Corner-filleted Flexure Hinges Research Articles

Dynamic photoelastic study of flexure hinges produced by additive manufacturing technology

There are many challenges in compliant mechanism redesign for additive manufacturing (AM) technologies, and in order to assess their applicability and propose adequate recommendations, the behavior of compliant elements has to be examined. Plastic materials are often used in AM technologies and are well suited for large volume compliant mechanisms due to their flexibility to strength ratio. However, they also have many disadvantages, notably a low fatigue strength and complex material behavior. Therefore, in this paper a photoelastic observations of corner-filleted flexure hinges manufactured from the transparent acrylic based photopolymer using the Digital Light Processing (DLP) AM technology subjected to the dynamic loading have been conducted in order to assess the fatigue strength and potentials of the photoelastic methods for the material behavior modeling. Three-point flexural tests on rectangular beam samples with the standardized dimensions printed in vertical and in horizontal orientation have been performed and the obtained data has been used for numerical simulations of corner-filleted flexure hinges. The specimens printed in different orientations exhibit significantly different anisotropic properties; the horizontally printed samples exhibit brittle behavior, while the samples printed vertically yields and consequently have much higher deformations, the calculated flexural moduli are also very different. Corner-filleted flexure hinges printed in vertical orientation and subjected to dynamic cantilever beam bending tests at relatively high stress amplitudes proved sufficient for the low dynamic compliant mechanisms applications. The qualitative photoelastic observations have shown that the photoelasticity is applicable in dynamic tests and useful in residual stress determination and stress concentration investigations.

Modeling of corner-filleted flexure hinges under various loads

Compliant mechanisms are widely applied in precision engineering, measurement technology and microtechnology, due to their potential for the reduction of mass and assembly effort through the integration of functions into fewer parts and an increasing motion repeatability through less backlash and wear, if designed appropriately. However, a challenge during the design process is the handling of the multitude of geometric parameters and the complex relations between loads, deformations and strains. Furthermore, some tasks such as the dimensioning by means of optimization or the modeling for a controller design require a high number of analysis calculations. From this arises the need for sufficient computational analysis models with low calculation time. Existing studies of analysis models are mostly based on selected load cases, which may limits their general validity. The scope of this article is the comparison of models for the analysis of corner-filleted flexure hinges under various loads, to determine their advantages, disadvantages and application fields. The underlying methods of the study can further be used to evaluate future models based on a broad selection of possible load cases.

Modeling of a Symmetric Five-Bar Displacement Amplification Compliant Mechanism for Energy Harvesting.

This paper presents an analytical model to determine a closed form mathematical representation for the output displacement of a displacement amplification compliant mechanism used for energy harvesting. A symmetric five-bar compliant mechanism with right-circular and corner-filleted flexure hinges was mathematically modeled and its displacement was determined using the Castigliano energy theorem. The stresses within the flexure joints, the weakest points in the mechanism body, were calculated. The mathematical model expresses both the displacement amplification and the stresses as functions of the design parameters and the load caused by the harvester. The developed model can be used to optimize the mechanism dimensions for maximum harvested power, while minimizing its structural stresses. The mechanism was also modeled numerically using finite element methods; both the analytical and numerical models were verified experimentally. The mathematical model of the mechanism was integrated with a model representing a piezoelectric energy harvester to calculate the open-circuit voltage. As a proof of concept, experiments were performed using an unimorph piezoelectric cantilever at low-frequency (less than 1 Hz) harmonic excitation inputs. The measured open-circuit voltage was found to be in agreement with that calculated using the proposed model, when integrated with the model representing the piezoelectric beam. The power generated by the piezoelectric harvester, equipped with the proposed displacement amplification mechanism, was more than a hundred times that without amplification.

