Optimizing the Qusai-static Folding and Deploying of Thin-Walled Tube Flexure Hinges with Double Slots

The thin-walled tube flexure（TWTF） hinges have important potential application value in the deployment mechanisms of satellite and solar array, but the optimal design of the TWTF hinges haven＇t been completely solved, which restricts their applications. An optimal design method for the qusai-static folding and deploying of TWTF hinges with double slots is presented based on the response surface theory. Firstly, the full factorial method is employed to design of the experiments. Then, the finite element models of the TWTF hinges with double slots are constructed to simulate the qusai-static folding and deploying non-linear analysis. What＇s more, the mathematical model of the TWTF flexure hinge quasi-static folding and deploying properties are derived by the response surface method. Considering of small mass and high stability, the peak moment of quasi-static folding and deploying as well as the lightless are set as the objectives to get the optimal performances. The relative errors of the objectives between the optimal design results and the FE analysis results are less than 7%, which demonstrates the precision of the surrogate models. Lastly, the parameter study shows that both the slots length and the slots width both have significant effects to the peak moment of quasi-static folding and deploying of TWTF hinges with double slots. However, the maximum Mises stress of quasi-static folding is more sensitive to the slots length than the slots width. The proposed research can be applied to optimize other thin-walled flexure hinges under quasi-static folding and deploying, which is of great importance to design of flexure hinges with high stability and low stress.

Kinematics modeling of a 6-PSS parallel mechanism with wide-range flexure hinges

A novel 6-PSS flexible parallel mechanism was presented,which employed wide-range flexure hinges as passive joints.The proposed mechanism features micron level positioning accuracy over cubic centimeter scale workspace.A three-layer back-propagation(BP) neural network was utilized to the kinematics analysis,in which learning samples containing 1 280 groups of data based on stiffness-matrix method were used to train the BP model.The kinematics performance was accurately calculated by using the constructed BP model with 19 hidden nodes.Compared with the stiffness model,the simulation and numerical results validate that BP model can achieve millisecond level computation time and micron level calculation accuracy.The concept and approach outlined can be extended to a variety of applications.

Reliability Analysis of Flexure Hinge Based on Kriging Method

The uncertainty widely exists in the engineering practice.Therefore,it is necessary to research the effect of uncertainty on the structural system. In this paper,the reliability and sensitivity of the flexure hinge, which is the key component of the compliant mechanisms,are investigated. The results of the reliability analysis can effectively guide the engineer to design and optimize the flexure hinge. In order to improve the calculating efficiency,the kriging method is introduced to estimate the failure probability and reliability sensitivity.

Simulation optimal design of a compliant mechanism with circular notch flexure hinges based on the equivalent beam methodology

This paper presents an in-depth study of Equivalent beam model (EBM).Firstly three-dimensional (3D) finite element analysis (FEA) model for circular flexure hinge developed by Zettl et al.was verified by the comparison with Smith's experimental results and the 3D FEA model was feasible within 5.5% error.Then the accuracy of Timoshenko short-beam due to shear force was verified based on finite element method.The results showed that the EBM has good accuracy within 5% error for 1≤r/t≤3.Finally the EBM methodology was applied for the simulation optimal design of a bridge-type compliant mechanism.The results showed that the EBM methodology has very high numerical efficiency and satisfactory accuracy for simulation optimal design of planar compliant mechanism with flexure hinges.

A large workspace flexure hinge-based parallel manipulator system

Parallel manipulator systems as promising precision devices are used widely in current researches. A novel large workspace flexure parallel manipulator system utilizing wide-range flexure hinges as passive joints is proposed in this paper, which can attain sub-micron-seale precision over the cubic centimeter motion range. This paper introduces the mechanical system architecture based on the wide-range flexure hinges, analyzes the kinematics via stiffness matrices, presents the control system configuration and control strategy, and finally gives the system performance test results.

