Flexure Stage Research Articles

Synthesis of parallel flexure stages with decoupled actuators using sum, intersection, and difference of screw systems

Parallel flexure systems (PFS) are used in high-precision positioning systems for a wide range of scientific, medical, and industrial applications. The controllability of the flexure system is optimized when actuators are decoupled and the output of any actuator does not affect the output of the others. In this paper, Screw Theory and Linear Algebra are used to perform the synthesis of parallel flexure systems. New procedures to compute the sum, intersection, and difference of screw systems are presented. These three operations are used to formulate the synthesis of PFS with decoupled actuators completely in terms of the freedom screw systems in combination with a graph representation of the mechanism and the implementation of constraint systems using Blanding’s rules. The methodology is illustrated with the design and redesign of three case studies: (i) a 2-DOF platform with cylindrical motion, (ii) three 3-DOF tip-tilt-piston platforms, and (iii) a 3-DOF platform with planar motion. The kinematic and static analyses for the solutions are performed analytically and then validated using finite element analyses. The designed PFS have very simple structures, high precision, and controllability.

A low-cost confocal microscope for the undergraduate lab

We demonstrate a simple and cost-efficient scanning confocal microscope setup for use in advanced instructional physics laboratories. The setup is constructed from readily available commercial products, and the implementation of a 3D-printed flexure stage allows for further cost reduction and pedagogical opportunity. Experiments exploring the thickness of a microscope slide and the surface of solid objects with height variation are presented as foundational components of undergraduate laboratory projects and demonstrate the capabilities of a confocal microscope. This system allows observation of key components of a confocal microscope, including depth perception and data acquisition via transverse scanning, making it an excellent pedagogical resource.

공간형 위치 결정 스테이지를 위한 타원형 및 포물선형 2 자유도 플렉셔 힌지에 대한 해석

With advancements in semiconductor manufacturing processes and the development of precision processing technology, flexure hinge-based ultra-precision positioning stages are widely used. In the flexure hinge, axial and bending stiffness properties greatly influence positioning performance. This study examined the stiffness properties of elliptic and parabolic 2-degrees-of-freedom (DOF) hinges, which have not been extensively discussed. The Timoshenko beam theory was applied to derive the stiffness equations for the axial and bending directions of each hinge. The stiffness properties were examined in several design conditions by comparing theoretical and finite element analyses. Based on the results of the analyses, an empirical formula in exponential form for the design of an elliptic hinge was constructed through surface-fitting. The elliptic hinge was found to be a better alternative to a circular hinge under certain design conditions by adjusting two design parameters. In the future, we will develop sophisticatedly designed hinges with improved axial and bending stiffness properties compared to the existing circular and elliptic hinges.

Dynamic response and collapse resistance of RC flat plate structures subjected to instantaneous removal of an interior column

Through quasi-static loading regimes, notable research efforts have been made in recent years towards understanding the structural behaviour and resistance mechanism of reinforced concrete (RC) flat plate structures against progressive collapse events. Nevertheless, dynamic responses, being an inherent nature of any progressive collapse, were unable to be adequately studied in these quasi-static studies. Moreover, fewer studies were performed on flat plate structures under dynamic loading conditions, especially their behaviours under large deformations, i.e., the post-punching stages. To fill this research gap, this paper presents three sequential dynamic tests performed on a 1/3-scaled 2 × 2-bay RC flat plate substructure specimen by instantaneously removing the interior column under three levels of additional gravity loads. In these tests, the substructure specimen was able to withstand the gravity loads up to 2.08 times the load capacities recommended by the DoD and GSA guidelines for nonlinear dynamic analyses. The dynamic responses of the specimen in the flexural, punching and post-punching stages were examined in detail. In addition, a high-fidelity finite element model was developed and validated by the experimental test results. The validated numerical model was subsequently used to quantify the dynamic load redistribution patterns, and the influences of two loading considerations (i.e., loading on the slab overhangs and load release time) on the dynamic responses were also investigated. Finally, the dynamic load increase effects were evaluated based on the analysis model results. The obtained load-based dynamic increase factors (DIFs) of the specimen under different gravity loads were between 1.11 and 1.46 in the pre-punching (flexural) stage, whereas they were no more than 1.06 in the post-punching stage.

