Design Of Compliant Mechanisms Research Articles

The Design and Testing of an Additive Manufacturing-Obtained Compliant Mechanism for the Complex Personalisation of Lenses in Clinical Optometry

The Design and Testing of an Additive Manufacturing-Obtained Compliant Mechanism for the Complex Personalisation of Lenses in Clinical Optometry

Enhancing the Design Space of Bistable Laminates by Tailoring the Attachment Boundary Conditions

Abstract Bistable and multistable laminates are structural elements with more than one stable equilibrium configuration. The bistability makes them very interesting for the design of compliant mechanisms. However, these laminates are extremely sensitive to boundary conditions and attachment methods. It has been shown prior in the literature that restrictive boundary conditions can lead to the loss of bistability or unwanted deformation modes. This article develops attachment concepts that leverage the structural behavior changes caused by boundary conditions to expand the design space of bistable elements for structural applications. A systematic means of using the boundary conditions to improve the stability margins and load introduction of bistable tape springs is demonstrated. The stability margins and the achievable angles have been quantified using an analytical model previously developed by Guest and Pellegrino. Subsequently, high-fidelity finite element (FE) simulations are done in abaqus™ to determine the limits of the proposed method in terms of localization effects. Based on the analytical model and simulation outcomes, layup, size, and attachment points are determined, and two prototypes are fabricated, illustrating the effectiveness of the proposed method in expanding the design space of traditional bistable tape springs.

A new cockroach-like compliant mechanism with SLA-3D printing for micromanipulation and micropolishing of biomaterials

The traditional compliant mechanisms often employ displacement amplification mechanisms to magnitude the workspace but their displacements are still smaller than 1 mm. Unlike previous studies, the present paper proposes a new conceptual design of compliant mechanism which is inspired from biomechanics of cockroach animal. The developed compliant mechanism for two specific functions, such as microgripper and micropositioner which can handle biomaterials. It can permit a large stroke over 1 mm. Modeling of the performances of the proposed mechanism are built by a couple of adaptive neuro fuzzy inference system (ANIFS) and particle swarm optimization (PSO) where PSO is to optimize the ANFIS. To enhance the performances of the mechanism, accelerated particle swarm optimization (APSO) is utilized to search the optimal design parameters. Lastly, the optimized mechanism is printed by Stereolithography (SLA) 3D technique, and the experimental verifications are performed. The results indicated that circumstance #1, the stroke is about 1.5279 mm, the frequency is 49.02103 Hz, the crosstalk error is 0.01108 mm, and the stress is 8.50514 MPa. In circumstance #2, the stroke is 1.44544 mm, the frequency is 54.51361 Hz, the crosstalk error is 0.0248 mm, and the stress is 8.35604 MPa. In last circumstance, the optimized results are achieved the stroke of 1.62369 mm, frequency of 51.62278 Hz, crosstalk of 0.028141 mm, and stress of 7.71713 MPa. The results indicated that the safety factor of three cases are over 2.5 to ensure a safe operation. The tested results are well satisfied with the simulated results.

IGA-based topology optimization in the design of stress-constrained compliant mechanisms

Topology design of compliant mechanisms has gained wide popularity among the scientific community, and their use in the mechanical engineering field is being of upmost importance. In this paper, an isogeometric analysis (IGA) formulation is used to solve the topology optimization problem of compliant mechanisms. Stress constraints are introduced in the problem to guarantee the attainment of realistic solutions. For this purpose, an overweight constraint is considered for the design process, replacing the use of local stress constraints. The material distribution in the domain is modeled with quadratic B-splines and with a uniform relative density within each element of the mesh. These strategies to define the material layout are used to compare the IGA-based formulation with the finite element (FEM) formulation. The IGA formulation provides several advantages with respect to the classical FEM-based approaches that are shown and analyzed with an input-parameters sensitivity analysis. The sensitivity analysis and the assessment of the importance of introducing of stress constraints in the problem are developed by solving two benchmark problems. Regarding the sensitivity analysis of input parameters, the results show that the ratio between the material and the springs stiffnesses is the parameter with the largest influence on the solutions of the problem. Moreover, the advantages of the IGA formulations over FEM formulations are related with the computational time, the smoothness of the structural borders, and the non-appearance of the checkerboard patterns. With respect to the stress constraints, the results show that they have to be considered in order to avoid instability and structural integrity problems.