A simple compliance modeling method for flexure hinges

Various types of flexure hinges have been introduced and implemented in a variety of fields due to their superior performances.The Castigliano’s second theorem,the Euler–Bernoulli beam theory based direct integration method and the unit-load method have been employed to analytically describe the elastic behavior of flexure hinges.However,all these methods require prior-knowledge of the beam theory and need to execute laborious integration operations for each term of the compliance matrix,thus highly decreasing the modeling efficiency and blocking practical applications of the modeling methods.In this paper,a novel finite beam based matrix modeling(FBMM)method is proposed to numerically obtain compliance matrices of flexure hinges with various shapes.The main concept of the method is to treat flexure hinges as serial connections of finite micro-beams,and the shearing and torsion effects of the hinges are especially considered to enhance the modeling accuracy.By means of matrix calculations,complete compliance matrices of flexure hinges can be derived effectively in one calculation process.A large number of numerical calculations are conducted for various types of flexure hinges with different shapes,and the results are compared with the ones obtained by conventional modeling methods.It demonstrates that the proposed modeling method is not only efficient but also accurate,and it is a more universal and more robust tool for describing elastic behavior of flexure hinges.

A closed-form nonlinear model for spatial Timoshenko beam flexure hinge with circular cross-section

Beam flexure hinges can achieve accurate motion and force control through the elastic deformation. This paper presents a nonlinear model for uniform and circular cross-section spatial beam flexure hinges which are commonly employed in compliant parallel mechanisms. The proposed beam model takes shear deformations into consideration and hence is applicable to both slender and thick beam flexure hinges. Starting from the first principles, the nonlinear strain measure is derived using beam kinematics and expressed in terms of translational displacements and rotational angles. Second-order approximation is employed in order to make the nonlinear strain within acceptable accuracy. The natural boundary conditions and nonlinear governing equations are derived in terms of rotational Euler angles and subsequently solved for combined end loads. The resulting end load-displacement model, which is compact and closed-form, is proved to be accurate for both slender and thick beam flexure using nonlinear finite element analysis. This beam model can provide designers with more design insight of the spatial beam flexure and thus will benefit the structural design and optimization of compliant manipulators.

Design and Dynamic Modeling of a 2-DOF Decoupled Flexure-Based Mechanism

Flexure mechanisms with decoupled characteristics have been widely utilized in precision positioning applications.However,these mechanisms suffer from either slow response or low load capability.Furthermore,asymmetric design always leads to thermal error.In order to solve these issues,a novel 2-DOF decoupled mechanism is developed by monolithically manufacturing sets of statically indeterminate symmetric（SIS） flexure structures in parallel.Symmetric design helps to eliminate the thermal error and Finite Element Analysis（FEA） results show that the maximum coupling ratio between X and Y axes is below 0.25% when a maximum pretension force of 200 N is applied.By ignoring the mass effect,all the SIS flexure structures are simplified to ＂spring-damper＂ components,from which the static and dynamics model are derived.The relation between the first resonant frequency of the mechanism and the load is investigated by incorporating the load mass into the proposed dynamics model.Analytical results show that even with a load of 0.5 kg,the first resonant frequency is still higher than 300 Hz,indicating a high load capability.The mechanism＇s static and dynamic performances are experimentally examined.The linear stiffnesses of the mechanism at the working platform and at the driving point are measured to be 3.563 0 N·μm-1 and 3.362 1 N·μm-1,respectively.The corresponding estimation values from analytical models are 3.405 7 N·μm-1 and 3.381 7 N·μm-1,which correspond to estimation errors of-4.41% and 0.6%,respectively.With an additional load of 0.16 kg,the measured and estimated first resonant frequencies are 362 Hz and 365 Hz,respectively.The estimation error is only 0.55%.The analytical and experimental results show that the developed mechanism has good performances in both decoupling ability and load capability;its static and dynamic performance can be precisely estimated from corresponding analytical models.The proposed mechanism has wide potentials in precision positioning applications.

LOADS INFLUENCE ANALYSIS ON NOVEL HIGH PRECISION FLEXURE PARALLEL POSITIONER

A large workspace flexure parallel positioner system is developed, which can attain sub-micron scale accuracy over cubic centimeter motion range for utilizing novel wide-range flexure hinges instead of the conventional mechanism joints. Flexure hinges eliminate backlash and friction, but on the other hand their deformation caused by initial loads influences the positioning accuracy greatly, so discussions about loads＇ influence analysis on this flexure parallel positioner is very necessary. The stiffness model of the whole mechanism is presented via stiffness assembly method based on the stiffness model of individual flexure hinge, And the analysis results are validated by the finite element analysis （FEA） simulation and experiment tests, which provide essential data to the practical application of this positioner system.

