Monolithic Flexure Research Articles

Optimal Design of the Monolithic Flexure Mount for Optical Mirror Using Response Surface Method

An optimal design of a simple beam-shaped flexure hinge mount supporting an optical mirror is presented. An optical mirror assembly is an opto-mechanically coupled system as the optical and mechanical behaviors interact. This side-supporting mount is flexible in the radial direction and rigid for the remaining degrees of freedom to support the mirror without transferring thermal load. Through thermo-elastic, optical and eigenvalue analysis, opto-mechanical performance was predicted to establish the objective functions for optimization. The key design parameters for this flexure are the thickness and length. To find the optimal values of design parameters, response surface analysis was performed using the design of experiment based on nested FCD. Optimal design candidates were derived from the response surface analysis, and the optimal design shape was confirmed through Opto-mechanical performance validation analysis.

Development of a Three-Axis Monolithic Flexure-Based Ground Reaction Force Sensor for Various Gait Analysis

In this letter, we developed a monolithic flexure-based three-axis ground reaction force (GRF) sensor to analyze various gaits, including walking, running, and jumping. The GRF sensor requires different force capacities on each axis. In order to satisfy the force range requirements, a simple circular cross-section flexure was designed. The use of a monolithic flexure allows the sensor to have broad measurement range with enhanced durability in a compact, simple and lightweight structure. The proposed sensor can measure vertical force up to 2400 N and shear force up to 240 N that can measure wide range of GRF for walking, running and jumping. The deformation of the flexure under applied force is measured through capacitance changes and these values are converted into the three-axis force. The performance of the sensor was evaluated through several experiments. An outsole GRF measurement system was designed by embedding two developed sensors. The resultant GRF data during several in-place motions were measured with the developed system.

A monolithic linear motion platform driven by a piezoelectric and fluidic pressure-fed dual mechanism.

This paper presents a novel dual-mode motion mechanism capable of achieving nanopositioning on a monolithic linear motion platform. Unlike conventional dual-mode stages that use piezoelectric (PZT)- and electromagnetic-combined or similar actuation mechanisms comprising two separate motion axes, the dual-mode actuation was developed by combining a PZT for a coarse motion and a fluidic pressure-fed mechanism (FPFM) for a fine motion and was implemented in a monolithic flexure stage fabricated by metal additive manufacturing. The FPFM actuates the flexure stage by pressuring the media in the fluidic channels created inside the flexure spring structures. Experimental tests were performed to investigate the performance of the dual-mode linear motion platform. The stiffness, damping, and frequency response functions of the dual-mode stage were experimentally characterized. The proportional-integral-differential control combined with dual-mode control was employed to control the position of the flexure stage while bidirectionally controlling the flow of compressed air for a fine motion. The FPFM motion showed a good response to 1nm stepwise input (every 10 psi), and it was implemented to provide up to ∼10nm fine motion along with the PZT coarse motion (1 µm). The hysteresis characteristics of the FPFM were also characterized and compensated to track the positioning error.

Contactless Optical Packaging Concept for Laser to Fiber Coupling

A novel method for the laser to fiber coupling is presented in which coarse alignment is achieved through micromachined v-grooves and mirrors in a fused silica substrate. Furthermore, fine repositioning is done in a noncontact manner by using a femtosecond laser to induce localized nanoscopic volume changes in specific locations within the bulk of the substrate, which, once combined with monolithic flexures within the substrate, produces a highly controlled motion. Using this principle, we overcome inherent manufacturing/assembly tolerances to achieve near theoretical coupling efficiency in a permanent manner. This proof of concept demonstrates a novel packaging principle where a sub-nm positioning resolution is achieved over tens of micrometers range of motion, efficiently overcoming intrinsic manufacturing tolerances.

