Compliant Mechanisms Research Articles

Optimal design of compliant displacement magnification mechanisms using stress-constrained topology optimization based on effective energy

In this paper, stress-constrained topology optimization is applied to the design of compliant displacement magnification mechanisms. By formulating the objective function based on the concept of effective energy, it is not necessary to place artificial spring components at the boundaries of the output and input ports as in previous methods. This makes it possible to design mechanisms that do not receive a reaction force at the output port, such as sensors. Furthermore, by imposing a constraint on the maximum stress evaluated in terms of the p-norm of the von Mises equivalent stress, problems such as stress concentration can be avoided. Several numerical examples of displacement magnification mechanisms are provided to demonstrate the effectiveness of the proposed method.

Fatigue damage stiffness degradation modeling of right circular flexure hinges

Flexure hinges are susceptible to fatigue damage under cyclic loading, resulting in performance degradation. This paper investigates the stiffness degradation of the right circular flexure hinges (RCFHs) under cyclic loading. Fatigue damage experiments are conducted to obtain the stiffness degradation curves, which can be divided into several stages by feature points. A relationship between feature lives and alternating stress amplitudes is established. A fatigue damage stiffness degradation piecewise curve model for RCFHs is proposed. The effect of notch stress concentration on fatigue damage is analyzed. Fatigue damage experiments under non-zero mean stress are conducted, and an equivalent fatigue stress equation is obtained. Finally, a generalized fatigue damage stiffness degradation model for RCFHs is developed, which establishes a relationship between residual stiffness and cycle number. On this basis, a fatigue damage performance modeling method for flexure hinge mechanisms is proposed. The fatigue damage performance of a compliant bridge mechanism was modeled and tested. The experimental results of input stiffness degradation are generally in agreement with the predicted results, which verify the validity of the method.

Design and disturbance rejection control of a piezoelectric nanopositioning stage

The article covers structural design and disturbance rejection control of a flexure-based compliant piezoelectric nanopositioning stage. The stage is devised using four-bar amplification mechanisms, auxiliary guiding mechanisms, and a compound parallelogram mechanism. Static and dynamic models of compliant mechanisms are analyzed based on a compliance matrix method. A modified Prandtl-Ishlinskii (PI) model with dead zone operators is used to describe the asymmetric hysteresis. Then, a global electromechanical dynamic model is built and identified. A comprehensive disturbance rejection controller (CDRC) combining a robust H∞ control and a disturbance observer-based (DOB) control is proposed for high trajectory tracking accuracy and anti-disturbance performance. The trajectory tracking accuracy of the stage can be up to 3 nm in experiments. As amplitudes of reference signals increases, relative tracking errors gradually decrease. System instability and oscillation caused by strong external disturbances are also reduced. Experimental results prove the effectiveness of the developed CDRC.

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.

(Non-)linear stiffness customisation of metallic additive manufactured springs

ABSTRACT Additive manufacturing (AM) facilitates the fabrication of compliant mechanisms through its free-form and design customisation capabilities. Specifically, the properties of kinetic mechanisms such as springs can be extended with regards to their inherent (non-)linear stiffness functions. This allows for the customisation of AM springs according to user preferences. By combining the design synthesis approach of building blocks with the structural optimisation approach for AM, it is possible to define and customise spring stiffness functionalities. The optimisation process employs an automated computational framework based on a genetic algorithm scheme, which has been demonstrated through randomised and reference case studies. This framework enables the attainment of linear, progressive (stiffening), and degressive (softening) stiffness curves. The manufacturability of the springs has been validated through laser powder bed fusion using stainless-steel material 17–4 PH (H900). The springs have resulted in an accuracy error of maximum 6.48% and precision error of maximum 5% through compression testing.

Design and Testing of a Novel Piezoelectric-Driven Microvibration Hammerhead

A novel microvibration hammerhead consists of a piezoelectric actuator and a double cross-shape compliant mechanism (DCCM) is presented in this paper. The output force of the piezoelectric actuator can be detected in real time by an inside-installed pressure sensor. A theoretical model including the stiffness, first natural frequency, and stress of the DCCM and the displacement output of the piezoelectric actuator are established, and then they are further analyzed using the finite element analysis method. The effects of the beam thickness on the static and dynamic properties are deeply analyzed and compared. A prototype micro hammering system is constructed by integrating the microvibration hammerhead assembly and controlling system. Various experiments are also carried out to verify the basic performance of the micro hammering system.

