In-plane Bending Research Articles

Electroconductive Polyaniline–Ag-ZnO Green Nanocomposite Material

Metal-conducting polyaniline (PANI)-based nanocomposite materials have attracted attention in various applications due to their synergism of electrical, mechanical, and optical properties of the initial components. Herein, metal-PANI nanocomposites, including silver nanoparticle-polyaniline (AgNP-PANI), zinc oxide nanoparticle-polyaniline (ZnONP-PANI), and silver-zinc oxide nanoparticle-polyaniline (Ag–ZnONP-PANI), were prepared using the two processes. Nanocomposite-based electrode platforms were prepared by depositing AgNPs, ZnONPs, or Ag–ZnONPs on a PANI modified glass carbon electrode (GCE) in the presence of 1-ethyl-3-(3-dimethyl aminopropyl) carbodiimide/N-Hydroxysuccinimide (EDC/NHS, 1:2) as coupling agents. The incorporation of AgNPs, ZnONPs, and Ag–ZnONPs onto PANI was confirmed by UV-Vis spectrophotometry, which showed five absorbance bands at 216 nm, 412 nm, 464 nm, 550 nm, and 831 nm (i.e., transition of π-π*, π-polaron band transition, polaron-π* electronic transition, and AgNPs). The FTIR characteristic signatures of the nanocomposite materials exhibited stretching arising from C–H aromatic, C–O, and C–N stretching mode for benzenoid rings, and =C–H plane bending vibration formed during protonation. The CV voltammograms of the nanocomposite materials showed a quasi-reversible behavior with increased redox current response. Notably, AgNP–PANI–GCE electrode showed the highest conductivity, which was attributed the high conductivity of silver. The increase in peak currents exhibited by the composites shows that AgNPs and ZnONPs improve the electrical properties of PANI, and they could be potential candidates for electrochemical applications.

Quasi-static experimental study on flexural performance of aluminum-reinforced laminated glass beams

Recently, in concern of safety, glass beams adhesively strengthened with other ductile materials have been putting forward by various pioneering researchers. As a light-weight and high-strength construction material, aluminum alloy has an elastic modulus close to glass and is expected to cooperate well with glass in reinforced glass beam (RG beam). In this paper, a series of exploratory experiments is carried out to investigate the structural performance of nine aluminum-reinforced glass beams (ARG beam) under in-plane four-point bending. Three PVB-laminated glass beams without reinforcement are also tested for comparison. The effects of height-to-width ratio and lateral restraint conditions are investigated. Based on the test results, the ARG beams are demonstrated to have better flexural performances than the unreinforced ones. Different failure modes are observed. The test results also show that previous analytical models on the RG beam may overestimate the in-plane flexural resistance, suggesting that further refined investigation is needed. Lateral buckling at the post-breakage stage is observed for the ARG beams with weaker lateral restraint and lower height-to-width ratio. The “M-N” approach (resistance domain method) based on the test measurement provides a conservative prediction for the lateral stability of the remaining compressive zone, indicating that the existing methods might be available for buckling verification at the post-breakage stage.

The Effect of Steel Beam Elastic Restraint on the Critical Moment of Lateral Torsional Buckling.

This paper reports the results of the next stage of the authors’ investigations into the effect of the elastic action of support nodes on the lateral torsional buckling of steel beams with a bisymmetric I-section. The analysis took into account beam elastic restraint against warping and against rotation in the bending plane. Such beams are found in building frames or frame structures. Taking into account the support conditions mentioned above allows for more effective design of such elements, compared with the boundary conditions of fork support, commonly adopted by designers. The entire range of variation in node rigidity was considered in the study, namely from complete freedom of warping to complete restraint, and from complete freedom of rotation relative to the stronger axis of the cross section (free support) to complete blockage (full fixity). The beams were conservatively assumed to be freely supported against lateral rotation, i.e., rotation in the lateral torsional buckling plane. Calculations were performed for various values of the indexes of fixity against warping and against rotation in the beam bending plane. In the study, formulas for the critical moment of bilaterally fixed beams were developed. Also, approximate formulas were devised for elastic restraint in the support nodes. The formulas concerned the most frequent loading variants applied to single-span beams. The critical moments determined in the study were compared, with values obtained using LTBeamN software (FEM). Good compliance of results was observed. The derived formulas are useful for the engineering design of this type of structures. The designs are based on a more accurate calculation model, which, at the same time offers simplicity of calculation.

