Synthesis Of Compliant Mechanisms Research Articles

The synthesis method of series-based bistable compliant mechanisms for rigid-body guidance problem based on geometrical similarity transformation of pole maps

Abstract Designing guidance mechanisms using bistable mechanisms with two stable positions is a common low-power solution for maintaining the guidance position without continuous external energy input. However, the coupling between kinematics and statics in compliant bistable mechanisms poses a challenge for their application in mechanism synthesis. To address this issue, this paper introduces the pole similarity transformation theory into the synthesis of compliant mechanisms and proposes a general synthesis method for planar serial-based compliant bistable mechanisms. This method models the compliant mechanism using the strain energy method and analyzes the bistable characteristics of the mechanism within its motion plane using the saddle point searching method. By doing so, the proposed method can identify stable positions without predetermined motion trajectories, making it more suitable for designing compliant bistable mechanisms with general planar motion. Additionally, this method utilizes the pole map to describe the stable positions of the rigid components in the compliant mechanism and establishes an information database for compliant bistable mechanisms. Through leveraging the pole similarity transformation, the pole maps of the mechanisms in the information database are matched with the pole map of the motion task, thus achieving the synthesis of planar serial-based compliant bistable mechanisms for the rigid-body guidance problem. The paper provides a detailed explanation of the mechanism synthesis process and demonstrates its application through a case study.

Application of genetic algorithm for the synthesis of path-generating compliant mechanisms

This study demonstrates a significant achievement in using the Genetic Algorithms technique to design compliant mechanisms capable of tracking a predetermined non-linear output path. The main objective of this research is to develop a computational optimization framework for generating mechanisms that satisfy the specified input requirements with the highest precision. The authors present a tool that incorporates a Python interface and ANSYS MAPDL software for modeling, solving, and optimizing compliant mechanisms. The optimization objective and algorithm are outlined, followed by a report of the results and recommendations for future research directions.

Synthesis of Compliant Parallel Mechanisms Using an Improved Beam-Based Method with the Optimization of Multiple Resonant Modes

This paper proposes an improved beam-based method to synthesize a compliant parallel mechanism (CPM) with multiple degrees of freedom (DoFs). The proposed method utilizes a structural optimization technique to synthesize a three-legged CPM with a single-beam structure constructed by two perpendicular segments in each leg to achieve the desired DoFs and fully decoupled motion. In addition, an objective function is proposed to optimize the primary resonant frequencies in actuating directions to targeted values to achieve the desired dynamic behaviors. A 4-DoF CPM, with one translation and three rotations, is synthesized using the improved beam-based method and all of the primary resonant frequencies are optimized to the targeted values. The 4-DoF CPM prototype is fabricated monolithically and evaluated experimentally in terms of its mechanical characteristics, workspace, and resonant modes. The obtained results show that the experimental stiffness and dynamic properties agree with the predictions. In particular, the prototype has good motion decoupling capability, as reflected by the high stiffness ratios of more than 500 between the non-actuating and actuating directions; the large workspaces of up to 4.0 mm and 7.2° for the translation and rotations, respectively; and the resonant frequencies being close to the targeted ones. In addition, the highest deviations between the predicted and experimental results are 9.49% and 9.13% for the stiffness and dynamic behaviors, respectively, demonstrating the correctness and effectiveness of the proposed method.

Compliant manipulator design method (COMAD) for the type synthesis of all serial and parallel multi-DoF compliant mechanisms, with example of a Schönflies motion generator

This article presents the compliant manipulator design method (COMAD) for the synthesis of serial and parallel multi-DoF compliant mechanisms. Currently, the freedom and constraint topology (FACT)-method results in flexure systems being a serial kinematic solution for multi-DoF motions. In the COMAD method parallel solutions are included too through 3 steps: (1) obtaining the serial and parallel kinematic solutions for an intended set of end-effector DoFs with the type synthesis of legs-method; (2) transforming each legtype into a flexure leg by using the FACT method; (3) combining legs in parallel to obtain complete compliant mechanism designs. It was applied for a compliant Schönflies motion generator – having three translations and one rotation – resulting in 5 different 4-DoF flexure legs. 4 designs were new compared to the result obtained using the FACT method. Then, a set of legs was combined in parallel resulting in a compliant Schönflies mechanism, which was manufactured. Its mobility was experimentally evaluated by modal analysis. The intended motions separately became visible during its first four eigenmodes. They are the mechanism’s DoFs as their stiffness is relatively low.