A 3-DOF piezoelectric driven nanopositioner: Design, control and experiment

In this paper, a novel 3-degree-of-freedom (DOF) nanopositioner was investigated in order to position objects with nanometer scale accuracy. Nanopositioners are used in a variety of real-world applications, e.g. biomedical technology and nanoassembly. In this work, a nanopositioner was firstly designed with the flexure diaphragm guider, capacitive sensors and walking piezoelectric actuators. The specifically designed monolithic flexure diaphragm guider was able to significantly restrict motions in the other unwanted directions. The walking piezoelectric actuator can enable the developed nanopositioner to have nanometer scale positioning accuracy and a large travel range. Then a closed-loop sliding mode control strategy was developed to overcome the effect of the actuator’s speed nonlinearity and its stability was analysed based on Lyapunov theory. Finally, experiments focused on coupling displacement and point-to-point movement were conducted. The observed results revealed that the ratio of coupling displacement to Z displacement was less than 0.1%, which means that the coupling displacement was less than 120 nm during the Z direction travel range of the nanopositioner from −80 μm to 80 μm. Moreover, the positioning accuracy in the Z direction of point-to-point movement was within 10 nm and the dynamic response settled within 0.2 s. Therefore, the experimental results showed that the novel piezoelectric driven nanopositioner has excellent performance in terms of coupling displacement and nanometer scale accuracy for point-to-point movement.

Design of a parallel robot with additively manufactured flexure hinges for a cryogenic work environment

Automation is ubiquitous in today’s industrial landscape and is finding its way into more and more highly specialised applications - also in the field of cryopreservation. The extreme work conditions in cryobanks place exceptionally high demands on the mechanical and electronic components used. The preservation and storage of biological samples take place at temperatures between -130 °C and -196 °C using liquid nitrogen as a cooling medium. The bearings and joints used in industrial parallel kinematic robots (for example, ball bearings or Cardan joints) jam at these ambient parameters and are unsuitable for an application within a cryobank. We, therefore, develop methods and technologies to enable fully automated handling of biological samples under cryogenic working conditions. The basis for this is a parallel kinematic robot structure that allows the drives to be placed outside the cold environment. In contrast, the rest of the robot structure can be actuated in a cryogenic container.In this context, the passive joints for this parallel robot are designed as additively manufactured monolithic flexure hinges. This paper presents the design, simulation, and construction of the parallel robot and focuses on the flexure hinges fabricated using the selective laser melting process (SLM). We describe the design of the flexure hinges, their intended use in the robot, and the experimental setup used for their validation. We also compare the operating parameters recorded in experiments (such as bending angle, bending moment) with the data obtained in finite element method simulations (FEM). In addition, we describe the geometric constraints and deviations of the manufactured joints due to the manufacturing process.

Role of fibre fragmentation on pseudo-ductility of thin-ply [±277/0]s carbon fibre laminates with high modulus 0° plies under compressive and flexural loading

Pseudo-ductile tensile, compressive and flexural behaviour was achieved in a thin-ply carbon fibre [±277/0]s laminate with different fibre types in the angle plies and 0° plies. The laminate with the present layup was tested in both tension and compression, the latter through an unconventional indirect compressive test method using a sandwich beam configuration and the compressive stress was derived by considering the change in position of the neutral axis. The tests demonstrated for the first time that pseudo-ductility and progressive failure can be obtained under compressive loading on thin-ply [±θm/0n]s laminates using a combination of intermediate modulus and high modulus fibre prepregs. Delamination was suppressed throughout the testing and only occurred at the final fracture of the angle plies. Multiple fibre fractures of the 0° plies were obtained within the laminate with the support of the surrounding angle plies in both loading cases. When the laminate was subjected to monolithic flexure, a gradual failure and significant amount of non-linearity occurred. This was primarily due to 0° ply fragmentation on both the compressive and tensile sides of the beam; the fragmentation on both sides resulted in shifts of the neutral axis, retarding the strain increase on the compressive side, delaying the final failure and achieving a higher failure strain in flexure than in compression.