Bend-Imitating Theory and Electron Scattering in Sharply-bent Quantum Nanowires

The concept of bend-imitating description as applied to the one-electron quantum mechanics in sharply-bent ideal electron waveguides and its development into a self-consistent theory are presented. In general, the theory allows one to model each particular circular-like bend of a continuous quantum wire as some specific multichannel scatterer being point-like in the longitudinal direction. In an equivalent formulation, the theory gives rise to rather simple matching rules for the electron wave function and its longitudinal derivative affecting only the straight parts of a wire and thereby permitting one to bypass a detailed quantum mechanical consideration of elbow domains. The proposed technique is applicable to the analytical investigation of spectral and transport properties related to the ideal sharply-bent 3D wire-like structures of fixed cross-section and is adaptable to the 2D wire-like structures, as well as to the wire-like structures in the magnetic field perpendicular to the wire bending plane. In the framework of bend-imitating approach, the investigation of the electron scattering in a doubly-bent 2D quantum wire with S-like bend has been made, and the explicit dependences of the transmission and reflection coefficients on geometrical parameters of a structure, as well as on the electron energy, have been obtained. The total elimination of the mixing between the scattering channels of a S-like bent quantum wire is predicted.

Shear strain evolution during tension-induced Lüders-type deformation of polycrystalline NiTi plates

This paper reports a new aspect of the Lüders-type deformation of NiTi. This is on the occurrence of lateral shear strains in a tension-induced Lüders deformation process. The phenomenon was studied by means of digital image correlation analysis. It was found that the lateral shear strains occurred in opposite directions within the Lüders band, apparently as an effort to self-accommodate the lateral displacement caused by the shear strains. The Lüders band propagation also changed from a single band mode to a branched mode when the lateral displacement, thus the in-plane bending moment, became too large. The branches, whilst having the same axial normal strain in the loading direction, were formed with opposite shear strains in double alternation between left and right of the sample and between the branches and the gaps between them, thus, to achieve the optimum self-accommodation. In addition, both the axial normal strain field and the lateral shear strain field were nonuniform after the Lüders-type deformation. These findings provide more insight and direct evidence for the explanation of the characteristics of Lüders deformation behaviour of NiTi.

Lithofacies, mineralogy, and pore types in Paleozoic gas shales from Western Peninsular Malaysia

An experimental study including Fourier Transform Infrared (FTIR), thin section petrography, scanning electron microscope (SEM) imaging, and low-pressure nitrogen adsorption analysis has been conducted to assess the mineralogy, lithofacies, pore types, and pore properties of the potential Paleozoic gas shales from Western Peninsula (WP) Malaysia. In WP Malaysia, shale samples from seven Paleozoic Formations were investigated and classified into four age categories. FTIR analysis documented the presence of aromatic out of plane and in plane bending, aliphatic CH bending, OH functional group, and presence of quartz, carbonates, kaolinite, and illite minerals. Four lithofacies identified from the petrographic analysis of the Paleozoic shale include silica-rich argillaceous mudstone (SAM), clay-rich siliceous mudstone (CSM), silica dominated lithofacies mudstone (SD), and mixed carbonate mudstone (MCM). In comparison, the mineral content and lithofacies found in Paleozoic shales are close to the Niutitang, Longmaxi, Marcellus, and Eagle Ford shales. Furthermore, with high organic matter content, laminated fabric, and with more brittle mineralogy, SD lithofacies would be a highly promising type of lithofacies in WP Malaysia. FESEM studies show that organic matter pores, interparticle pores, and intraparticle pores are the main pore types. Pore sizes analyze through N2 adsorption reveal radii of lesser than 25 nm contribute mainly to porosity and total pore volume. Micropore volume of the WP Malaysia shale was found to be greatly similar to hot shales from USA and China, while surface area values of only older Paleozoic shales, i.e., S-D and Devonian, are close to USA shales.