Investigating the Surface and Microstructure of Electrodeposited Cu Films

Both morphology and microstructure play a crucial role in determining the properties of an electrodeposited polycrystalline thin film and its performance in different applications. We have investigated the morphology of Cu films electrodeposited from a chloride-containing acid sulfate electrolyte by applying a combination of conventional ex-situ AFM and in-situ High-Speed AFM (HS-AFM). For the HS-AFM studies, a film was grown on a microelectrode, 30µm in diameter and imaged in-situ in real time. The high-speed flexure stage of HS-AFM enables it to scan the surface of the film up to 1000 times faster than the conventional AFM [1], which provides many details about how the film growth is proceeding and how the structure coarsens with deposition time [2]. Here, we compare data from films prepared by continuous and pulse deposition. We also present microstructural data obtained with the help of focussed ion beam milling.[1] Oliver D Payton, Loren Picco, and Thomas Bligh Scott. High-speed atomic force microscopy for materials science. International Materials Reviews, 61(8):473-494, 2016.[2] Aswathi Koorikkat, Oliver Payton, Loren Picco, and Walther Schwarzacher. Imaging the surface of a polycrystalline electrodeposited cu film in real time using in situ high-speed AFM. Journal of the Electrochemical Society, 167(16):162510, 2020.

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.

Numerical investigation on RC T-beams strengthened in the negative moment region using NSM FRP rods at various depth of embedment

The application of Near Surface Mounted (NSM) method to strengthen reinforced concrete (RC) members in flexure through the use of Fiber Reinforced Polymer (FRP) rods has become a subject of interest to designers and researchers over the past few years. This technique has been extensively applied, and there is still a need for more experiments, analytical, and numerical studies to determine the effects of their parameters on the flexural performance of RC members. Therefore, a detailed 3D nonlinear finite element (FE) numerical model was developed in this study to predict the load-carrying capacity and the response of RC T-beams strengthened in the negative moment region accurately through the use of NSM FRP rods at different depth of embedment which are placed under three-point bending loading. The model was, however, designed with due consideration for the nonlinear constitutive material properties of concrete, yielding of steel reinforcement, NSM rods, and cohesive behaviors to simulate the contact between two neighboring materials. Moreover, the findings of the numerical simulations were compared with those from the experiments by other investigators which involve two specimens strengthened with NSM FRP rods added to one unstrengthened control specimen. The results, however, showed that the mid-span deflection responses of the predicted FE were in line with the corresponding data from the experiment for all the flexural loading stages. This was followed by the use of the validated FE models to analyze the effect of several properties of the FRP materials to provide more information than the limited experimental data available. It was discovered that the FE model developed is appropriate to be applied practically and economically with more focus on the parametric studies based on design to precisely model and analyze flexural negative moment strengthening for the RC members through the use of NSM FRP rods.

Investigations on piezo actuated micro XY stage for vibration-assisted micro milling

Vibration assisted machining is an advanced non-conventional precision machining technique aiming at improving the machining performance by superimposing a small amplitude, high-frequency vibration either on the tool or on the workpiece. This article presents the mechanical design, electromechanical simulation, and experimentation on the developed prototype of the flexural hinged micro XY stage for the vibration-assisted micro-milling system. The micro XY stage comprises three layers of flexural hinge structure surrounding the central parallel kinematic structure. The finite element analysis method is adopted to evaluate the static structural stiffness and harmonic behaviour. Two multilayer piezoelectric stack actuators drive the micro XY stage in X and Y directions. The experimental results show that the micro XY stage has a vibrating work area of 17.06 µm × 17.11 µm with a hysteresis nonlinearity and cross-coupling displacements on both axes. Therefore, an electromechanical model is essential to compensate for the hysteresis behaviour and cross-coupling displacements. Open-loop tracking control experiments determine the accuracy of the developed electromechanical model. Implementing a combined hysteresis and cross-coupling displacement compensation approach into the electromechanical model resulted in an open-loop tracking error of 7% for the synchronised circular path and a maximum deviation of 0.6 µm from the linear path.

