Flexure Hinges Research Articles

Six-Bar Linkages With Compliant Mechanisms for Programmable Mechanical Structures

Abstract Programmable mechanical structures are formed by autonomous and adaptive cells and can reproduce meshes known from the finite element method. Furthermore, they can change their structure not only through morphing, but also by self-reconfiguration of the cells. A crucial component of the cells, which can preserve the underlying geometry of a triangular mesh, are six-bar linkages. The main part of the present contribution concerns the six-bar linkages as a fully 3D-printable compliant mechanism where each revolute joint of the six-bar linkage is replaced with a notch flexure hinge with the circular contour. The utilization of notch flexure hinges presents two significant drawbacks. First, notch flexure hinges do not maintain the center of rotation. Second, although compliance is an inherent and desirable characteristic of flexural hinges, it gives rise to secondary or parasitic motion. The compliance subsequently lead to alterations in the underlying geometry of a triangular mesh. For self-reconfiguration of the cells, an efficient model is needed to predict the positioning errors. Therefore, the flexure hinge is represented by three distinct models, namely a finite element model, a beam model, and a simplified linearized model based on translational and rotational spring elements. These models are compared and evaluated in succession first to identify the parameters of the simplified model and later on, the simplified model is used to show the deviations of a medium-scaled programmable structure with respect to the idealized behavior. The current work brings us closer to both the development of programmable mechanical structures and the prediction of positioning errors during self-reconfiguration.

Design of a Novel Flexible Spherical Hinge and Its Application in Continuum Robot

Abstract Compliant mechanisms, which can be integrally machined and without assembly, are well suited as joints for continuum robots (CRs), but how to incorporate the advantages of the compliant mechanism into the arm design is a key issue in this work. In this paper, a novel type of flexible spherical-hinged (FSH) joint composed of tetrahedron elements with a fixed virtual remote center of motion (RCM) at the bottom is proposed, and then extended to the CR and end-effector. In the arm design, the error compensation principle is used to offset the parasitic motion of the CR under external load (pressure and torque) and improve the bending and torsional isotropy of the arm through different series combinations, and then the stiffness model of the FSH joint and the statics model of the CR are developed using the 3D chain pseudo-rigid body model (3D-CPRBM) and tested. The results show that the 3D-CPRBM can effectively predict the deformation of the FSH joint and the CR. Moreover, the maximum standard deviation of the bending angle of the FSH joint in each direction is only 0.26 deg, the repeatable positioning accuracy of the CR can reach 0.5 deg, and the end-effector has good gripping ability and self-adaptive capability.

Design and Analysis of XY Large Travel Micro Stage Based on Secondary Symmetric Lever Amplification.

This study presents a newly developed piezoelectric drive mechanism for the purpose of designing, analyzing, and testing a micro-positioning platform driven by piezoelectric actuators. The platform incorporates a piezoelectric ceramic actuator and a flexible hinge drive and features a symmetrical two-stage lever (STSL) amplification mechanism and a parallelogram output structure. The implementation of this design has led to notable enhancements in the dynamic properties of the platform, thereby eliminating the undesired parasitic displacement of the mechanism. An analytical model describing the fully elastic deformation of the platform is established, which is further verified by finite element simulation. Finally, the static and dynamic performances of the platform are comprehensively evaluated through experiments. A closed-loop control strategy is adopted to eliminate the nonlinear hysteresis phenomenon of the piezoceramic actuator (PEA). The experimental results show that the piezoelectric micro-actuator platform has a motion range of 97.84 μm × 98.03 μm; the output coupling displacement error is less than 1%; the resolutions of the two axes are 8.1 nm and 8 nm, respectively; and the x-axis and y-axis trajectory tracking errors are both 0.6%. The piezoelectric micromotion platform has good dynamic properties, precision, and stability. The design has a wide application potential in the field of micro-positioning.

FBG displacement sensor with hyperbolic flexible hinge structure

This paper proposes a design method for a fiber Bragg grating (FBG) displacement sensor with a hyperbolic flexible hinge structure. A compact FBG displacement sensor with strong micro displacement measurement capability was fabricated. The final assembly testing showed that the sensor achieved good linearity with a linearity of 0.53%F·S at a range of 50 mm. The sensitivity was measured as 24.45 pm mm−1, hysteresis error as 1.1%FS, and repeatability error as 0.659%. The testing results demonstrated that the fabricated FBG displacement sensor exhibited strong practicality and good stability, making it suitable for long-term displacement monitoring of slope safety.