RNA kink-turns are highly anisotropic with respect to lateral displacement of the flanking stems

Kink-turns are highly bent internal loop motifs commonly found in the ribosome and other RNA complexes. They frequently act as binding sites for proteins and mediate tertiary interactions in larger RNA structures. Kink-turns have been a topic of intense research, but their elastic properties in the folded state are still poorly understood. Here we use extensive all-atom molecular dynamics simulations to parameterize a model of kink-turn in which the two flanking helical stems are represented by effective rigid bodies. Time series of the full set of six interhelical coordinates enable us to extract minimum energy shapes and harmonic stiffness constants for kink-turns from different RNA functional classes. The analysis suggests that kink-turns exhibit isotropic bending stiffness but are highly anisotropic with respect to lateral displacement of the stems. The most flexible lateral displacement mode is perpendicular to the plane of the static bend. These results may help understand the structural adaptation and mechanical signal transmission by kink-turns in complex natural and artificial RNA structures.

Ripple Patterns Spontaneously Emerge through Sequential Wrinkling Interference in Polymer Bilayers.

We report the formation of "ripple" patterns by the sequential superposition of nonorthogonal surface waves excited by the spontaneous buckling of polymeric bilayers. Albeit of a different nature and micron scale compared to the familiar sedimentary ripples caused by gentle wave oscillations, we find commonalities in their topography, defects, and bifurcations. The patterns are rationalized in terms of a defect density that depends on the relative angle between generations, and a constant in-plane bending angle that depends on skin thickness. A minimal wave summation model enables the design of ripple and checkerboard surfaces by tuning material properties and fabrication process.

Concrete-filled and bare 6082-T6 aluminium alloy tubes under in-plane bending: Experiments, finite element analysis and design recommendations

The application of aluminium alloys in structural engineering is growing owing to their high strength-to-weight ratio, aesthetic appearance and excellent resistance to corrosion. However, the low modulus of elasticity of aluminium poses adverse effects on the flexural response of structural members made of aluminium alloys. In case of tubular members, the performance can be improved with the addition of concrete infill. Research on the flexural response of concrete-filled aluminium alloy tubes is still minimal. This study presents experimental and numerical investigations on the behaviour of concrete-filled and bare 6082-T6 aluminium alloy tubular members under in-plane bending. In total 20 beams, including 10 concrete-filled aluminium alloy tubular (CFAT) and 10 bare aluminium alloy tubular (BAT) specimens, were tested. The specimens comprised of square and rectangular hollow sections and were filled with 25 MPa nominal cylinder compressive strength concrete. The experimental results are reported in terms of failure mode, flexural strength, flexural stiffness, ductility and bending moment versus mid-span deflection curve. Compared to the BAT specimens, the counterpart CFAT specimens have shown remarkably improved flexural strength, stiffness and ductility due to the concrete infill and the improvement is more pronounced for the specimens with thinner sections. Finite element models of BAT and CFAT beams were developed by taking into account the nonlinearities in geometry and material and validated against the experimental data. A parametric study considering a broad range of cross-sections and different concrete grades was conducted based on the validated models. The FE results have shown that the flexural strength of the BAT and CFAT members increases with the increase of cross-sectional aspect ratio, wall thickness and concrete grade. The results obtained from experiments and numerical analysis for BAT members were used to assess the flexural capacity predictions and the applicability of the slenderness limits provided in the European standards. It was demonstrated that the slenderness limits provided by Eurocode 9 are conservative for Class A aluminium sections. Hence, revised Class 1, Class 2 and Class 3 limits are proposed which appear to be better applicable to Class A aluminium alloys. In the absence of design specifications for CFAT flexural members, the design rules for concrete-filled steel tubular flexural members provided by Eurocode 4 were adopted and the material properties of steel were replaced with those of aluminium alloy. It was shown that the proposed design methodology is suitable for the design of CFAT flexural members. Moreover, a slenderness limit for compact sections of CFAT flexural members is proposed based on Eurocode 4 framework.