Investigation of side plate connections in an S-CFST column frame under a column-loss scenario

The progressive collapse resistance of four full-scale special-shaped columns composed of concrete-filled steel tubes (S-CFST column)-steel beam assemblies was studied in this paper. The failure modes, deflection profiles, vertical resistance development mechanisms and internal force development at the assumed plastic hinge section under the influence of infilled concrete, various span-to-height ratios of the steel beam and different connection details were compared. The test results showed that the fracture failure of all the specimens first occurred near the full penetration weld of the bottom beam flange or the bottom cover plate at the end of the side plate. Fracture failure of the steel beam web or shear plate occurred through the bolt holes. The beam chord rotation ranged from 0.055 to 0.088. The concrete infilled steel tube improved the ductility of the assembly and resulted in the development of the catenary mechanism, while reducing the span-to-height ratio of the steel beam resulted in the delay of the initiation of the mixed mechanism stage. Additionally, the development of the catenary mechanism was more sufficient for the specimen with the concrete infilled steel tube than the specimen without the concrete infilled steel tube under the same vertical displacement. The results showed that the ACPSP connection can avoid premature fracture of the full penetration weld and improve its progressive collapse resistance. By reducing the span-to-height ratio of the steel beam and using the ACPSP connection, the beam-column assemblies experienced not only the flexural and mixed mechanism stages but also the catenary mechanism stage. The GSPCP connection was proposed to improve the stress concentration in the ACPSP connection. Through further analysis by the verified finite element model, it is evident that the GSPCP connection can further improve the progressive collapse resistance of the S-CFST column-steel beam joint assembly.

Quantification of model uncertainties of the energy-based method for dynamic column removal scenarios

The Alternative Load Path (ALP) method is widely used to assess progressive collapse resistance of reinforced concrete (RC) structures by notional removal of one or more load-bearing elements. In general, a nonlinear time history analysis (NTHA) is needed to perform such an analysis if dynamic effects are explicitly taken into account. To avoid cumbersome nonlinear dynamic analyses, the energy-based method (EBM) is a promising technique to predict the maximum dynamic responses of a structural system. In this article, the accuracy and precision of the EBM is evaluated based on a validated finite element model of a tested RC slab subjected to a sudden column removal scenario, in particular in relation to the investigation of tensile membrane action (TMA). Influences of dynamic effects are evaluated, i.e. in relation to strain rate effects, damping, and the time duration of support removals. Strain rate effects are observed to have only slight influences on the dynamic responses. The strain rate dependency of reinforcement is found to have a more significant influence on the responses in TMA stage, although also to a limited extent. The magnitude of the load has a significant influence on the dynamic response, as do increasing damping ratios due to the corresponding significant energy dissipation. Finally, the dynamic response reduces with increasing time duration of the column removal. Based on the results of the stochastic analyses, the EBM is observed to perform well based on a comparison with the results of NTHA in both flexural and TMA stages. Furthermore, in relation to the analyzed case studies on reinforced concrete slabs, the model uncertainty of the responses obtained through the EBM compared with the NTHA is found to be represented well by a lognormal distribution with mean of 0.95 and a standard deviation of 0.20, for evaluating the loads of first rupture of reinforcement. Furthermore, a lognormal distribution with mean 0.96 and standard deviation 0.13 is found appropriate to represent the model uncertainty on ultimate load-bearing capacity predictions. Model uncertainties are also obtained with respect to the model predictions for displacements at the moment of the first rupture of reinforcement, displacements at the ultimate load-bearing capacities, and both loads and displacements at second load peaks.

Collapse-resistant performance of a single-story frame assembly and multi-story sub-frame under an internal column-removal scenario

To elucidate the differences in the collapse behavior between a single-story beam-column assembly and multi-story frame, two 1/3-scale two-bay composite frames, including a single-story composite beam–column assembly and a three-story composite sub-frame, were designed and quasi-statically tested. The load–displacement responses, failure modes, and internal force development of the two frames were analyzed and compared in detail. Furthermore, the resistance mechanisms of the two specimens were explored, and the respective contributions of different load-resisting mechanisms to the total resistances were quantitatively separated to gain deeper insights. The experimental tests indicated that Vierendeel action was present in the two-dimensional multi-story frames, which led to an uneven internal force distribution among the three stories. The collapse resistance of TSDWA-3S in the flexural stage was not significantly increased by the structural redundancy provided by the additional story, as compared to that of TSDWA-1S. Although the development of the load response was similar in the two specimens at flexural stage, the collapse mechanisms of the multi-story composite frame were much more complicated than those of the single-story beam–column assembly, and the combined action between stories was critical in determining the internal force redistribution and rebalancing of the remaining structure.