Topology Optimization Design of Multi-Input-Multi-Output Compliant Mechanisms with Hinge-Free Characteristic and Totally Decoupled Kinematics

A new multi-constraint optimization model with the weighted objective function is proposed to design the multi-input-multi-output (MIMO) compliant mechanisms. The main feature of this work is that both the two notable problems related to the de facto hinge and the movement coupling are tackled simultaneously in the topological synthesis of MIMO compliant mechanisms. To be specific, the first problem is the severe stress concentration in the flexible hinge areas, and it is solved by the introduction of input and output compliances into the objective function, which could facilitate the optimization to strike a good balance between structural flexibility and stiffness. The second problem is the high degree of control complexity caused by the coupled outputs and inputs, and it is addressed by achieving the complete decoupling with two groups of extra constraints that are used to suppress the input coupling and the output coupling, respectively. As the most common and effective topology optimization method, the Solid Isotropic Material with Penalization (SIMP)-based density method is adopted here to obtain the optimized configurations. After the analytical sensitivity deduction related to the weighted objective function and constraints, two typical numerical examples are presented to demonstrate the validity of the proposed topology optimization framework in designing the hinge-free and completely decoupled MIMO compliant mechanisms.

Elasto-Kinematics and Instantaneous Invariants of Compliant Mechanisms Based on Flexure Hinges

The kinematic synthesis of compliant mechanisms based on flexure hinges is not an easy task. A commonly used method is the equivalent rigid model, which involves replacing the flexure hinges with rigid bars connected with lumped hinges using the already known methods of synthesis. This way, albeit simpler, hides some interesting issues. This paper addresses the elasto-kinematics and instantaneous invariants of flexure hinges with a direct approach, making use of a nonlinear model to predict their behaviour. The differential equations that govern the nonlinear geometric response are given in a comprehensive form and are solved for flexure hinges with constant sections. The solution to the nonlinear model is then used to obtain an analytical description of two instantaneous invariants: the centre of instantaneous rotation (c.i.r.) and the inflection circle. The main result is that the c.i.r. evolution, namely the fixed polode, is not conservative but is loading-path dependent. Consequently, all other instantaneous invariants are loading-path dependent, and the property of instantaneous geometric invariants (independent of the motion time law) can no longer be used. This result is analytically and numerically evidenced. In other words, it is shown that a careful kinematic synthesis of compliant mechanisms cannot be addressed by only considering the kinematics as rigid mechanisms, and it is essential to take into consideration the applied loads and their histories.

Design of compliant mechanisms based on compliant building elements. Part I: Principles

In this paper, we present a new design method and principle, i.e., Compliant Building Elements (CBE), for compliant mechanisms that adopts a systematic and synthetic approach to generate practicable flexure designs. The CBE is unique in that it encodes a compliant system's quantitative information, including elasticity, geometry, location, and orientation, in a parametric matrix. Based on the matrix, a degree-of-freedom (DOF) concept is defined to describe permitted motions of a flexure; next, the screw theory is used to guide the design and synthesis of compliant mechanisms from DOF decomposition to actuator layout selection. In CBE, a compliant system consists of three types of compliant elements, i.e., compliant elements formed by serial or parallel connections and basic compliant elements. The synthesis procedure is a top-down and iterative process, starting from laying out the stage topology to finally optimizing the compliant connection elements and types (i.e., serial or parallel), where the iteration stops when the stage characteristics meet the design requirements. A library of various compliant elements is provided to help the designers quickly generate the initial stage topological designs and optimize the performance with reduced design iterations. The matrix-based design method for compliant mechanisms, i.e., CBE, which is analogous to the screw-based type synthesis for rigid parallel mechanisms, enables early-stage flexure system design via building compliant blocks just like building LEGO® bricks.

Optimization for a New XY Positioning Mechanism by Artificial Neural Network-Based Metaheuristic Algorithms.