Modeling and Analysis of a Novel 3R Parallel Compliant Mechanism

This paper presents and investigates a new three-rotation (3R) parallel compliant mechanism that uses compliant rods to achieve three rotations. The mechanism is designed for use in pointing devices or as a spatial parallel manipulator. The mobility analysis is based on the Cosserat rod model and Lagrangian dynamics equations. The dynamics equations are then effectively solved using the back-propagation neural network and chaos-enhanced accelerated particle swarm optimization. After studying the mobility of the moving platform, a simplified model is proposed and used for kinematic analysis. The analysis of motion includes discussions on forward kinematics, inverse kinematics, singularities, and the workspace. Furthermore, experiments with a prototype are conducted to verify the accuracy and stability of the mobility analysis and the simplified model.

Graphic Transfer Matrix Method for Kinetostatic and Dynamic Analyses of Compliant Mechanisms

Abstract Kinetostatic and dynamic analyses of compliant mechanisms with complex configurations continue to be an attractive issue for obtaining a process-concise and result-accurate solution. In this paper, the transfer matrix method (TMM) is improved for a unified linear kinetostatics and dynamic modeling of compliant mechanisms with complex serial-parallel configurations in an oriented graphic way. In detail, the transfer matrices of typical building blocks commonly used in compliant mechanisms are summarized and derived. Then, a graphic transfer matrix modeling procedure capturing both the kinetostatics and dynamics of general compliant mechanisms is introduced. The displacement amplification ratio, input/output stiffness, parasitic error, natural frequencies, and frequency response of a typical compliant microgripper and a planar parallel three-degrees-of-freedom (3DOF) nanopositioner are calculated with such a graphic transfer matrix method. The advantages of the proposed modeling method lie in its convenience and uniformity in formulating both the kinetostatic and dynamic behaviors of a class of compliant mechanisms with distributed and lumped compliances in a transfer matrix manner, which has minimal DOF and is easily programmed.

Macro–microscale topological design for compliant mechanisms with special mechanical properties

This paper proposes a macro–microscale topology optimization approach for constructing compliant mechanisms with deterministic mechanical characteristics based on the essential properties of structural materials. The topology optimization process is divided into two scales: in macroscale optimization, the flexibility matrix factor is used as the constraint function, and the Augmented Lagrangian method is used to transform the constrained optimization problem into an unconstrained model, and the free materials optimization approach is used to generate a compliant mechanism with multiple material attribute elements at the macroscale. In microscale optimization, each microstructures are optimized to obtain special mechanical properties issued from macroscale optimized results. Within the allowable elastic deformation range, the compliant mechanism with arbitrary mechanical properties can be designed, and several numerical examples demonstrate that the compliant mechanisms have expected motion characteristics. The proposed method solved the quantitative design of mechanical properties of compliant mechanisms and can be extended to other fields of compliant mechanisms using macro–microscale topology optimization.

A multi-material Proportional Topology Optimization approach for compliant mechanism problems

This paper presents an extension for the Proportional Topology Optimization (PTO) algorithm to solve multi-material topology optimization of compliant mechanism problems. The objective function is firstly transformed from maximization of output displacement into maximization of mutual strain energy. In this setting, the contribution of each element to the objective function can be evaluated, facilitating the application of the PTO algorithm. The objective function is further multiplied by minus one so that a familiar form of minimization can be obtained. When multiple materials are involved, the problem is decomposed into several two-phase sub-problems based on the alternating active phase algorithm (AAPA). Using the PTO algorithm, each material is distributed into elements proportionally to the contribution of that material in the mutual strain energy. Due to the fact that the mutual strain energy can be either negative or positive, a modification has been made in the PTO inner loop to update the pseudo-density (the design variables). The applicability and feasibility of the developed approach are illustrated through several numerical examples.

Kinematic Analysis of three degrees of freedom planar parallel continuum mechanisms

Parallel continuum mechanisms are a type of compliant mechanisms comprising a rigid end-effector connected to a fixed frame by flexible and slender elements in a closed-kinematic morphology, being their flexibility the source of mobility. Solving the position problem involves the static equilibrium of the whole device considering the nonlinear large deformations of slender elements. Numerical iterative solutions are already available to solve real-time simulations. However, an assembled solution, which meets both geometric conditions and static equilibrium, is needed to start the process. A comprehensive Kinematic Analysis in the classical sense is not fully established yet. The aim of the paper is to propose a procedure that solves the full inverse and forward kinematic problems for planar three degrees of freedom systems, hence obtaining the multiple solutions arising from the closed-loop structure and the multiplicity of the deformation mode of slender links. From those solutions, finding of the different aspects that comprise the workspace is possible, as well as determining singularities and instability loci.