10-pm-order mechanical displacement measurements using heterodyne interferometry.

In this paper, we present 10-pm-order mechanical displacement measurements using heterodyne interferometry. The measuring system includes a single-path heterodyne interferometer and a phase meter based on a phase-locked loop (PLL). It is not easy to measure a mechanical displacement of 10 pm or less owing to electronics and environmental noises in the interferometer. To solve this problem, the improvement of the noise floor is required for the phase meter. A PLL algorithm, which is programmed on a field-programmable gate array module, is used for efficient noise reduction of the phase meter. The interferometer combined with a stiff piezoelectric flexure stage is placed in a vacuum chamber. The measurement comparisons and the noise floor evaluations are performed between air and vacuum to evaluate effects from their environments. The interferometer has two spatially separated beams with different frequencies and two balanced optical arms. The measurement results demonstrate that the system combined with the above components is capable of measuring mechanical displacements of 11 pm in air and vacuum. A noise floor of 0.2 pm/Hz between 50 Hz and 100 Hz can be obtained in vacuum. In this paper, the setup of the interferometer, the signal processing of the PLL, experiments, and results are discussed.

Experimental investigation of composite joints with concrete-filled steel tubular column under column removal scenario

This paper conducted an experimental investigation on the performance of composite joints with concrete filled steel tubular (CFST) column under column removal scenario. Four specimens with or without reinforced concrete (RC) slab were prepared. The failure mode, vertical resistance and section strain of the joints were analyzed in terms of deformation process, load-displacement curves and strain-displacement curves of the specimens. Finally, the axial force, arch mechanism, interaction between RC slab and steel beam, and vertical resistance distribution of the specimens are discussed. The experimental results show that the lower flanges of steel beams of both the composite joints with or without RC slab fractured at both sides successively at the later loading stage. The local buckling occurred at the top outside stiffening ring plate of the composite joint without RC slab at the early loading stage. For the composite joints with RC slab, longitudinal cracks along the beam span were observed in the slabs. The concrete close to the joint area at mid-span was crushed. Moreover, the resistance mechanism of the composite joint with and without RC slab under column removal scenario can be divided into the flexural mechanism stage, mixed mechanism stage, catenary mechanism stage and failure stage. The RC slab contributes to the development of arch mechanism that improves the resistance of joints. In addition, the premature failures of steel beam flange and the interaction between RC slab and steel beam would weaken the catenary meschanism.

Investigation of different steel intermediate moment frame connections under column-loss scenario

Abstract This paper investigated experimentally the progressive collapse risk of three one-third scale single story, two-bay steel frames under column-loss event. Progressive collapse was simulated by applying a vertical loading on the middle column. In these tests, three different types of steel beam-to-column connections were studied. These included: one shear-connection specimen that signified the prevalent type of steel beam-column joints, and two different steel intermediate moment frame (IMF) connections conforming to ANSI/AISC 358–16. The three tested specimens along with another two 2D steel frames with IMF connection, tested in the literature, were used to calibrate 3D finite element (FE) models prepared using ABAQUS software. The validated FE models were then employed to investigate the risk of progressive collapse for eleven different types of steel IMF beam-column joints under middle column-loss scenario. Out of the eleven specimens, eight connections were designed as per ANSI/AISC 358–16; two joints were in accordance with EN 1993-Eurocode 3 and the last connection was in conformance with the 2007 Turkish-Earthquake Code (TEC-2007). Performance of different IMF connections was compared based on their modes of failure and load-displacement response in both flexural and catenary action stages.

Effect of concrete infill walls on the progressive collapse performance of precast concrete framed substructures

Precast concrete (PC) frames are considered vulnerable to progressive collapse as inadequate ties between precast components can lead to a loss of structural continuity. In previous studies, slabs and masonry infill walls were found able to mitigate the progressive collapse behaviours of reinforced concrete (RC) frames. However, progressive collapse physical tests of PC frames with prefabricated concrete infill walls are scarce. Therefore, laboratory tests of three PC specimens, including bare frame, semi-infilled frame and fully infilled frame, are conducted in the paper under a centre column loss scenario. Reinforcement detailing and specimen setup are introduced and recorded results are discussed. Observations during test indicate that failure of the PC bare frame is governed by the pull out of anchorage bars at the beam-exterior column joint. Moreover, the infilled specimen leads to a substantial increase in load-carrying capacity at both the flexural stage and catenary action stage when compared with the bare frame. Based on numerical simulation, it can be concluded that the size and position of the opening have a significant impact on structural resistance of an infilled PC frame, especially on the resistance at the flexural stage.