This paper devotes a new method in modeling and optimizing to handle the optimization of the XY positioning mechanism. The fitness functions and constraints of the mechanism are formulated via proposing a combination of artificial neural network (ANN) and particle swarm optimization (PSO) methods. Next, the PSO is hybridized with the grey wolf optimization, namely PSO-GWO, which is applied to three scenarios in handling the single objective function. In order to search the multiple functions for the mechanism, the multiobjective optimization genetic algorithm (MOGA) is applied to the last scenario. The achieved results showed that the fitness functions are well-formulated using the PSO-based ANN method. In the scenario 1, the stroke achieved by the PSO-GWO (1852.9842 μm) is better than that gained from the GWO (1802.8087 μm). In the scenarios 2, the stress gained from the PSO-GWO (243.3183 MPa) is lower than that achieved from the GWO (245.0401 MPa). In the scenario 3, the safety factor retrieved from the PSO-GWO (1.9767) is greater than that achieved from the GWO (1.9278). In the scenario 4, by using MOGA, the optimal results found that the stroke is about (1741.3 μm) and the safety factor is 1.8929. The prediction results are well-fitted with the numerical and experimental verifications. The results of this paper are expected to facilitate the synthesis and analysis of compliant mechanisms and related engineering designs.

Topology optimization of compliant mechanisms with distributed compliance (hinge-free compliant mechanisms) by using stiffness and adaptive volume constraints instead of stress constraints

Many approaches have been developed for the synthesis of compliant mechanisms via topology optimization. Most of these approaches produce mechanisms with lumped compliance if not extended appropriately, such as with stress constraints. With mechanisms with lumped compliance, the deformation is concentrated in regions of small dimensions (referred to as “de facto hinges” or “one-node connected hinges”) causing notch overstresses. Some extensions to these approaches overcome this by forcing mechanisms with distributed compliance (also referred to as “hinge-free compliant mechanisms”). However, the currently known extensions have a number of drawbacks. Stress constraints, for example, make the optimization formulation highly nonlinear and non-convex. In this paper, a new extension is presented that permits the synthesis of mechanisms with distributed compliance by combining a constraint for the allowed structural stiffness with an adaptive volume constraint. The presented optimization approach can be easily solved using linear optimization. The basis for the extension presented in this paper is the modal synthesis approach, which permits the synthesis of transverse-load-insensitive compliant mechanisms. The methodology developed is tested on suitable design examples.

Topological synthesis of fluidic pressure-actuated robust compliant mechanisms

This paper presents a robust density-based topology optimization approach for synthesizing pressure-actuated compliant mechanisms. To ensure functionality under manufacturing inaccuracies, the robust or three-field formulation is employed, involving dilated, intermediate and eroded realizations of the design. Darcy’s law in conjunction with a conceptualized drainage term is used to model the pressure load as a function of the design vector. The consistent nodal loads are evaluated from the obtained pressure field using the standard finite element method. The objective and load sensitivities are obtained using the adjoint-variable approach. A multi-criteria objective involving both the stiffness and flexibility of the mechanism is employed in the robust formulation, and min–max optimization problems are solved to obtain pressure-actuated inverter, gripper, and contractor compliant mechanisms with different minimum feature sizes. Limitations of the linear elasticity assumptions while designing mechanisms are identified with high pressure loads. Challenges involved in designing finite deformable pressure-actuated compliant mechanisms are presented.

Topology Optimization and Prototype of a Multimaterial-Like Compliant Finger by Varying the Infill Density in 3D Printing.

This study presents a multimaterial topology optimization method for design of multimaterial compliant mechanisms. Traditionally, the objective function in topology optimization for design of structures is to minimize the strain energy (SE). For synthesis of compliant mechanisms, the objective function is usually to maximize the mutual potential energy (MPE). To design an adaptive compliant gripper for grasping size-varied objects, a multicriteria objective function considering both the SE and MPE at two different output ports is proposed in this study. In addition, based on the fact that different infill densities in three-dimensional (3D) printing leads to prototypes with different equivalent mechanical properties, this article proposes that a multimaterial design can be approximated by varying the values of infill densities in different portions of a 3D-printed component, which enables the multimaterial designs to be prototyped using the general low-cost, single-material fused deposition modeling 3D printing machines. The proposed method is used to design and prototype a bi-material compliant finger which is 3D printed using a flexible thermoplastic elastomer with infill densities of 30% and 100%. The experimental results demonstrate that the bi-material finger is a better design in terms of reducing the driving force while increasing the output displacement at the fingertip comparing to the single-material finger design with the same volume and weight. Furthermore, a two-finger gripper with two identical multimaterial-like compliant fingers is prototyped and installed on a six-axis industrial robot. The experimental tests are performed to demonstrate the effectiveness of the presented design.