Modelling and performance analysis of a curvature-adjustable multiple-axis flexure hinge based on Bézier curve

In order to solve the uniqueness of the compliance equations and each notch profile, a curvature-adjustable multiple-axis flexure hinge with complex notch profiles is designed and investigated based on Bézier curve in this paper. The hinge can evolve into multiple-axis flexure hinges with single and hybrid, symmetric and asymmetric notch profiles composed of the ellipse, circle, hyperbola and parabola. In addition, analytical compliance equations in six degrees of freedom based on the Castigliano’s Second Theorem are proposed. Then, a simplified notch profile classification method based on a binary quadratic implicit equation is proposed. Moreover, analytical compliance equations are validated by finite element analysis. The maximum relative error between the finite element analysis and the analytical results is 6.07%. Finally, the compliance, precision of rotation and stress are investigated based on structural parameters. The results show that the change in the rotation centre does not significantly affect the axial and bending compliance for the flexure hinge with a specific single and flush Bézier curve notch profile. Moreover, the flexure hinge with a notch profile consisting of ellipse and hyperbola has the highest rotational precision. The proposed curvature-adjustable multiple-axis flexure hinge can provide more compliance options for the design of compliant mechanisms.

Three-Dimensional Material Mask Overlay Topology Optimization Approach With Truncated Octahedron Elements

Abstract This paper presents a 3D material mask overlay topology optimization approach using truncated octahedron elements and spheroidal masks. Truncated octahedron elements provide face connectivity between two juxtaposed elements, thus eliminating singular solutions inherently. A novel meshing scheme with Tetra-Kai-Decaheral or TKD (generic case of truncated octahedron) elements is proposed. The scheme is extended to parameterized generic-shaped domains. Various benefits of implementing the elements are also highlighted, and the corresponding finite element is introduced. Spheroidal negative masks are employed to determine the material within the elements. Seven design variables define each mask. A material density formulation is proposed, and sensitivity analysis for gradient-based optimization is developed. fminconmatlab function is used for the optimization. The efficacy and success of the approach are demonstrated by solving structures and compliant mechanism design problems. Compliance is minimized for the former, whereas a multi-criteria arising due to flexibility and stiffness measures is extremized for optimizing the mechanisms. Convergence of the optimization is smooth. The volume constraint is satisfied and remains active at the end of the optimization.

Modelling of a general lumped-compliance beam for compliant mechanisms

Compliant mechanisms are crucial in a wide range of applications, and straight flexure beams with uniform thickness serve as their fundamental building blocks. While techniques and methods exist to estimate the sophisticated load-displacement behavior of these beams, dealing with the nonlinear large deformation and parametric design of complex compliant mechanisms using these beams remains a significant challenge. To address this challenge, an analytical model has been developed to integrate six independent geometric parameters into a general lumped-compliance beam, known as the general lumped-compliance beam model (GLBM). This approach enables the determinate synthesis of force-displacement characteristics in compliant mechanisms that feature any two flexure beams connected in series, such as the conventional lumped-compliance beam, distributed beam, inverted beam, and folded beam. The closed-form beam constraint model (BCM) is utilized to derive the GLBM that accurately captures geometric nonlinearity and load-dependent effects. To demonstrate the effectiveness of this modeling technique, we verified five specific configurations of the GLBM using nonlinear finite element analysis (FEA). In addition, we selected two representative compliant mechanisms, a revolute joint and a bistable mechanism, for nonlinear analysis and experimental validation, which further showcases the efficacy of this proposed GLBM.

Buckling-induced instability in topology optimization of compliant constant-force mechanisms

Compliant constant-force mechanisms are compliant mechanisms that provide a nearly constant force over a prescribed deflection range. Topology optimization is an effective method for compliant constant-force mechanism design. However, instabilities caused by buckling often cause the optimization algorithm to fail to converge. This study analyzes the causes of buckling-induced instability and proposes methods to avoid this instability. A mechanism with three torsional springs is proposed, and its three force–displacement curves are analyzed. These bifurcated force–displacement curves cause the optimization algorithm to be unstable. Several topology optimization models with buckling constraints are proposed for designing compliant constant-force mechanisms. Their effects are tested and analyzed in numerical examples with different target constant forces and constant-force strokes. Almost all optimization results have three hinges, corresponding to a proposed mechanism with three torsion springs. A slight change in their initial design causes a large change in the force–displacement curve, which eventually leads to buckling-induced instability. This instability can be avoided by constraining the buckling load calculated at the configuration near the start of the constant-force stroke.