Influence of interlayer shear studs on the behaviour of cement stabilised rammed earth under compression, tension and shear

Cement stabilised rammed earth (CSRE) has been used for the construction buildings since the last 6–7 decades across the world (Australia, Europe, Asia, Africa, and countries such as New Zealand and the United States). The rammed earth is a monolithic construction, where the processed earth is compacted in layers. The interfacial bond strength between the compacted layers is weak, and hence there is a weak link among the compacted layers of CSRE. The major issues with CSRE walls are (1) catastrophic shear failures under compression and shear and (2) poor flexure and shear strength. Introducing short shear studs at the interfaces of the compacted rammed earth layers is one possibility to enhance the shear and the flexure strength of the CSRE. The paper focuses on evaluating the compressive strength, interface shear strength, shear stress-shear strain relationships, and the flexural strength of steel studs embedded CSRE for the first time. The results reveal that due to the introduction of shear studs, (a) the interfacial shear strength and diagonal shear strength of CSRE improved significantly, (b) The ultimate moment-resisting capacity doubles and (c) the steel studs embedded CSRE wallette showed ductile failure. The results clearly demonstrated that introducing steel studs among the compacted layers of CSRE could help avoid sudden catastrophic failures of CSRE walls under out of plane bending.

Non-telecentric two-photon microscopy for 3D random access mesoscale imaging

Diffraction-limited two-photon microscopy permits minimally invasive optical monitoring of neuronal activity. However, most conventional two-photon microscopes impose significant constraints on the size of the imaging field-of-view and the specific shape of the effective excitation volume, thus limiting the scope of biological questions that can be addressed and the information obtainable. Here, employing a non-telecentric optical design, we present a low-cost, easily implemented and flexible solution to address these limitations, offering a several-fold expanded three-dimensional field of view. Moreover, rapid laser-focus control via an electrically tunable lens allows near-simultaneous imaging of remote regions separated in three dimensions and permits the bending of imaging planes to follow natural curvatures in biological structures. Crucially, our core design is readily implemented (and reversed) within a matter of hours, making it highly suitable as a base platform for further development. We demonstrate the application of our system for imaging neuronal activity in a variety of examples in zebrafish, mice and fruit flies.

Plane bending fatigue behavior of interstitial-free steel at room temperature

Abstract Interstitial-free steels are widely used as thin sheet for automobile external panels. For this type of application, essential properties of the steel are deep-drawability and stretch-formability. However, low-strength interstitial-free steel is nearly pure iron and work on fatigue fracture behavior of this steel might be adopted as a basic study to understand the behavior of high-strength steels used for structural components. In this study, the fatigue fracture behavior of low-strength interstitial-free steel has been studied at room temperature in air and in an argon atmosphere. Fractographic observations on fatigue fracture surfaces reveal a mixed type of fracture mode (intergranular and transgranular cracking) for all specimens. The major portion of intergranular fracture has been found at the regions of low and medium crack lengths. Further increase in the crack length causes a decrease in the proportion of intergranular cracking and, finally, the fracture mode becomes completely transgranular. At the same test temperature, the proportion of intergranular fracture drastically decreased when the test was carried out in the argon atmosphere.