A Curved Compliant Differential Mechanism With Neutral Stability

AbstractDifferential mechanisms are remarkable mechanical elements that are widely utilized in various systems; nevertheless, conventional differential mechanisms are heavy and difficult to use in applications with limited design space. This paper presents a curved differential mechanism that utilizes a lightweight, compliant structure. This mechanism acquires its differential characteristic by having a high rotational stiffness when the mechanism is symmetrically actuated on two sides, while having a low rotational stiffness when actuated only on one side. To make the mechanism neutrally stable, the intrinsic elastic strain energy required for deformation of the compliant differential is compensated for by the reintroduction of potential energy, which is provided by two preloaded springs. The rotational stiffness of the one-sided actuation of the compliant differential mechanism around the neutral position is hypothesized to be adjustable by changing the preload of the springs. The stiffness can be positive, zero, or negative, indicating that the mechanism can be neutral or bistable. This hypothesis is investigated using a simulated model in Ansys Parametric Design Language (APDL) using optimized parameters to achieve the desired stiffness for the mechanism. The simulated model is validated using an experimental setup for both the one-sided and symmetrical actuation stages. The experimental results showed a high correlation with the simulation results. The mechanism with optimized dimensions and preload demonstrated neutral stability over a 16deg range. Bistability was discovered for preloads greater than the optimized preload. At θ = 0, a linear relationship was discovered between the spring preload and the rotational stiffness of the mechanism. Furthermore, an output/input kinematic performance of 0.97 was found for the simulated results and 0.95 for the experimental results.

Design and Analysis of an Active Swing Decoupling Compliant Mechanism With Multiple Co-Directional Input Branches

AbstractIn this work, we propose a novel bio-inspired swing decoupling mechanism supporting high precision motion systems, which is composed of multiple co-directional input branches with a rigid swing unit and an anti-rotational guiding unit. By actively adjusting the input displacements, the decoupling mechanism can switch between the swing and translational modes, where the parasitic rotations can be significantly suppressed by the anti-rotational guiding unit. With this, fully decoupled X and Y linear motions are obtained in the presence of co-directional input branches. A theoretical model of the decoupling mechanism is also established to accurately describe the decoupling behavior, which is verified by finite element simulations. A prototype of the proposed swing decoupling mechanism is fabricated and instrumented with comprehensive experimental apparatus, where the experimental results effectively validate the excellent decoupling performance and demonstrate good potentials to precision engineering applications.

Automated Forearm Prosthesis Controlling Using Fiber Bragg Grating Sensor

This paper describes the automation of a forearm prosthesis using the signal collected by a Fiber Bragg Grating (FBG) sensor. The FBG sensor is applied to one subject's forearm to measure the deformation as a result of the index and middle fingers when moved individually. It is possible to control a one joint model prosthesis allied to a compliant hand mechanism through signal analyses. Each finger movement has its features, such as its amplitude, which opens the possibility of using those to control different parts of the prosthesis, joint rotation by the middle finger, and compliant hand movement by the index finger. This paper presents results regarding prosthesis assembling, Hypertext Transfer Protocol (HTTP) communication latency between prosthesis and computer and tests with pre-acquired and processed FBG signal data. The prosthesis wrist rotation movement is related to the middle finger signal, and its compliant mechanism actuation is due to index finger signal. The communication between prosthesis and the computer had a mean latency of 140 ms and a standard deviation of 18 ms. The results demonstrate the potential for using the sensor system and automated prosthesis in other applications involving real-time forearm sensing, multi-finger signal analysis, and prosthetic movement.

Compliant Suction Gripper With Seamless Deployment and Retraction for Robust Picking Against Depth and Tilt Errors

Applying suction grippers in unstructured environments is a challenging task because of depth and tilt errors in vision systems, requiring additional costs in elaborate sensing and control. To reduce additional costs, suction grippers with compliant bodies or mechanisms have been proposed; however, their bulkiness and limited allowable error hinder their use in complex environments with large errors. Here, we propose a compact suction gripper that can pick objects over a wide range of distances and tilt angles without elaborate sensing and control. The spring-inserted gripper body deploys and conforms to distant and tilted objects until the suction cup completely seals with the object and retracts immediately after, while holding the object. This seamless deployment and retraction is enabled by connecting the gripper body and suction cup to the same vacuum source, which couples the vacuum picking and retraction of the gripper body. Experimental results validated that the proposed gripper can pick objects within 79 mm, which is 1.4 times the initial length, and can pick objects with tilt angles up to 60 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{\circ }$</tex-math></inline-formula> . The feasibility of the gripper was verified by demonstrations, including picking objects of different heights from the same picking height and the bin picking of transparent objects.

Additive manufactured continuum mechanisms based on shape-programmable and micro-sized building blocks

ABSTRACT Micro-additive manufacturing techniques have the potential to meet the demand for miniaturised functional components for minimally invasive surgical instruments. These techniques create monolithic, compliant mechanisms with micro-sized free-form structures that can be tailored to patient-specific surgical procedures. The automated design synthesis of the mechanisms using building blocks results in structures that are shape-programmable. This is achieved through an algorithmic-based computational workflow, which automatically converts user-specified 2D and 3D curves into discrete curve segments. The actuated motion of the mechanisms can be designed to move in a specific way, both forwardly and inversely. The mechanisms are manufactured using micro-laser powder bed fusion and hardenable stainless steel 17-4 PH. By carefully selecting the process parameters, it is possible to 3D-print micro-sized features such as a compliant beam thickness of 80 μm and an actuation hole of 100 μm. Both 2D planar curved mechanisms and 3D spatial curved mechanisms have been implemented and experimentally validated.