An enhanced proportional topology optimization with virtual elements: Formulation and numerical implementation

This paper presents an improved non-sensitivity structural topology optimization method incorporating virtual elements with unstructured polygonal meshes. Specifically, we employ the recently developed gradient-free proportional topology optimization (PTO) approach, for the first time, together with a new material distribution formula suitable for both minimum compliance and compliant mechanism problems. In order to improve performance, we integrate a linear virtual element method (VEM) module into the PTO algorithm. The linear VEM has a desirable characteristic: it does not require numerical integration and, more importantly, is less sensitive to small-edge elements, thus, significantly reducing computational time. Additionally, we utilize virtual elements with unstructured polygonal meshes inside PTO to suppress one-node connection instabilities. Furthermore, the Heaviside-type operator in the main PTO algorithm loop enhances the optimized results by encouraging the density variables to approach discrete (0/1) solutions more effectively. We demonstrate the performance of our developed method in terms of computational speed, diversity of applications, and improved black-and-white (0/1) structures through several benchmark examples of compliance and compliant mechanism designs.

Generalized model and performance analysis of two-axis flexure hinges based on quadratic rational Bézier curve

This article presents a generalized model of two-axis flexure hinges based on quadratic rational Bézier curve. The generalized closed-form compliance equations are derived based on the virtual work theory and the superposition relationship of the deformation. Then, how to determine the number of sensitive axes, the location of the primary and secondary sensitive axes, and the configuration of the notch profile are discussed. There are 20 types of notch profiles derived from single or mixed, symmetrical or asymmetrical curves. And, the correctness of the compliance equations is verified by finite-element analysis. The maximum relative error does not exceed 10%. Finally, the precision of rotation, the maximum stress, and the effect of structural parameters on the compliance are analyzed. The results show that for two-axis flexure hinges with a flush single curve notch profile, the proximity of the center of rotation to the load end does not significantly affect the axial compliance as well as the torsional compliance. For hybrid two-axis flexure hinges with symmetric structure, the ability to maintain the center of rotation under lateral forces is better than that under the same torque. The proposed generalized model provides a reference for the design of spatial compliant mechanisms.

Test Methods for the Mechanical Characterization of Flexure Hinges

BackgroundThe design of compliant mechanisms requires detailed knowledge about the stiffness properties of their flexible segments. However, there are no standardized test methods for flexure hinges, and therefore the influence of manufacturing-specific effects, such as anisotropy, on the stiffness properties cannot be quantified.ObjectiveThis paper presents novel test methods for variable cross-section flexure hinges subjected to large deformations and pure bending loading, which determine the bending stiffness of flexure hinges over their entire deflection range using a universal testing machine.MethodsThe novel test methods for flexure hinges are based on the tensile test, the four-point bending test (FPBT), and the column bending test (CBT). These test methods were initially formulated for constant cross-section specimens, but are adapted in this study to examine variable cross-section specimens. The derived test methods are validated by using isotropic materials with well-known properties and by comparing the calculated deflections with deflections measured by means of image processing.ResultsThe deflection validation shows that the adapted CBT (aCBT) is accurate over the entire deflection range, achieving curvature of up to kappa =0.40;text {mm}^{-1}, whereas the maximum curvature in the adapted FPBT (aFPBT) is limited by the test methodology to about kappa =0.15;text {mm}^{-1}. At small strains, the flexural modulus determined in the aCBT and aFPBT agrees well with the Young’s modulus determined in the tensile test, as would be expected for isotropic materials.ConclusionThe aCBT proves to be a suitable test method for flexure hinges at large deflections, whereas the stiffness characterization at small deflections can be performed with both the aCBT and the aFPBT. The presented test methods validated on isotropic materials form the basis for characterizing anisotropic flexure hinges with geometry-dependent stiffness properties.

Design of a variable-diameter wheel with a novel distributed compliant mechanism

Compliant variable-diameter mechanisms enable adaptation of variable-diameter wheels to both road and soft terrain. Conventional compliant variable-diameter mechanisms, in which every wheel-foot is an independent load-bearing structure, rely heavily on rigid-body mechanisms. To overcome the structure restriction and improve their performances, we introduce a novel compliant mechanism in which circumferentially distributed leaf springs or combination springs with large deformation range are used as flexible components. The springs constitute the closed outer ring and the overall load-bearing structure in the wheel. A novel screw transmission mechanism was designed to achieve motions with two degrees of freedom. Based on the geometric relationships, a dimensional design method for the mechanism is proposed. The chained beam-constraint-model and integration methods are introduced to obtain the spring deflections and maximum hub rotation angle. These methods can be used for further design of the transmission mechanism. The wheel design is then verified experimentally. The results indicate that the required design targets were achieved. Thus, the proposed mechanism diversifies the structure type and design of compliant mechanisms and expands the applicability of variable-diameter wheels in mobile platforms.