Structural and biochemical characterisation of the N-carbamoyl-β-alanine amidohydrolase from Rhizobium radiobacter MDC 8606.

N-carbamoyl-β-alanine amidohydrolase (CβAA) constitutes one of the most important groups of industrially relevant enzymes used in the production of optically pure amino acids and derivatives. In this study, a CβAA-encoding gene from Rhizobium radiobacter strain MDC 8606 was cloned and overexpressed in Escherichia coli. The purified recombinant enzyme (RrCβAA) showed a specific activity of 14 U·mg-1 using N-carbamoyl-β-alanine as a substrate with an optimum activity at 55 °C and pH 8.0. In this work, we report also the first prokaryotic CβAA structure at a resolution of 2.0 Å. A discontinuous catalytic domain and a dimerisation domain attached through a flexible hinge region at the domain interface have been revealed. We identify key ligand binding residues, including a conserved glutamic acid (Glu131), histidine (H385) and arginine (Arg291). Our results allowed us to explain the preference of the enzyme for linear carbamoyl substrates, as large and branched carbamoyl substrates cannot fit in the active site of the enzyme. This work envisages the use of RrCβAA from R. radiobacter MDC 8606 for the industrial production of L-α-, L-β- and L-γ-amino acids. The structural analysis provides new insights on enzyme-substrate interaction, which shed light on engineering of CβAAs for high catalytic activity and broad substrate specificity.

Effects of structural changes on antibacterial activity and cytotoxicity due to proline substitutions in chimeric peptide HnMc

Owing to the rapidly increasing emergence of multidrug-resistant pathogens, antimicrobial peptides (AMPs) are being explored as next-generation antibiotics. However, AMPs present in nature are highly toxic and exhibit low antibacterial activity. Simple modifications, such as amino acid substitution, can enhance antimicrobial activity and cell selectivity. Herein, we show that HnMc-W, substituted by the Phe1Trp analog of HnMc, a chimeric peptide, resulted in membranolytic antibacterial action and enhanced salt tolerance, whereas HnMc-WP1 with one Ser9Pro substitution resulted in a proline-kink helical structure that increased salt-tolerant antibacterial effects and reduced cytotoxicity. In addition, the HnMc-WP2 peptide, designed with a PXXP motif, had a flexible central hinge in its α-helical structure due to the introduction of two Pro and two Gln (X positions, by deletion of two Gln at positions 16 and 17) residues instead of Ser at position. HnMc-WP2 exhibited excellent antibacterial effects without cytotoxicity in vitro. Moreover, its potent antibacterial activity was demonstrated in a drug-resistant Pseudomonas aeruginosa-infected mouse model in vivo. Our findings provide valuable information for the design of peptides with high antibacterial activity and cell selectivity.

Design and analysis of the power-trigonometric function-shaped flexure hinges.

In this paper, a generalized flexure hinge model, that is, power-trigonometric function-shaped flexure hinges (PTFHs), is proposed. The power function and trigonometric function in the curve function are changed, which obtains different notch types of flexure hinges to meet the needs of flexure hinges in different scenarios. For the flexure hinge model, the notch curve equation of the hinge is presented first, and the influence of the degree of power function, degree of trigonometric function, and other parameters on the structure of the curve is analyzed. Then, the compliance and rotation precision equations of the flexure hinge are derived based on Castigliano's second theorem. Both equations are verified using the finite element method and achieve errors of less than 8.5%. Then, based on the flexure hinge equation, the influence of the size parameters on the compliance and rotation precision of the hinge is analyzed, and a new comparison method is proposed. Parameter β is defined to analyze the influence of five parameters on β. Through the comparison of PTFHs and three commonly used flexure hinges, the results prove that the proposed PTFHs have better comprehensive performance. Then, the flexure hinge is statically analyzed. Finally, a test system for flexure hinges is established to verify the performance of the model.

Insights into Bending Stiffness Modeling of Elementary Flexure Hinges

Flexure hinges are widely used in mechanical devices, especially for micro- or even nano-scale applications, where conventional joints based on conjugate surfaces prove unsuitable. However, to achieve accurate motion of devices whose joints are flexure hinges, knowledge of stiffness models that correlate applied forces or bending moments with the resulting displacements is required. Nonlinear bending models are typically too complex and difficult to implement. Therefore, it is preferred to use linear models, which admit analytical solutions. The purpose of this paper is to show what is lost in terms of accuracy in reducing a nonlinear bending stiffness model associated with a flexure hinge when simplifications are made to obtain an analytical solution. An analysis of the simplification process leading to a linear stiffness model and its analytical solution is presented. From this study arises an increased awareness of flexure joints in terms of the accuracy obtained with their stiffness models, suggesting important information to the user in choosing the level of complexity required to model them in a specific application. A comparison between analytical and numerical results is provided in the form of maps and tables so as to make that choice as clear as possible.