Micro-displacement amplifying mechanism driven by piezoelectric actuator

Piezoelectric actuator has high stiffness, high frequency and infinite control precision, but a short output displacement which is often 1/1 000 of its length. In order to meet the requirements that tools feeding should be long-travel, high-frequency and high-precision in non-circular precision turning, a new one-freedom flexure hinge structure is put forward to amplify the output displacement of piezoelectric actuator. Theoretical analysis is done on the static and dynamic characteristics of the structure, differential equations are presented, and it is also verified by the finite element method. It's proved by experiments that the output displacement of the structure is 293 μm and its resonant frequency is 312 Hz.

DEVELOPMENT OF A 3-DOF MICRO-POSITIONING WORKPIECE TABLE

In order to achieve active grinding control, a novel numerical controlmicropositioning workpiece table with a resolution of 6 nm has been developed. The table is drivenby three piezoelectric actuators mounted on the base. An elastic structure with three half-notchflexure hinges is designed to apply preload to the piezoelectric actuators. The position of flexurebinges is also elaborately designed with consideration to reduce the bending deformation of themoving part. Three capacitive sensors are used to form close loop control system. Considering thetable as a damped 3-DOF mass-spring system, the models of static and dynamic stiffness and errorowing to the action of external forces have been established. In order to make the table have highresolution and positioning accuracy, an error compensation algorithm is implemented by using theestablished models. The experimental testing has been carried out to verify the performance of theworkpiece table and the established models of the micropositioning workpiece table.

A Novel 2D Piezo-Nanopositioning Stage Based on Triangle Amplifier Mechanism

To satisfy the demand on dynamic performance and load characteristics of piezoelectric actuators in aeronautics and astronautics fields,a novel 2Dpiezo-nanopositioning stage utilizing a triangle amplifier mechanism is proposed.The stage is driven by piezoelectric rhombic units in both X and Ydirections,which is composed of four piezoelectric stacks.Theoretical static model develops the relationships among output force,displacement,static stiffness and the structure parameters of the platform.The experimental results of the prototype show that the output performances in X and Ydirections are similar and both of them are within an 8% deviation from the theoretical values.The stroke of the stage reaches 41.6μm and 42.9μm in Xand Ydirections,respectively,and is directly proportional to the amplitude of the input sinusoidal voltage 10 Hz.Moreover,the nano-positioning stage is featured with bidirectional symmetrical output characteristic and millisecond starting characteristic,whose minimum output displacement step is 50 nm.

An Inverse Kinematic Analysis Modeling on a 6-PSS Compliant Parallel Platform for Optoelectronic Packaging

Multiple degree of freedom motion platform is always one of the important components in optoelectronic packaging systems,its characteristics have a vital impact on the performances of optoelectronic packaging.This paper presents a 6-Prismatic-Spherical-Spherical compliant parallel platform for optoelectronic packaging.This platform is a kind of parallel layout structure,which uses the piezoelectric motors as active joints and the large-stroke flexure hinges are employed as passive joints.An inverse kinematic modeling based on elastokinematic analysis is analyzed and deduced.The elastokinematic analysis considers the elastic deformation of the large-stroke flexure hinges in movement process,and improves the positioning accuracy of the compliant parallel platform in applications.The finite element analysis model and the prototype of the compliant parallel platform are developed,and the validity of the proposed method is finally verified.This paper provides a theoretical reference and experimental data for the inverse kinematic analysis of six degrees of freedom motion compliant parallel platforms with large-stroke flexure hinges.

Development of XY scanner with minimized coupling motions for high-speed atomic force microscope

The design and fabrication processes of a novel scanner with minimized coupling motions for a high-speed atomic force microscope （AFM） were addressed. An appropriate design modification was proposed through the analyses of the dynamic characteristics of existing linear motion stages using a dynamic analysis program, Recurdyn. Because the scanning speed of each direction may differ, the linear motion stage for a high-speed scanner was designed to have different resonance frequencies for the modes, with one dominant displacement in the desired directions. This objective was achieved by using one-direction flexure mechanisms for each direction and mounting one stage for fast motion on the other stage for slow motion. This unsymmetrical configuration separated the frequencies of two vibration modes with one dominant displacement in each desired direction, and hence suppressed the coupling between motions in two directions. A pair of actuators was used for each axis to decrease the crosstalk between the two motions and give a sufficient force to actuate the slow motion stage, which carried the fast motion stage, A lossy material, such as grease, was inserted into the flexure hinge to suppress vibration problems that occurred when using an input triangular waveforrn. With these design modifications and the vibration suppression method, a novel scanner with a scanning speed greater than 20 Hz is achieved.