Design and test of a compact compliant gripper using the Scott–Russell mechanism

This paper presents the design, modeling, fabrication, and test of a monolithic compliant gripper for micro-manipulation applications. A compact compliant mechanism that enables in-principle straight-line parallel jaw motion is obtained, by combining the Scott–Russell mechanism and the parallelogram mechanism. The right-circular corner-filleted (RCCF) flexure hinge is adopted to achieve a large displacement of lumped-compliance joints. A pseudo-rigid-body model (PRBM) method with the help of the virtual work principle is performed to obtain parametric analytical models including the amplification coefficient and kinetostatics. Finite element analysis (FEA) is conducted to validate the analytical model and capture adverse parasitic motions of jaws. A monolithic prototype was fabricated, the test results of which show satisfactory performances.

Empirical compliance equations for conventional single-axis flexure hinges

In consideration of the stress concentration, unified compliance equations for conventional single-axis hinges are presented. The relationship between the stress concentration and the compliance of corner-filleted flexure hinges is first analyzed. Considering the stress concentration, coupled with a wide range of geometrical parameters, empirical compliance equations for conventional flexure hinges, are then obtained by using the exponential model. Subsequently, the proposed equations are unified. To verify the validity and accuracy of these equations, the characteristics of a bridge-type flexure-based mechanism are then analyzed by the proposed equations and finite element analysis, respectively. The results of compliances and displacement amplification ratios obtained by these two methods are in good agreement. It demonstrates that the empirical compliance equations could be obtained by exponential model, and these equations can be unified.

Design and Optimization of a New Hollow Circular Flexure Hinge for Precision Mechanisms

Flexure hinges have been used in many precision mechanisms where repeatable, friction free motion and high precision are required. Many kinds of flexure profiles have been proposed during the past decade. This paper presents a new type of flexure hinge which combines circular longitudinal axis beams to form hollow joint. This novel design will help to improve the range of motion, reduce stress level and increase the maximum load before yielding. Due to its special design, the cavity inside the hinge can also be filled with an elastomeric filler material to provide vibration damping. In order to synthesis this hinge, shape optimization integrating genetic algorithm and response surface methodology is used. The optimization procedure is programmed in MATLAB whereas finite element analysis in ANSYS is also embedded into the codes to enhance the calculation process. The new flexure hollow hinge is compared to the conventional straight-axis solid hinges (circular, elliptical and corner-filleted flexure hinges) in terms of stiffness, rotational precision and stress levels. It is also supposed that this new design would increase the precision of the mechanism due to reducing the parasitic motion. Finite element analysis in ANSYS is used to verify for the viability of the design before it can be fabricated and tested.

A novel piezostack-driven jetting dispenser with corner-filleted flexure hinge and high-frequency performance

This paper presents a new jetting dispenser which is applicable to high-frequency microelectronic packaging. In order to achieve high frequency glue jetting and improve the stability of jetting dispensers, we redesign a novel displacement amplifying mechanism, and a new on–off valve jetting dispenser driven by piezoelectric actuators is developed. Firstly, the core part of this jetting dispenser—the displacement amplifying mechanism with a corner-filleted flexure hinge—is proposed and a comparison with the previous structure is carried out; then the characteristic dimensional parameters of the amplifying mechanism are determined by theoretical calculation and finite element analysis. Secondly, a prototype of the dispenser with the displacement amplifying mechanism is fabricated based on the determined parameters. We use a laser displacement sensor to test the displacement of the needle, and a maximum amplifying displacement output of 367 µm is obtained under an applied 200 V to the piezoelectric actuator, which is consistent with the simulation result and meets the requirement of high displacement output. Thirdly, we build an integrated testing system. Mixed glycerol/ethanol is chosen as the experimental dispensing glue, and the experiment and analysis of a droplet diameter are conducted. A higher jetting frequency of 400 Hz and a smaller droplet diameter of 525 µm are achieved with the glycerol/ethanol mixture, and the characteristics of consistency and temperature influencing the droplet diameter are verified by experiments.