Development of a New Apparatus for SI Traceable Small Mass Measurements Using the Voltage Balance Method at NMIJ

Toward establishing a measurement system for small masses and forces based on the new definition of the kilogram, a measurement apparatus that uses the voltage balance method was developed. The main components of the apparatus are a mass balance mechanism, an automatic mass translation system, and a capacitance actuator for balancing the gravity force acting on the small object and the electrostatic force. The electrostatic force is calibrated by using the electrical methods that are traceable to the electrical standards. Therefore, the voltage balance method realizes SI traceable and absolute measurements of small masses. To improve the method, new technical approaches, such as the use of a monolithic flexure hinge for the balance mechanism, a double equal capacitor system for the electrical control, and a new type of buckling spring, were implemented. To evaluate the performance of the apparatus, an experiment of the mass of a 500- $\mu \text{g}$ aluminum wire weight was conducted. A result of the weighing of the 500- $\mu \text{g}$ weight was $499.8~\mu \text{g}$ . The basic performance of the new apparatus for small mass measurements was confirmed.

The OpenFlexure Block Stage: sub-100 nm fibre alignment with a monolithic plastic flexure stage.

As 3D printers become more widely available, researchers are able to rapidly produce components that may have previously taken weeks to have machined. The resulting plastic components, having high surface roughness, are often not suitable for high-precision optomechanics. However, by playing to the strengths of 3D printing-namely the ability to print complex internal geometries-it is possible to design monolithic mechanisms that do not rely on tight integration of high-precision parts. Here we present a motorised monolithic 3D-printed plastic flexure stage with sub-100 nm resolution that can perform automated optical fibre alignment.

Innovative concept of compliant mechanisms made by additive manufacturing

The complete redesign for Additive Manufacturing of compliant mechanism structures enables CSEM to develop innovative concepts to drastically reduce the need of machining and assembly after additive manufacturing. Support structures under flexure blades are thus minimised and the overall process becomes more streamlined. Moreover, this concept allows us to easily design and produce monolithic cross flexure pivots with interlocked flexible blades. Based on this concept, CSEM is now developing new architectures of Compliant Mechanisms based on Additive Manufacturing (COMAM) for the European Space Agency (ESA) in the frame of a GSTP research project. The past and current work of design, 3D printing and testing on several compliant mechanisms are presented. These demonstrators will be used as use-case for future high-precision and harsh environment applications such as cryogenic and space.

Topology optimization of leaf flexures to maximize in-plane to out-of-plane compliance ratio

In fields requiring precision manipulation, monolithic flexures are frequently used to guide motion. They utilize the structure's predictable elastic deformation, when a force is applied, to facilitate linear and rotational motions. Amongst the several common flexure designs, leaf flexures are the best suited to ‘large’ displacement tasks. Their range is typically restricted by the actuator's supplied force, such that reducing stiffness in the motion direction beneficially increases displacement. However, high out-of-plane stiffness is required to support structural loads and reject parasitic motions. In this work, topology optimization is investigated to maximize the in-plane to out-of-plane compliance ratio of a leaf flexure. The minimization of out-of-plane compliance in leaf flexures is also investigated for comparison. In both cases, the optimized structures resemble trusses. Compliance ratio optimized structures offer performance 1.5 to 6 times greater than standard leaf structures, with reduced mass. From the results, a parameterized flexure design is suggested, which can replace leaf flexures in 3D printed mechanisms. A parallelogram linear flexure guide is analyzed as an example of a practical implementation of the optimized design.

Optimal design of a piezo-actuated 2-DOF millimeter-range monolithic flexure mechanism with a pseudo-static model