Failure modes of bonded wrapped composite joints for steel circular hollow sections in ultimate load experiments

The concept of an innovative bonded joining technology where welding is not required is presented as an alternative to traditional welded connection for steel circular hollow section (CHS). Wrapped composite joints have potential to greatly improve fatigue endurance when applied in multi-membered truss structures, e.g. offshore jackets for wind turbines. This paper focuses on characterization of resistance and understanding of failure modes of wrapped composite joints in static experiments, as the prerequisite for harvesting its potential for high fatigue endurance. Wrapped composite joints at two scales and with two different angles of X-joint geometry are made with GFRP composite material wrapped around steel sections without welding, and tested in 3 monotonic loading cases, tensile, compression and in-plane bending, until failure. Counterpart welded joints are tested at the smaller scale for stiffness, elastic limit and ultimate load comparisons. Two general failure modes of wrapped composite joints, debonding and fracture of the composite material are identified and quantified by surface strain measurements through 3D digital image correlation (DIC) technique. Testing results indicate that wrapped composite joints have 30% to 56% larger stiffness and 3% to 68% larger ultimate load compared to welded counterparts. Debonding and final pull-out of steel brace member from the composite wrap is predominant failure mode in tensile experiments at both scales while cracking of the composite material is the governing failure mode in the bending experiment. In tensile, compressive and bending experiments failure load of wrapped composite joints exceeds the yield resistance of the steel CHS indicating opportunity to optimize the composite wrapping thickness and length.

Experimental and theoretical analyses on semi-rigid pin joints under in-plane direction bending in modular reticulated shell

A new semi-rigid pin joint equipped with a simple assembly procedure provides a promising solution for the realization of modular and rapid assembly of steel-reticulated shells. Because the novel joint can adapt to the complex curvature change of the reticulated shell, it can be arranged in the middle of the reticulated shell member. Moreover, this type of arrangement can significantly reduce the number of assembled joints in the reticulated shell. The purpose of this study was to explore the anti-rotation performance of semi-rigid pin joints in the in-plane bending direction of a reticulated shell. First, through static loading experiments, the mechanical properties of the semi-rigid pin joints were investigated. The parameters considered in the experiment included the diameter of the wing plate pin, thickness of the wing plate, and diameter of the screw rod. To evaluate the static performance of the joint, the parameters of the joint, such as the initial stiffness, ultimate bending moment, and failure mode, were analyzed in detail. The results revealed that the semi-rigid pin joint exhibited good bending stiffness under in-plane direction loads. Simultaneously, a finite element model of the semi-rigid pin joint was established using ABAQUS, and several parameters of the joint were analyzed under the premise of agreement between the test and finite element model. Finally, a theoretical analysis model was established based on the power function model to predict the bending moment-rotation angle (M-Φ) curves of the semi-rigid pin joints under different parameter combinations. The results proved that the prediction formula provided accurate results compared with the experimental results.

The analysis of root canal curvature and direction of maxillary lateral incisors by using cone-beam computed tomography: A retrospective study.

The aim of this study was to investigate root canal curvature and direction of maxillary lateral incisors in Shandong, China.Cone beam computed tomography (CBCT) images of 176 maxillary lateral incisors of 88 patients were collected in Shandong Province, China. Software included with CBCT was used to measure the angle of root canal curvature of maxillary lateral incisors on the maximum bending plane. In addition, the direction of each root canal was recorded. The data were statistically analyzed by SPSS 17.0 software package.The results showed that all the samples had a single canal (Vertucci's type I). The incidence of straight root canals, curved root canals, and S-type root canals was 39.2%, 58%, and 2.8%, respectively. The difference in the mean angle of root canal curvature failed to identify any differences between the left and right side (P > .05). The most curved root canal of maxillary lateral incisors oriented in the palato-distal direction.The maxillary lateral incisors were mainly curved root canals of which the proportion of moderate curvature was the largest. Software included with CBCT would provide some valuable information for root canal instrumentation of maxillary lateral incisors.

Nonlinear large deformation of a spherical red blood cell induced by ultrasonic standing wave.