Substructure compliance matrix model of planar branched flexure-hinge mechanisms: Design, testing and characterization of a gripper

This paper proposes an analytical compliance-based matrix method to model the quasi-static, small-displacement response of planar branched flexure-hinge over-constrained mechanisms. It studies structurally- and kinematically-branched flexible mechanisms comprising several chains that are connected in complex series-parallel configurations and that are acted upon by multiple external/reaction loads. These architectures are substructured or decomposed into simpler chains whose compliances are evaluated from known individual segment compliances. The substructured-chain compliances are subsequently combined with external loads to solve for unknown displacements and reactions and to further evaluate parameters relevant to the mechanism behavior. The method is applied to the design and analysis of a novel displacement-amplified gripper with right circularly corner-filleted flexure hinges. The mechanism's mechanical amplification, stiffness, and grip force are evaluated when either full or partial compliance (flexure-based only) is assumed. The analytical model predictions are confirmed by finite element analysis and by experimental testing of a proof-of-concept prototype. Subsequent analytical-model simulation highlights the relationships between the main geometric parameters and the gripper's performance qualifiers.

A Piezo-Actuated High-Precision Flexible Parallel Pointing Mechanism: Conceptual Design, Development, and Experiments

A high-precision pointing mechanism for intersatellite optical communication is presented in this paper, which employs flexure hinges as the passive joints and orients its moving platform by means of six piezoelectric actuators. The proposed mechanism features submicroradian resolution and microradian repeatability within a submilliradian pointing range. A corner-filleted flexure hinge considering manufacturing tolerance with high motion accuracy and large displacement is designed based on performance analysis, and the theoretical analysis is also validated by FEA simulation and experimental testing within a 5% error margin. The parameters of the parallel mechanism are synthesized by multiobjective optimization on the basis of inverse kinematics model. Moreover, the workspace determination and the FEA analysis of the optimized mechanism are also performed. Finally, a high-precision pointing prototype is fabricated and the performance testing has been implemented, which validate the effectiveness of the proposed system.

A novel analytical model for flexure-based proportion compliant mechanisms

Abstract This paper proposes a novel analytical model for flexure-based proportion compliant mechanisms. The displacement and stiffness calculations of such flexure-based compliant mechanisms are formulated based on the principle of virtual work and pseudo rigid body model (PRBM). According to the theory and method, a set of closed-form equations are deduced in this paper, which incorporate the stiffness characteristics of each flexure hinge, together with the other geometric and material properties of the compliant mechanism. The rotation center point for a corner-filleted flexure hinge is investigated based on the finite element analysis (FEA) and PRBM. An empirical equation for the rotational angle is fitted in this paper in order to calculate accurately the position of the end-point of the flexure hinge. The displacement proportion equation for such mechanisms is derived according to the new approach. Combining the new proposed design equation and the existed stiffness equation, a new proportion compliant mechanism with corner-filleted flexure hinges is designed by means of the least squares optimization. The designed models are verified by finite element analysis.

Planar Compliances of Symmetric Notch Flexure Hinges: The Right Circularly Corner-Filleted Parabolic Design

This study proposes a general analytical compliance model for symmetric notch flexure hinges composed of segments with constant width and analytically defined variable thicknesses. Applying serial combination and longitudinal/transverse mirroring of base segments, the in-plane compliances of the full flexure are obtained as functions of one quarter-flexure compliances. The new right circularly corner-filleted parabolic flexure hinge is introduced as an illustration of the general analytical modeling algorithm. Experimental testing and finite element simulation confirm the analytical model predictions for an aluminum flexure prototype. The planar compliances sensitivity to the relevant geometric parameters is also studied.

New empirical stiffness equations for corner-filleted flexure hinges

Abstract. This paper investigates the existing stiffness equations for corner-filleted flexure hinges. Three empirical stiffness equations for corner-filleted flexure hinges (each fillet radius, r, equals to 0.1 l; l, the length of a corner-filleted flexure hinge) are formulated based on finite element analysis results for the purpose of overcoming these investigated limitations. Three comparisons made with the existing compliance/stiffness equations and finite element analysis (FEA) results indicate that the proposed empirical stiffness equations enlarge the range of rate of thickness (t, the minimum thickness of a corner-filleted flexure hinge) to length (l), t/l (0.02 ≤ t/l ≤ 1) and ensure the accuracy for each empirical stiffness equation under large deformation. The errors are within 6% when compared to FEA results.