A bio-inspired B-Spline Offset Feature for structural topology optimization

In this paper, we propose a B-Spline Offset Feature (BSOF) for feature-driven topology optimization. The feature is inspired from the geometric morphology of worms characterized by an elongated cylindrical, bilaterally symmetric, and well-segmented body along a highly deformable directrix. B-spline is used to define the directrix with its outward and inward offsets outlining the BSOF. This definition endows the BSOF with high deformability such as self-folding and self-intersection. To construct the implicit level-set function (LSF), the BSOF is decomposed into a sequence of segments whose LSFs can easily be constructed by Kreisselmeier–Steinhauser (KS) function. Regular or irregular shaped segments are identified by the deformation gradient. Irregular segments involving geometrical singularities, e.g. distorted and concave segments, are replaced with convex hulls. The stiffest structure design and compliant mechanism synthesis are studied to illustrate the effectiveness and advantages of the proposed BSOF for topology optimization.

Analysis of planar compliant mechanisms based on non-linear analytical modeling including shear and lateral contraction

Compliant mechanisms are commonly used in precision engineering while analyzing their deflection is particularly challenging. Often, FEM simulations are chosen in an iterative process. Analytical approaches that consider pure bending, shear or other effects are usually limited to the mechanism as a system. However, certain configurations comprise compliant elements with different aspect ratios. The aim of this paper is to integrate the theories of shear and lateral contraction into a unified form with the existing theory of bending for large deflections and make them applicable individually for specific sections of continuous compliant mechanisms. Recommendations are made as to when which theory should be used. Building on that, a comprehensive tool for analyzing compliant mechanisms developed in Python is introduced. The tool offers the possibility to create arbitrary compliant mechanisms including branched links and various boundary conditions. A tool for parametric studies allows to optimize the given geometry for realizing a specific motion task. Further, FEM and measurement results correlate well with the application results. The presented user interface can be beneficial for the accelerated analysis and synthesis of compliant mechanisms.

Multiresolution Topology Optimization of Large-Deformation Path-Generation Compliant Mechanisms with Stress Constraints

Topology optimization is a powerful numerical tool in the synthesis of lightweight structures and compliant mechanisms. Compliant mechanisms present challenges for topology optimization, as they typically exhibit large displacements and rotations. Path-generation mechanisms are a class of mechanisms that are designed to follow an exact path. The characteristics of compliant mechanisms therefore exclude the validity of linear finite-element analysis to ensure the proper modeling of deformation and stresses. As stresses can exceed the limit when neglected, stress constraints are needed in the synthesis of compliant mechanisms. Both nonlinear finite-element analysis as well as the consideration of stress constraints significantly increase computational cost of topology optimization. Multiresolution topology optimization, which employs different levels of discretization for the finite-element analysis and the representation of the material distribution, allows an important reduction of computational effort. A multiresolution topology optimization methodology is proposed integrating stress constraints based on nonlinear finite-element analysis for path-generation mechanisms. Two objective formulations are used to motivate and validate this methodology: maximum-displacement mechanisms and path-generation mechanisms. The formulation of the stress constraints and their sensitivities within nonlinear finite-element analysis and multiresolution topology optimization are explained. We introduce two academic benchmark examples to demonstrate the results for each of the objective formulations. To show the practical, large-scale application of this method, results for the compliant mechanism structure of a droop-nose morphing wing concept are shown.

Synthesis of compliant mechanisms with selective compliance – An advanced procedure

By means of compliant mechanisms, given deformations can be realized in a controlled manner, in order to fulfill the typical task of conventional mechanisms. Compliant mechanisms with distributed compliance show large flexible areas and can therefore divert from the desired, mechanism-like behavior. Selective compliant mechanisms are advanced mechanisms with distributed compliance which nevertheless come close to such a behavior. In this paper, a new approach to the synthesis of this type of compliant mechanisms is presented. Compared to previous synthesis methods, this approach is more suitable for the synthesis of mechanisms with many output degrees of freedom, since the optimization process is more stable. With this new synthesis approach, an incremental linearization of the optimization problem is performed, which allows for the use of a linear optimization algorithm. The new synthesis approach is tested with two examples of compliant mechanisms with a few output degrees of freedom and a shape adaptive mechanism with many output degrees of freedom.