Abstract Flexure-based displacement amplifiers are frequently used to magnify the small stroke of piezoelectric actuators. In this paper, a hybrid rhombus-lever multistage displacement amplifier with an improved boundary constraint is proposed to develop a parallel millimeter-range XY monolithic mechanism while retaining a relatively high dynamic frequency. A concise pseudo-static model developed by the authors is utilized to analyze the kinetostatic and dynamic performances of the designed flexure mechanism and then the geometric parameters are optimized in terms of both kinetostatics and dynamics. Different from the previous Lagrange-based dynamic methods for compliant mechanisms, cumbersome calculations of the kinetic and elastic energies as well as adopting Lagrange’s equation are all avoided. With the proposed pseudo-static model, the kinetostatics and dynamics of the flexure mechanism can be analyzed concurrently in a programmed statics-similar way, suggesting its superiority for fast performance prediction and parameter optimization during the early stage of design. Finally, a prototype of the XY monolithic mechanism is manufactured and experimentally tested for evaluating its performances. Experimental results show that the designed flexure mechanism has a motion range in excess of 1.2 mm × 1.2 mm with a resonance frequency of 128 Hz. The cross-coupling error is measured to be less than 2%, indicating an acceptable decoupling performance.

Design of an adjustable bipod flexure for a large-aperture mirror of a space camera.

An adjustable bipod flexure (ABF) technique for a large-aperture mirror of a space camera is presented. The proposed flexure mount can decrease the surface distortions caused by the machining error and the assembly error of the mirror assembly (MA) in a horizontal optical testing layout. Through the analysis of the compliance matrix of conventional bipod flexure, the positional relationship between the rotation center and the apex of the flexure is investigated. Then, the principle of the adjustable flexure, known as the trapezoidal switching principle, is proposed based on the analysis result. The structure and application of the flexure are also described. The optical performance of the mirror mounted by the adjustable flexures in different misalignments was performed using finite element methods. The result shows that the astigmatic aberration due to gravity is effectively reduced by adjusting the mount, and the root-mean-square value of the mirror can be minimized with the misalignment between the flexure pivot and the neutral plane minimized. New monolithic bipod flexures, based on the optimal regulating variable Δu according to the measurement results, are manufactured to replace the ABFs to secure the mirror's safety against launch loads. Modal analysis verified the mechanical safety of the MA with respect to the new monolithic flexures.

Determinate Synthesis of Symmetrical, Monolithic Tip–Tilt–Piston Flexure Stages

This paper mainly deals with the determinate design/synthesis of a class of symmetrical and monolithic flexure mechanisms. Each is composed of six identical in-plane wire beams with uniform square cross sections. These flexure stages can provide three out-of-plane tip–tilt–piston motions for applications in high-precision or miniaturization environments. A generic symmetrical structure is proposed at first with a group of defined parameters considering constraint and noninterference conditions. Normalized static analytical compliance entries for the diagonal compliance matrix of a generic structure are derived and symbolically represented by the parameters. Comprehensive compliance analysis is then followed using the analytical results, and quick insights into the effects of parameters on compliances in different directions are gained. Case studies without and with actuation consideration are finally discussed. As a second contribution, a physical prototype with three actuation legs is monolithically fabricated (using computer numerical control milling machining), kinematically modeled, and experimentally tested, which shows that the desired out-of-plane motion can be generated from the in-plane actuation.

Measurement of cantilever spring constant using an electrostatic sensing and actuating force measurement system

We report the measurement of the spring constant of a cantilever using an electrostatic sensing and actuating force measurement system. The force measurement system consists of three main parts: a monolithic flexure stage, a three-electrode capacitor, and a digital controller. The most important feature of the system is the utilization of the three-electrode capacitor simultaneously as a position sensor and an electrostatic force generator. This allows us to constantly adjust and maintain gap distances between three electrodes, which is critical for this design to generate precise electrostatic compensation force. The force measurement system was partly upgraded and its performance was improved. The uncertainty estimation for the upgraded force measurement system is given. By measuring the spring constant of a commercially available cantilever force sensor, we demonstrate that the force measurement system is capable of calibrating the cantilever spring constant. The spring constant of the cantilever force sensor was measured to be (2227 ± 63) mN m−1 (coverage factor k = 2), corresponding to a relative expanded uncertainty of 2.8%.