A Passively Conforming Soft Robotic Gripper with Three-Dimensional Negative Bending Stiffness Fingers.

Robot grippers that lack physical compliance have a difficult time dealing with uncertainty, such as fragile objects that may not have well-defined shapes. Existing soft robotic grippers require a large empty workspace for their actuated fingers to curl around the objects of interest, limiting their performance in clutter. This article presents a three-dimensional structure that exhibits negative stiffness in every bending direction used as fingers in a class of soft robotic grippers. Our approach exploits a compliant mechanism in a conical shape such that a transverse external contact force causes the fingers to bend toward the contact, enabling passive conformation for an adaptive grasp, even in clutter. We show analytically and experimentally that the proposed fingers have a negative bending response and that they conform to objects of various diameters. We demonstrate a soft robotic gripper with three self-conforming fingers performing the following: (1) fingertip grasping, (2) power grasping, and (3) semipassive grasping in clutter. Grasping experiments focus on picking fruits, which exemplify delicate objects with unmodeled shapes with significant variation. The experimental results reveal the ability of the self-conforming structure to smoothly envelope a broad range of objects and demonstrate a 100% grasp success rate in the experiments performed. The proposed passively conforming fingers enable picking of complex and unknown geometries without disturbing nearby objects in clutter and without the need for complex grasping algorithms. The proposed structures can be tailored to deform in desired ways, enabling a robust strategy for the engineering of physical compliance for adaptive soft structures.

Application of the ellipse of elasticity theory to the functional analysis of planar compliant mechanisms

In the last decades, a wide range of methods have been proposed for the analysis of compliant mechanisms. In this investigation, the theory of the ellipse of elasticity is tailored to the linear kinetostatic analysis of flexible systems. The proposed approach exploits the antiprojective polarity transformations of the conic associated to the generic two-port elastic suspension. According to the presented method, the elastostatic features of flexible elements with complex geometries, and of compliant mechanisms with serial, parallel, and hybrid topologies, can be represented by a unique geometric entity. As a consequence, the deflection analysis problem is reduced to a geometric problem with a straightforward solution. A specific procedure is developed both at the element and at the mechanism levels, to completely describe field of displacements and loads distribution in the elastic suspension. The application of the method is exemplified considering the analysis of different flexures and of a compliant four-bar linkage.

Aspects Related to the Design and Manufacturing of an Original and Innovative Marker Support System for Use in Clinical Optometry

The compliant mechanism studied in this paper is used in the structure of an assembly necessary for the temporary mounting of visual markers on glasses frames. Proper correction of vision defects in patients is a field of study in healthcare that has grown in complexity, along with all aspects of technology, over the past decades. As such, along with better lenses and frames, including custom solutions, the devices used to determine the patient’s specific parameters need to be more complex and precise. However, this is only part of the problem: while many devices exist that take measurements such as interpupillary distance with great precision, these come at a very high cost and do not take into account aspects related to real-life usage of the lenses, such as the patient’s position, angle, etc. Given the considerations above, this paper approaches the design, simulation, realization and testing of a working model of a frame used to support markers used in the optometry process. The design proposed in this paper assumes that the system used can be used while the glasses are mounted on the patient’s face, without influencing in any way their position in front of the patient’s eyes. Furthermore, the system must allow assembly and disassembly with minimal effort, to allow the patient to perform some movements without changing the position of the frame, as well as the easy access to the markers mounted on the spectacle frame. The main scope of the paper is to design and choose the correct constructive solution of a compliant mechanism for this important clinical optometric application in terms of geometric parameters, material and technology used to obtain appropriate performances. The authors highlight how the parameters and manufacturing technology for the device were chosen, and a finite element analysis is used to simulate the mechanical behaviour of the mechanism and to choose the optimal variant in terms of the desired displacement between three proposed materials for the given application. After justifying the choice of the constructive solution, several physical models of optometric support markers were realised using Fused Deposition Modeling (FDM), and Polyethylene terephthalate glycol (PETG) or polylactic acid as materials. Furthermore, an electro-pneumatic experimental test stand was developed to simulate and test the functionality of the device and to validate the proposed model.

Kinematic and Dynamic Analysis of a Compliant Mechanism to Generate Different Flapping-Wing Paths Based on Vibration Characteristics

Kinematic and Dynamic Analysis of a Compliant Mechanism to Generate Different Flapping-Wing Paths Based on Vibration Characteristics