional heuristic approaches struggle to precisely control the nonlinear mechanical behavior of pneumatic soft actuators to achieve desired deformations. To address this challenge, this work proposes the first gradient-based inverse design framework that integrates nonlinear finite element modeling, three-dimensional shape parameterization, and pneumatic actuation mechanics. By leveraging gradient-based optimization, the method directly tailors the actuator’s geometric configuration to realize complex, target deformation patterns. This approach overcomes the limitations of conventional design strategies, enabling high-fidelity customization of soft actuator behavior. Experimental validation demonstrates excellent agreement between simulated and measured deformations of the designed actuators, significantly enhancing the accuracy and capability of demand-driven soft actuator design.

This study addresses the challenge of designing three-dimensional pneumatic soft actuators capable of efficient bending performance under large deformations. The authors propose a novel 3D nonlinear topology optimization framework based on a porous hyperelastic constitutive model, which, for the first time, enables topology optimization to handle extreme deformations in soft actuator design. The method consistently accounts for both geometric and material nonlinearities while incorporating manufacturability constraints. Leveraging stereolithography-based 3D printing, numerical simulations, and experimental validation, two optimized actuators were fabricated and demonstrated significant bending responses under prescribed pneumatic pressure. The close agreement between experimental results and simulation predictions confirms the effectiveness and advancement of the proposed approach.

In soft robot design, shape, material distribution, and actuation are highly coupled, rendering traditional approaches inefficient for joint optimization due to the high computational cost of high-dimensional nonlinear simulations and the inapplicability of gradient-based methods. This work proposes a low-dimensional, structured design embedding based on shared basis functions that unifies these three aspects through a continuous deformation mapping and spatial material field encoding within a common latent space. The representational capacity of this approach predictably improves with the number of basis functions, remains compatible with black-box simulators, and enables end-to-end joint optimization. Experiments across multiple dynamic tasks demonstrate that the method achieves significantly better performance than neural network and voxel-based baselines using fewer parameters, and consistently outperforms sequential optimization strategies.

This study addresses the challenge of dynamic modeling for mechanisms with variable topology, particularly when constraints such as joint locking, static friction, or ideal contact lead to abrupt changes in degrees of freedom. To ensure physically consistent and continuous dynamic behavior during topological transitions, the work proposes a set of physically coherent switching conditions. Building upon this foundation, two nonsmooth dynamics frameworks are developed: one based on redundant coordinates employing projected equations of motion, and another using minimal coordinates formulated via Voronets equations. The computational characteristics of both approaches are systematically compared. The proposed methodology is successfully validated on a planar 3R mechanism and a 6-DOF industrial manipulator under joint-locking scenarios, significantly enhancing the accuracy and feasibility of forward dynamics simulations for complex systems with varying topology.

This work addresses key challenges in multi-material topology optimization—namely, limitations on the number of candidate materials, redundant design spaces, and difficulties in ensuring physically valid material interpolation—by introducing a generalized shape function (gSF) method. The approach employs an n-dimensional linear shape function to map the multi-material simplex domain onto a compact design space, using natural coordinates as design variables to determine material densities. By integrating density filtering with a barycentric-projection strategy, the method rigorously enforces barycentric coordinate properties. For the first time, it establishes a generalized n-linear shape function applicable to arbitrary dimensions, thereby overcoming conventional constraints on material count and enabling a highly scalable optimization framework. The method successfully optimizes 2D and 3D structures—including compliant mechanisms—with up to 24 and 15 materials, respectively, achieving smooth convergence of objective functions and demonstrating its efficiency, generality, and engineering applicability.