Comparison of milligram scale deadweights to electrostatic forces

This paper presents a comparison of milligram scale deadweights to electrostatic forces via an electrostatic sensing & actuating force measurement system. The electrostatic sensing & actuating force measurement system is designed for measuring force below 200 mN with an uncertainty of few nanonewton. The force measurement system consists of three main components: a monolithic flexure stage, a three-electrode capacitor for position sensing and actuating and a digital controller. The principle of force measurement used in this system is a static force balance, i.e. a force to be measured is balanced by a precisely controlled, electrostatic force. Four weights of 1 mg to 10 mg were tested in this comparison. The results of the comparison showed that there exist extra stray electrostatic forces between the test weights and the force measurement system. This extra electrostatic force adds a bias force to the measurement result, and was different for each weight. In principle, this stray electrostatic force can be eliminated by installing a metal housing to isolate the test weight from the system. In the first section, we briefly introduce the electrostatic sensing and actuating force measurement system, and then we describe the experimental setup for the comparison and the results. Finally, we give a discussion and outlook.

EBSD-Analysis of Microstructural Changes Below Wire-EDMed Surfaces

An example for such an application are notched monolithic flexure hinges (cf. Fig. 1), which are analyzed within a larger project for the construction of micro-manipulators at RWTH Aachen University. During the bending of such hinges, the rim zone of the notch is undergoing high tensile strain. In order to predict the operating functionality, the microstructural damage introduced by W-EDM cutting therefore needs to be known in dependence of the cutting parameters.

Siskiyou Corporation

Abstract With over 40 years experience, Siskiyou provides a diverse range of micromanipulators, microscope sample positioners, motion control systems, and modular opto-mechanical building blocks to life science and photonics researchers, enabling applications from precision beam control to patch clamping. As a company, our goal is simple—to offer the highest quality product at an economical price and to support our customers with superior service. All products are designed and manufactured in the United States—in Grants Pass, OR. We were the first company to offer 80 pitch adjusters and we are the only manufacturer of monolithic flexures for azimuth/elevation adjustment. Siskiyou specializes in putting many axes of adjustment in a small volume. Let us help build your next experiment!!

Bipolar Piezoelectric Buckling Actuators

A nonlinear piezoelectric amplification mechanism utilizing structural buckling is presented, and its static and dynamic properties are measured and analyzed. Buckling is a pronounced nonlinear effect that occurs at a structurally singular point. A small piezoelectric displacement on the order of 10 μm results in a large buckling displacement on the order of millimeter. Furthermore, the usable stroke is doubled if both sides of the singular point can be reached resulting in bipolar motion. Despite the large gain, buckling is an erratic, singular phenomenon; the side on which deflection will occur is unpredictable. In this paper, multiple design concepts are presented for regulating the buckling direction as well as for extending its usable stroke to bipolar motion. Nonlinear force-displacement relationships are modeled and measured. Nonlinear dynamic analysis using phase planes reveals that the buckling actuator can generate bipolar motion above a specific amplitude. Below this amplitude, it generates only monopolar oscillation. The proposed design concepts are implemented on monolithic flexure mechanisms, and prototype buckling actuators are tested to verify the concepts. Experiments show promising results: 20 N of peak-to-peak output force, and 6.2 mm of bipolar displacement generated by piezoelectric actuators with free displacement of 42 μm.

Contact Mode MEMS Position Sensors with Piezoresistive Detection

Abstract Measuring of linear position with contact MEMS sensors is a promising option for achieving sub-nm resolution, as demanded by micro-/nanotechnology community [1] . The position of specific point of interest can be calculated by bending detection of cantilevers or more complex MEMS flexures via different techniques: optical, capacitive, piezoelectric, etc. Prototyping of strain sensing devices with sidewall piezoresistors has been preferred in the present study due to multiple advantages, like: very few restrictions in flexures design, very high signal sensitivity and linearity, temperature and noise stability and CMOS compatibility. Comprehensive results obtained at characterization of contact MEMS position sensors, comprising two rigid members, monolithic flexures with various layouts and electrically identical piezoresistors for strain detection, are presented. Design approach for setting the sensitivity in the range from 20 μV/μm.V to 2 mV/μm.V has been demonstrated. Recently achieved results report extremely high temperature immunity of the sensor signal.