Optimal Control for X-Ray Microscopes

In this article, a systematic framework for designing the control for fine positioning (scanning) stages of X-ray microscopes is presented. This framework facilitates designs that simultaneously achieve specifications on positioning resolution and tracking bandwidth while guaranteeing robustness of the closed loop device to unmodeled uncertainties. We use robust optimal control techniques for modeling, quantifying design objectives and system-specific challenges, and designing the control laws. The control designs were implemented on a three degree of freedom piezoactuated flexure stages dedicated for fine positioning of X-ray optics. Experimental results demonstrate significant improvements in positioning performance of 134%, 150%, and 132% in tracking bandwidths along the lateral (X), vertical (Y), and beam (Z) directions, respectively, when compared to proportional-integral-derivative controller designs. This was achieved while keeping similar or better positioning resolution and robustness measures. Fast scanning for X-ray imaging was demonstrated in both the step scan and flyscan modes, where bandwidth was improved by over 450 times with flyscan compared to the step scan.

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.

Visual sensing based ultra-high precision motion control with compensated mechanical drift across different stages

Ultrahigh precision motion control across different stages in a multistage system plays a central role in many micro/nanoscale applications. However, it remains a challenge due to the mechanical drift. Here, we propose a visual sensing based approach to implement the cooperative motion control in a multistage platform. In this method, microsized beads are attached to individual stages and taken as visual sensing probes. By tracking the motion of visual sensing probes, the positions of individual stages are measured. The principle of the proposed method is presented, followed by the experimental demonstration of the real-time mechanical drift compensation and high-precision cooperative motion control in a home-made dual piezoelectric flexural stage platform. With the proposed method, ultrahigh precision motion control between the two stages are achieved in a 3-D manner, with closed-loop motion control resolution of 1.5, 1.3, and 4.2 nm for X , Y , and Z axes, respectively. The proposed method provides an effective approach for ultrahigh precision motion control across different stages, which is believed to be significant for nanoscale manipulation related applications.

Effect of material removal on workpiece dynamics in milling: Modeling and measurement

This paper provides an investigation on the workpiece dynamics variation arisen from the material removal in both modeling and measurement aspects. To this end, finite element analysis, receptance coupling and inverse receptance coupling are employed in the modeling of the workpiece dynamics considering the material removal during the milling process. The fixed-free workpiece is divided into three components as machined, unmachined and fixed boundary condition in the receptance coupling model. The fixed boundary condition receptances are determined through the inverse receptance coupling to mathematically acquire the fixed boundary condition of the experimental setup flexibility that causes significant difference between the modeling and measurement results. Besides that, with the novel application of the inverse receptance coupling, it is analytically predicted the variation of the workpiece natural frequency as the material is removed in the milling process. This new application has been verified with the experimental studies conducted on a single degree of freedom flexure stage and a good agreement between the predicted and measured natural frequencies has been achieved. Furthermore, it has been observed that the receptance coupling results agree well with the ones obtained via the finite element analysis in the modeling of the fixed-free workpiece dynamics.

Cutting force modeling and accurate measurement in milling of flexible workpieces

Abstract This paper presents the cutting force modeling and the experimental verification for the model with the accurate measurement of the milling forces through the dynamic compensation of the workpiece-dynamometer assembly dynamics in the milling of the flexible workpieces. To this end, time domain simulation containing both the tool and workpiece dynamics in two directions and a mechanistic force model are used to numerically estimate the cutting forces. Single and two degree of freedom flexure stages, which represent the workpiece flexibility, were designed and constructed to perform the experimental validation. For the accurate measurement of the cutting forces, inverse-based filtering compensation method is employed. It has been found that the measured cutting forces are significantly distorted by the workpiece flexibility and they can not provide reliable information about the milling mechanics and dynamics. However, by the use of the inverse-based filtering approach, the actual cutting forces acting on the tool/workpiece have been accurately obtained and they are in reasonable agreement with the computed ones. Furthermore, it has been observed that the variation in the workpiece dynamics due to the material removal in the milling plays a crucial role for the accurate cutting force compensation.