Topology optimization using the unsmooth variational topology optimization (UNVARTOP) method: an educational implementation in MATLAB

This paper presents an efficient and comprehensive MATLAB code to solve two-dimensional structural topology optimization problems, including minimum mean compliance, compliant mechanism synthesis and multi-load compliance problems. The Unsmooth Variational Topology Optimization (UNVARTOP) method, developed by the authors in a previous work, is used in the topology optimization code, based on the finite element method (FEM), to compute the sensitivity and update the topology. The paper also includes instructions to improve the bisection algorithm, modify the computation of the Lagrangian multiplier by using an Augmented Lagrangian to impose the constraint, implement heat conduction problems and extend the code to three-dimensional topology optimization problems. The code, intended for students and newcomers in topology optimization, is included as an appendix (Appendix A) and it can be downloaded from https://github.com/DanielYago together with supplementary material.

Non-linear analytical modeling of planar compliant mechanisms

Compliant mechanisms are state of the art in technical applications, especially in precision engineering. They mostly achieve their motion due to bending-dominated deformation of their compliant segments, i.e. flexure hinges. Accurately analyzing a compliant mechanism in dependence of specific flexure hinges is still a challenging task due to the monolithic design and non-linearities caused by large deflections. Most existing accurate analytical models are restricted to single hinges. Therefore, this paper presents a non-linear analytical approach to calculate the elasto-kinematic properties of arbitrary planar compliant mechanisms. The approach is based on the theory for large deflections of rod-like structures. As a typical example, a compliant parallel four-bar linkage with varying compliant segments is investigated by means of the proposed analytical approach. The motion and deformation behavior are numerically calculated with the use of MATLAB®. It is shown, that the analytical results are in good correlation with FEM-based simulations and measurements of a manufactured prototype. To demonstrate the generality of the proposed method, two further and more complex mechanism examples are considered. As a result, the implemented modeling approach allows an accurate and fast analysis as well as synthesis of manifold planar compliant mechanisms with distributed or concentrated compliance.

Analysis and Synthesis of Underactuated Compliant Mechanisms Based on Transmission Properties of Motion and Force

This article analyzes and designs the transmission structure for underactuated compliant mechanisms (UCMs). The transmission structure of UCMs consists of serial and parallel transmission chains. At first, the UCMs are classified systematically according to the number and distribution of the serial and parallel transmissions. Next, the active and passive transmission properties of motion and force in UCMs are analyzed on the defined four subspaces of tangent and cotangent spaces of joint space. Synthesizing the classification and the transmission properties of UCMs, the congruent relationship between mechanical structure and transmission function is established, and different cases of UCMs are discussed and compared. A novel type of UCMs can achieve the independent regulation of passive stiffness, active force, and active motion that is useful for improving the transmission performance in robotic and prosthetic hands. Finally, a functional oriented design method is proposed and used to design a single-actuator two-fingered gripper for enveloping and precision grasps. The results demonstrate the validity of the proposed method.

On the Geometry of Stiffness and Compliance Under Concatenation

Abstract Eigentwists and eigenwrenches capture the stationary stiffness behavior of compliant mechanisms and can be related to a mechanism’s primary kinematic behavior. The nature of concatenation of multiple mechanism building blocks is not well understood. In this paper, we consider the mechanics of concatenation and develop design rules that capture the geometric nature of concatenation in terms of eigenwrenches and eigentwists. The rules are illustrated through mechanisms from the literature and an example design problem. The design rules have potential to provide intelligent guidance for systematic building block synthesis of compliant mechanisms.

An adaptive bubble method for structural shape and topology optimization

An adaptive bubble method is presented in this paper for shape and topology optimization design of stiffest structures and compliant mechanisms. With the aim of overcoming the shortcomings of the traditional bubble method and retaining all its advantages, the proposed method achieves a comprehensive integration of topological derivative, implicit model and fixed grid. The topological derivative is devoted to the iterative positioning of new holes inside the design domain. Each of the holes is described by smoothly deformable implicit curve (SDIC) characterized by very few parameters and high deformation capacity. Since the structural model could be implicitly constructed using the SDICs, the finite cell method (FCM) is applied to facilitate the mechanical analysis of the implicit model with fixed Eulerian mesh. Two new concepts, i.e., the topological derivative threshold and the total influence region of inserted holes, are further introduced to adaptively control the numbers and positions of new holes so that the numerical stability of topology optimization could be well guaranteed. It is shown that the adaptive bubble method no longer needs the mesh updating process and can perform the merging and separating operations of holes straightforwardly. Numerical examples concerning the stiffest structure design and the compliant mechanism synthesis are tested to demonstrate the universality of the present method, especially its capability of being integrated within CAD systems directly without post-processing.