Hybrid flexure hinges

This paper designs and analyzes the hybrid flexure hinge composed of half a hyperbolic flexure hinge and half a corner-filleted flexure hinge. As it is transversely asymmetric, it has different performance when the fixed and free ends switch. Considering the diversion of rotation center from midpoint, closed-form equations are formulated to characterize both the active rotation and all other in-plane parasitic motion by the Castigliano's second theorem. The maximum stress is evaluated as well. These equations are verified by the finite element analysis and experimentation. The compliance precision ratios are proposed to indicate flexure hinges' ability of preserving the rotation center when they have the same displacement at the free end. The hybrid flexure hinges are compared with five kinds of common notch flexure hinges (circular, corner-filleted, elliptical, hyperbolic, and parabolic flexure hinges) quantitatively based on compliance, precision, compliance precision ratios, and the maximum stress. Conclusions are drawn regarding the performance of these six kinds of flexure hinges.

Design methodology and performance analysis of application-oriented flexure hinges

Flexure hinges are widely employed in miniature and ultra-precision equipments with the development of precision engineering. In this paper, Castigliano's theorem and Labotto quadrature formula are utilized to derive the compliance matrix. An exclusive longitudinal section of corner-filleted flexure hinges is proposed and the curve of the cross-section is expressed by basic design parameters (r0, d, and l) and machining error parameter (η). The influences of parameters are analyzed by the defined evaluation indexes, i.e., rotation capacity, relative flexibility, and relative rotation error, which are used to assess the quality of flexure hinges. The analysis results indicate small d and optimized values of r0, l, and η will improve flexure hinges' performances. The proposed method is verified by finite element method and experiments within a 5% margin of error.

An Improved Puncture Access Tip-Retraction Mechanism

An Improved Puncture Access Tip-Retraction Mechanism

Multi-Agent Deployment based on Homogenous Maps and a Special Inter-Agent Communication Protocol

This paper proposes a novel analytical model for flexure-based proportion compliant mechanisms. The displacement and stiffness calculations of such flexure-based compliant mechanisms are formulated based on the principle of virtual work and pseudo rigid body model(PRBM). According to the theory and method, a set of closed-form equations are deduced in this paper, which incorporate the stiffness characteristics of each flexure hinge, together with the other geometric and material properties of the compliant mechanism. Displacement proportion, input stiffness, and output stiffness calculations can simply be performed for any serial compliant mechanism. Corner-filleted and circular flexure hinges that are utilized as connectors in proportion compliant mechanisms in this paper. Two types of flexure-based compliant proportion mechanisms based on the novel analytical model are designed and optimized based on these proposed equations. Finite element analysis results show that these design equations are reliable and easier to be used in the design of such proportion compliant mechanisms. This proposed novel analytical model gives a new viewpoint on the design of flexure-based proportion compliant mechanisms.Multi-Agent Deployment based on Homogenous Maps and a Special Inter-AgentCommunication Protocol

A Novel Analytical Model for Flexure-based Proportion Compliant Mechanisms

This paper proposes a novel analytical model for flexure-based proportion compliant mechanisms. The displacement and stiffness calculations of such flexure-based compliant mechanisms are formulated based on the principle of virtual work and pseudo rigid body model(PRBM). According to the theory and method, a set of closed-form equations are deduced in this paper, which incorporate the stiffness characteristics of each flexure hinge, together with the other geometric and material properties of the compliant mechanism. Displacement proportion, input stiffness, and output stiffness calculations can simply be performed for any serial compliant mechanism. Corner-filleted and circular flexure hinges that are utilized as connectors in proportion compliant mechanisms in this paper. Two types of flexure-based compliant proportion mechanisms based on the novel analytical model are designed and optimized based on these proposed equations. Finite element analysis results show that these design equations are reliable and easier to be used in the design of such proportion compliant mechanisms. This proposed novel analytical model gives a new viewpoint on the design of flexure-based proportion compliant mechanisms.Multi-Agent Deployment based on Homogenous Maps and a Special Inter-AgentCommunication Protocol