FlipWalker: Self-Inverting Robot Locomotion Inspired by ‘Jacob’s Ladder’ Falling Block Illusion Toy

This study presents a novel, underactuated robot locomotion system inspired by the Jacob's Ladder illusion toy, aimed at overcoming challenges encountered by wheeled locomotion on rugged and soft terrains. The system comprises interconnected body segments using flexible wires, offering inherent robustness and scalability due to its simple design. The motion is achieved through servo-controlled rotations, with joint locations adapting as segments pivot around each other. These segments utilize wires as hinges and tension-based constraints, enabling perpetual rotations, thereby propelling the robot forward while remaining flat on the ground. The manufacturing process involves rapid 3D printing for housing and CNC machining for PCB board fabrication. Flexible hinges are attached using threaded bolts, providing tension adjustability. The robot's microcontroller setup involves separate controllers for each body segment, communicating with a central offboard microcontroller for sensor data aggregation, configuration determination, and servo control. This modular design ensures easy addition and removal of segments without disrupting the overall electrical connectivity. The developed locomotion system showcases potential for enhanced adaptability and performance in challenging terrains.

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.

New twists of a TAIL: novel insights into the histone binding properties of a highly conserved PHD finger cluster within the MLR family of H3K4 mono-methyltransferases.

Enhancer activation by the MLR family of H3K4 mono-methyltransferases requires proper recognition of histones for the deposition of the mono-methyl mark. MLR proteins contain two clusters of PHD zinc finger domains implicated in chromatin regulation. The second cluster is the most highly conserved, preserved as an ancient three finger functional unit throughout evolution. Studies of the isolated 3rd PHD finger within this cluster suggested specificity for the H4 [aa16-20] tail region. We determined the histone binding properties of the full three PHD finger cluster b module (PHDb) from the Drosophila Cmi protein which revealed unexpected recognition of an extended region of H3. Importantly, the zinc finger spacer separating the first two PHDb fingers from the third is critical for proper alignment and coordination among fingers for maximal histone engagement. Human homologs, MLL3 and MLL4, also show conservation of H3 binding, expanding current views of histone recognition for this class of proteins. We further implicate chromatin remodeling by the SWI/SNF complex as a possible mechanism for the accessibility of PHDb to globular regions of histone H3 beyond the tail region. Our results suggest a two-tail histone recognition mechanism by the conserved PHDb domain involving a flexible hinge to promote interdomain coordination.

Anisotropic flexure hinges: Manufacturing and mechanical characterization for application in pressure-actuated morphing structures

Shape-morphing structures based on pressure actuation promise efficiency gains and performance improvements in aeronautics, but require complex three-dimensional geometries. The compliance of these morphing structures originates from local areas of reduced wall thickness. However, the required high wall thickness ratios are challenging for integral fabrication from high-performance fiber-reinforced plastics, which are demanded to achieve high load-bearing capacity. This study investigates different woven flexure hinges made from a hybrid yarn of glass fibers and the polyamide PA6 for application in pressure-actuated cellular structures. The flexure hinges are mechanically characterized under pure axial and pure bending loading in a tensile and a column bending test method specifically derived for flexure hinges. The specimen quality is further assessed by permeability testing, optical microscopy, and thermogravimetric analysis. This study shows that the stiffness of anisotropic flexure hinges can be determined in simple mechanical tests without the need for complex modeling of reinforcing fibers or consideration of manufacturing-specific effects. The mechanical properties of a double-layer hinge configuration are superior to those of a single-layer configuration, whereas integrating additively manufactured PA6 inlays into the woven preform offers an effective approach for achieving high wall thickness ratios. The most promising hinge configuration is selected for the integral fabrication of the aeronautical morphing structure, which consists of multiple pressurized cells.

A three-stage amplification piezoelectric-actuated micro-gripper with adjustable output displacement: design, modeling, and experimental evaluation

Abstract With the development of science and technology, the performance requirements of micro-gripper are getting higher and higher. Therefore, this paper designs a new piezoelectric-driven micro-gripper with large and adjustable output displacement, which can adjust the output range and compensate the errors caused by flexible mechanism. By adjusting the output displacement, the micro-components of different sizes can be clamped. The three-stage amplification mechanism is adopted, which utilizes triangle and lever amplification. Using the pseudo-rigid body method, the flexible hinge is analyzed; the statics, kinematics and dynamics models are established. Through finite element method, the magnification ratio of the micro-gripper is obtained, then the structure of the micro-gripper is further optimized. The output displacement and the magnification of the single-arm of the micro-gripper under 135 V are 223.8 μm and 24.2 times, respectively. This paper provides a basis for the wide application of micro-gripper.