Compliance Modeling of a Compliant Stage with Symmetric Configuration

This paper presents the compliance modeling of a compliant stage with symmetric configuration. Empirical compliance equations for the circular flexure hinge are first introduced. Using the matrix method, the output compliance of a compliant stage with symmetric configuration is then obtained. Finally, the compliances derived from the proposed theoretical model and finite element analysis (FEA) are compared. It indicates that the results calculated by the theoretical model are in good agreement with those derived from FEA, which demonstrates the accuracy of the theoretical model.

Characteristics of Statically Indeterminate Symmetric Flexure Structures

Statically indeterminate symmetric(SIS)flexure structures are symmetric structures with“clamped-clamped”boundary conditions.The static indeterminacy and topological symmetry significantly attenuate the parasitic motions associated with statically determinate flexure structures.Hence,SIS flexure structures feature decoupled linear and angular motions,improved motion accuracy,high stiffness,and high stability.Although SIS flexure structures have been more frequently utilized as prismatic joints,they can also be utilized as revolute joints.This study systematically investigates the characteristics of SIS flexure structures.Based on the unified compliance models of a single flexure hinge,analytical compliance models of two fundamental types of SIS flexure structures are established.In 1-degree-of-freedom or planar applications,multiple SIS-based structures can also be integrated into various configurations to transmit linear or angular motions.Corresponding stiffness models are also established.The characteristics and possible applications of the SIS flexure structures are computationally investigated through case studies.Ultimately,several SIS prototypes are manufactured,and the modeling accuracy of the established stiffness models is experimentally verified.

A high precision profilometer based on vertical scanning microscopic interferometry

A profilometer used for 3 dimension measurement of micro-surface topography is presented. The instrument is based on the vertical scanning microscopic interferometry （VSMI）. A Linnik type interference microscope is used and the interferograms which present changes of surface profile are recorded with a CCD camera. A developed nano-positioning work stage with an integrated optical grating displacement measuring system realizes the precise vertical scanning motion during profile measurement. By a white-light phase shifting algorithm of arbitrary step, frames of interferograms are processed by a computer to rebuild and evaluate the measured profile. Because of the specialty of VSMI, the profilometer is suitable for both smooth and rough surface measurement. It can also be used to measure curved surfaces, dimension of micro electro mechanical systems （MEMS）, etc. The vertical resolution of the profilometer is 0.5 nm, and lateral resolution 0.5 μm.

Notch Flexure as Kirigami Cut for Tunable Mechanical Stretchability towards Metamaterial Application

Kirigami is an art of paper cutting,which can be used in mechanical metamaterials,actuators,and energy absorption based on its deployable and load-deflection characteristics.Traditional cuts with zero width produce undesirable plastic deformation or even tear fracture due to stress concentration in stretching.This study proposes to enlarge the cut width into a notch flexure,which is applied to an orthogonality-cutted kirigami sheet,which buckles out of plane into a 3D configuration patterns under uniaxial tension.The use of compliant beam as the notch makes the stress distribution around the cuts more uniform in both elastic and elastoplastic regime.The experimental and numerical results show that by tuning the geometric parameters of cuts and material properties of the sheets,the trigger condition of 3D patterns can be adjusted.Potential capability of tunable phononic wave propagation in this kirigami-inspired metamaterial is demonstrated.This design methodology offers a theoretical guide for kirigami-based structures.

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 insideinstalled 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.

Design and experiment of concentrated flexibility-based variable camber morphing wing

The morphing wing has a significant positive effect on the aerodynamic performance of the aircraft.This paper describes a leading-edge of variable camber wing with concentrated flexibility based on the geared five-bar mechanism.The driving points of morphing skin formed by the glass fibre composite sheet were optimized to make the skin deformation smooth.A geared fivebar kinematic mechanism rigidly connected to the skin was proposed to drive the leading-edge deformation.Besides,a new kind of concentrated flexure hinge was designed using the pseudorigid-body method and applied to the joint between the rigid mechanism and the skin.Finally,the leading-edge prototypes with traditional hinges and flexure hinges were produced,respectively.The feasibility of the concentrated flexibility leading-edge was verified through the comparative experiments of ground deformation.Simultaneously,aerodynamic analysis was carried out to compare the concentrated flexure leading-edge wing with the original airfoil.