A generalized analytical compliance model for transversely symmetric three-segment flexure hinges

This paper presents a generalized compliance model for a three-segment notch flexure hinge with transverse symmetry. This flexure hinge configuration is most frequently employed in planar-motion, small-displacement compliant mechanisms. The axial and bending compliances are derived for this flexure hinge based on the compliances of two flexure components. The derivation is generalized such that it can be applied to various segment geometries. Using this open-ended model, a three-segment right elliptical corner-filleted flexure hinge design was analyzed. This geometric configuration introduces additional geometric parameters, which can be used to optimize the compliance of the flexure hinge without modifying its gross dimensions. The results of the analysis were validated in part by modifying the geometric parameters of the center segment and elliptical corner fillets to form limiting cases corresponding to several previously investigated configurations, namely right elliptical, three-segment right circular corner-filleted, and right circular geometries. Finite element analysis simulation and experimental testing were used to further validate the three-segment right elliptical corner-filleted analytical model. Additional simulations based on the analytical model were performed to highlight the influence of geometric parameters on compliances and to investigate shear effects for short flexure hinges.

Precision of Rotation Analysis of Two-axis Rectangular Cross-section Corner-filleted Flexure Hinges

A two–axis rectangular cross–section corner–filleted flexure hinge as an alternative to the conventional flexure hinges for 3D multi–degrees of freedom compliant mechanisms is presented. The 3D mechanical model of two–axis flexure hinge is established,and the precision of rotation of the flexure hinge is developed on the basis of Castigliano's theorem. The closed–form formulas for the flexure hinge are obtained by the method of substitution. Aiming at errors arising from rotation center deviation of the flexure hinge,the results show that compared with analytical model and the finite element simulation,the error margins are within 7%. It is prove that the analytical model is accurate. Finally,the influence of the structural parameters on the precision of rotation of the flexure hinge is analyzed,and it is concluded that the precision is proportional to the Young's modulus or the shear modulus of the material. When the minimum thickness δ and the minimum width b of the flexure hinge are defined,whether the precision of rotation of the flexure hinge reduces or improves depending on the increment or decrement of the radius R or the beam length l. But the influence of the beam length l is more obvious. When the radius R and the beam length l of the flexure hinge are defined,whether the precision of rotation of the flexure hinge is improved or reduced depends on the increment or decrement of the minimum thickness δ or the minimum width b. Some theoretical principles for engineering design of flexure hinges are provided from the above conclusions.

Stiffness characterization of corner-filleted flexure hinges

The paper formulates the closed-form stiffness equations that can be used to characterize the static, modal, and dynamic behavior of single-axis corner-filleted flexure hinges, which are incorporated into macro/microscale monolithic mechanisms. The derivation is based on Castiliagno’s first theorem and the resulting stiffness equations reflect sensitivity to direct- and cross-bending, axial loading, and torsion. Compared to previous analytical work, which assessed the stiffness of flexures by means of compliances, this paper directly gives the stiffness factors that completely define the elastic response of corner-filleted flexure hinges. The method is cost-effective as it requires considerably less calculation steps, compared to either finite element simulation or experimental characterization. Limit calculations demonstrate that the known engineering equations for a constant cross-section flexure are retrieved from those of a corner-filleted flexure hinge when the fillet radius becomes zero. The analytical model results are compared to experimental and finite element data and the errors are less than 8%. Further numerical simulation based on the analytical model highlights the influence of the geometric parameters on the stiffness properties of a corner-filleted flexure hinge.