Analytical Modeling and Application for Semi-Circular Notch Flexure Hinges

Flexure-based compliant mechanisms can be used to achieve bio-imitability and adaptability in the applications of biomedical engineering. However, a nonlinear load-displacement profile increases the design complexity of this type of compliant mechanism, especially when the cross-section of the flexure hinge is not constant. This paper proposes two general analytical models by analyzing the compliance and stress characteristics of the semi-circular notch flexure hinge undergoing large deflections, which is a typical variable cross-section of a flexure hinge, based on the Castigliano’s second theorem and the finite elements analysis method. As a case study for verification, three compliant four-bar linkage mechanisms are designed based on the proposed design approach, the design method proposed by Howell, and the equations proposed by Lobontiu, respectively. The results show that the design accuracy is improved 36% in comparison with designs from Howell and Lobontiu. Finally, a flexure-based artificial finger is designed and manufactured based on the proposed optimization approach. The performance test of the prototype shows that the artificial finger has good bio-imitability and adaptability with respect to joint movements.

Three-dimensional ultra-wide elastic metamaterial with inertial amplification mechanisms having optimized flexure hinges

The aim of this paper is to obtain an ultra-wide low-frequency stop band in three dimensions by using inertial amplification mechanisms. A two-stage remote center flexure mechanism design is introduced that allows 3D assembly of inertial amplification mechanisms while enabling ends of the inertial amplification mechanisms to bend in two orthogonal axes so that broadband excitations coming from all directions can be impeded. Cross flexure and split flat flexure hinges that restrain undesired torsional, in-plane and out-of-plane bending modes of the inertial amplification mechanisms are utilized for the first time in order to maximize the stop band frequency range. An octahedron and 3D arrays of octahedrons are generated with the use of these mechanisms. By making design improvements and topological changes on the mechanisms forming the octahedron, the stop band of the octahedron is widened. Finally, the bandwidth is maximized by optimizing the thicknesses of the flexures in the inertial amplification mechanisms. Eventually, a 3D elastic metamaterial with an ultra-wide band gap between 33.7 Hz and 457.5 Hz is obtained, yielding arithmetic mean normalized bandwidth of 172.6%.

A Compact Three-Dimensional Two-Layer Flexible Hinge

The paper proposes a new three-dimensional flexible hinge formed of several serially linked straight- and circular-axis segments that are disposed of in two layers. The novel hinge configuration is capable of large displacements and can be implemented in precision-compliant mechanisms that need to cover large spatial workspaces. Based on simplified geometry, an analytical compliance model is formulated that connects the loads to the displacements at one end of the hinge. Finite element simulation and experimental prototype testing of actual-geometry hinge configurations confirm the analytical model predictions. A related compliance-based analytical model evaluates the maximum loads that can be applied to the hinge and the resulting displacements. The two small-deformation analytical models are subsequently utilized to investigate the relationship between geometric parameters and the hinge performance qualifiers.

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.

A new type of low-stress flexible hinge displacement amplifying mechanism

A new type of low-stress flexible hinge displacement amplifying mechanism

Design and evaluation of a stick-slip piezoelectric actuator with flexure hinge mechanism inspired by the earthworm.

In this work, a new bionic piezoelectric actuator inspired by the earthworm is proposed, fabricated, and tested. The operating principle of the actuator imitates the crawling motion of the earthworm. The piezoelectric stack is embedded in the stator with a flexure hinge mechanism. One side of the stator is inspired by the earthworm body. Then the elongation of the piezoelectric stack is transmitted to the driving tip to produce oblique displacement under such a stator. The vertical and horizontal components are used to press and drive the slider, respectively. The principle of the proposed actuator is described in detail. The static deformation is investigated by the FEM method. A dynamic model of the actuator is developed to further reveal the motion characteristics of the slider via theoretical analysis. Finally, the output characteristics of the proposed BPA are tested. The experimental results show that the actuator achieves a maximum output speed of 12.72 mm/s at a voltage of 100V and a frequency of 710Hz. The maximum output force is 3 N under a locking force of 2 N. Besides, the displacement resolution is tested at 87nm at a frequency of 710Hz, which indicates that the developed actuator can be applied in the field of precision actuation.

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.