Generalized element-node complete model and its implementation for the optimal design of a piezo-actuated compliant amplifier

Compliant amplification mechanisms are widely applied to extend the stroke of stacked piezoelectric actuators. Accurate modeling of static and dynamic performances is crucial for the optimal design of complex compliant mechanisms. By generalizing the planar element-node model-based finite element method, this paper proposes a new modeling method capable of describing the spatial complete kinetostatics and dynamics for compliant mechanisms. On the basis of the widely reported complete compliance models for flexure hinges, a versatile stiffness model is established for the hinge with an arbitrary notch shape through the force equilibrium model. The generalized model is then demonstrated by applying for modeling and optimizing a compliant mechanism with dual-stage amplification. The verification through finite element simulations suggests that the maximum modeling error for the kinetostatic and first six resonant frequencies for the mechanisms with and without structural optimizations is less than 20%. Finally, the open-loop and closed-loop performance tests on the prototype with optimized parameters are conducted, demonstrating the effectiveness of the developed modeling and optimization methods.

RCM adjustment for a double-parallelogram based RCM mechanism used for MIS robots

The inevitable errors in the manufacturing, assembly, and testing of a remote center-of-motion (RCM) mechanism lead to the erroneous link parameters which deviate its geometry. Consequently, the motion, as well as the force, become non-zero at the entry port to the patient’s body which is undesirable. To address this issue, the current work first presents the accurate kinematic model of the RCM of an exemplary double-parallelogram-based RCM mechanism. Thereafter, it introduces the RCM adjustment concept and a flexure-based compliant mechanism to nullify/minimize the said deviation. For the analytical design of the flexure element, this paper makes the required design calculations and performs the finite element analysis. It is followed by the disclosure of the RCM Adjustment System and a systematized method of RCM adjustment for a mechanically constrained RCM device. The devised system is based on the prescribed compliant mechanism design and is advantageous, over the traditional RCM adjustments. The potential of the proposed concept lies in the fact that it is not limited to the adopted mechanism only rather, it is extendable to other mechanisms as well which was missing in the prior art. In addition, it offers a more simplified and economical design. Further, an initial prototype of the exemplary mechanism is manufactured using laser micromachining and rapid prototyping techniques. Both analytical as well as physical validations have been performed which proved the efficacy of the proposed kinematic modeling concept. Furthermore, the prototype of the introduced RCM Adjustment System is manufactured as a single-piece design which demonstrated its effectiveness. The preferred embodiment of the same is the said double-parallelogram-based RCM mechanism which is most widely used for robot-assisted minimally invasive surgery (RAMIS). It is designed in a SolidWorks environment and manufactured using Al6101-T6 and SS304 as link material, and a variety of standard elements.

Design of compliant mechanisms for origami metamaterials

Design of compliant mechanisms for origami metamaterials

A Problem-Independent Machine Learning (PIML) enhanced substructure-based approach for large-scale structural analysis and topology optimization of linear elastic structures

Structural analysis for structures composed of highly heterogeneous materials which often involves the solution of large-scale linear algebraic equations is very time-consuming even within the linear elastic regime. Furthermore, the tremendous computational cost of iterative large-scale finite element analysis also prevents the widespread use of topology optimization as a powerful design tool especially when the desired design resolution is very high. In order to break the bottleneck hindering the efficient solutions of large-scale structural analysis and design optimization problems, in the present article, a general machine learning (ML) enhanced substructure-based framework is proposed. The essential idea is resorting to the classical substructure-based finite element analysis approach and establishing an implicit mapping between the parameters characterizing the material distribution within a substructure and the corresponding condensed stiffness matrix/numerical shape functions through offline trained deep neural networks. In contrast to most of the existing ML enhanced approaches, the proposed framework is truly independent of the forms of structural geometry, boundary condition and external load, and can be applied to solve various boundary value problems governing by the same type of partial differential equation once the offline training is completed. Armed with modern artificial intelligence techniques, the proposed approach in some sense revives the classical substructure approach in finite element analysis. Compared with the traditional paradigm, it can achieve 104–105 times solution efficiency for tested large-scale examples with satisfactory accuracy. The effectiveness of the approach was also validated for the non-adjoint topology optimization problems, i.e., 3D compliant mechanism design. Finally, to demonstrate the proposed approach’s capability in dealing with extremely large-scale three-dimensional problems, a three-dimensional topology optimization problem with about 109 design variables and 3×109 degrees of freedom (Dofs) is solved on a laptop without resorting to any parallel computing techniques.

A DFAM FRAMEWORK FOR THE DESIGN OF COMPLIANT STRUCTURES

AbstractAdditive manufacturing methods present prospects for designed mechanical deformation via the integration of controlled anisotropic lattice structure forms. Their assimilation into a Design for Additive Manufacturing (DfAM) process would create a novel framework for the design of compliant mechanisms (CM). The method uses lattice structures to replace rigid multi-part mechanisms, with integrated and controlled flexibility into a single, compact, and precise component. In recent years, a lot of research has gone into making algorithms that enable users to generate CMs for their designs. But by relying on algorithms to design solutions, are they neglecting to fully understand how these mechanisms work. This work undertakes the design and development of a novel DfAM Framework, that utilises controlled lattice structure deformations to create a standardised method of CM design. The authors have developed a method for this, whilst allowing users to tailor CMs to their design, by using a wide selection of pretested structures. Indicating suitable structures for their design using an integrated novel taxonomy. The framework is tested and developed using a series of case studies.

Design of a torsional compliant mechanism with given discrete torque-deflection points for nonlinear stiffness elastic actuator

AbstractOwing to inherent flexibility, compliant actuator with physical elastic elements can implement compliant interactions between robot and environment. Nonlinear stiffness elastic actuators (NSEAs) use one motor to adjust position and stiffness, which improve compactness of variable stiffness actuators, and consider high torque/force resolution and high bandwidth. The primary challenge of designing a NSEA is designing a reliable compliant mechanism with a given torque-deflection profile. In this study, a general design method of torsional compliant mechanism through given discrete torque-deflection points was proposed, where a chain algorithm based on 2R pseudo-rigid-body model was used to describe the large deformation in elastic elements. Moreover, the theoretical model of stiffness of a compliant mechanism based on series flexible beams was developed. Based on the proposed model, the dimensional parameters of proposed compliant mechanism were designed satisfying the condition of the given torque-deflection points. Finally, simulation and physical experiment of the designed compliant mechanism through three given torque-deflection points are conducted to show the effectiveness of the proposed method. The designed compliant mechanism was tested and evaluated in the self-developed NSEA.

Pure-displacement formulation and bulk modulus propagation for topology optimization with pressure loads

This work proposes a pure-displacement formulation for topology optimization with pressure loads and the use of a continuous boundary propagation technique. This technique allows controlling the non-solid (fluid or void) constitutive behavior by disseminating the desired bulk modulus to holes in the solid domain. The novelty of the proposed approach is to enable the distribution of solid, fluid, and void simultaneously with one design variable field. A density-based topology optimization approach is considered, and a gradient-based interior point algorithm is used. The linear elasticity equilibrium equations are discretized by the finite element method and solved with a sparse direct solver. The sensitivities are calculated by the discrete adjoint method with automatic differentiation. The optimization problems encompass compliance minimization (in 2D and 3D) and a compliant mechanism design to maximize the output displacement. Three examples evaluate the proposed formulation: the internally-pressurized lid, the piston head, and the inverter-compliant mechanism. The results show that different designs are obtained by considering different constitutive behavior for the non-solid phase.

On Non-Penalization SEMDOT Using Discrete Variable Sensitivities

This work proposes a non-penalization Smooth-Edged Material Distribution for Optimizing Topology (SEMDOT) algorithm, which is a typical elemental volume fraction-based topology optimization method, by adopting discrete variable sensitivities for solid, void, and assumed boundary elements instead of the continuous variable sensitivities used in the penalization one. In the proposed non-penalized SEMDOT algorithm, the material penalization scheme is eliminated. The efficiency, effectiveness, and general applicability of the proposed non-penalized algorithm are demonstrated in three case studies containing compliance minimization, compliant mechanism design, and heat conduction problems, as well as thorough comparisons with the penalized algorithm. In addition, the length scale control approach is used to solve the discontinuous boundary issue observed in thin and long structural features. The numerical results show that the convergency of the newly proposed non-penalization algorithm is stronger than the penalization algorithm, and improved results can be obtained by the non-penalized algorithm.