A computational model is developed to investigate the nonlinear static deformation of a spherical (osmotically swollen) red blood cell (RBC) induced by ultrasonic standing wave. The ultrasonic standing wave can generate steady acoustic radiation stress to deform the cell, and in turn, the deformed cell reshapes the acoustic field. This is a real-time coupling problem between the acoustic field and the mechanical field. In the computational model, the acoustic radiation stress acting on the RBC membrane is modeled by adopting the nonviscous momentum flux theory. The RBC membrane is modeled as a hyperelastic shell considering the in-plane elasticity, bending elasticity, and surface tension of the membrane. The volume conservation constraint of the membrane sealing fluid is applied to ensure the osmotic balance of the membrane. To address this real-time coupling problem, the computational model is implemented by a finite element method algorithm. The numerical results are compared with the existing theoretical model and experimental data, and the strain hardening trend of the experimental data is successfully predicted, which verifies the accuracy and effectiveness of the computational model. The computational model can accurately extract the mechanical properties of cells from acoustic deformation experiments, which is helpful for the diagnosis of some human diseases.

Experimental and numerical study on the performance of new prefabricated connections for free-form grid structures

Free-form grid shell structures are widely used for stadiums, airport terminals, exhibition pavilions, shopping malls and warehouses, however, the shape of the grid surface is usually complex. A flexible joint that can adapt to the curvature variation of the free-form surface is therefore important for assembling such structures. To meet the demand of various curvatures for single-layer free-form grid structures, a new type of prefabricated bolted joint is introduced in this paper. A series of in-plane bending tests were conducted to investigate the initial stiffness and the moment resistance of the joints. Coupon tests were carried out to study the material properties and provide parameters for a numerical study. FE models considering the geometric and material nonlinearity were developed and validated by the tests. Parametric studies were then carried out using the developed FE model to investigate the influencing geometric factors of the in-plane behaviours semi-rigid joints. The results demonstrated that the initial in-plane stiffness of the joints is dominantly controlled by the endplate thickness, the side plate thickness, the bolt diameter and the bolt row distance, while the moment resistance of the joint is governed by the endplate thickness, the side plate thickness, the sleeve cross-sections and the bolt row distance. Subsequently, FE analysis was carried out using the validated FE models to investigate the out-of-plane behaviour of the proposed assembled joint. The experimental and numerical study showed that the proposed joint has good rotational capacity and load-bearing resistance, therefore has the potential to be applied in the design and construction of free-form grid structures.

Calcium carbonate nanoparticles of quail’s egg shells: Synthesis and characterizations

Abstract Avian eggshell is a natural biomaterial that has been used as an alternative natural source of CaCO3 and is accessible in big amounts from egg manufacturing. This study was planned to estimate CaCO3 in quail’s eggshell because it has a probable use in the progress of a novel choice of many applications. Physical properties: mineralogical documentation of the natural eggshell nanoparticles were approved using XRD and FTIR to explore the chemical bond or molecular structure of the materials. Micrographs were obtained using FESEM/EDX and TEM to identify the morphology and size of nanoparticles. The results showed that quail eggshell was soft, with white to light sand color, and a smooth texture which allows good deposition of different color spots, from black to brown spots. The resulted of eggshells signifies almost 8.4% w/w of the overall weight (12.2) gram of quail egg and 91.60% w/w of the micropowder to the full weight of (0.94) gram of quail eggshell. The results presented that calcium is the main element in an eggshell; frequently occurs in a formula of CaCO3 and the crystal construction was almost pure calcite. FTIR spectra for quail eggshell demonstrated the existence of the out of plane bending, the asymmetric stretching, and the plane bending styles of the carbonate groups, specific of normal dolomite, situated at 873 cm–1, 1405 cm–1, and 710 cm–1, respectively. The FESEM and TEM for nanoparticles were shown calcite CaCO3 nanoparticles with an ordinary size of ≤ 100 nm for FESEM and with a variety size of ≤ 50 nm for TEM. Unfortunately, eggshell is an egg product manufacturing deposit. These incomes will let fast developments in proportional studies of the organic elements of avian eggshell and their purposeful consequences by usages of eggshell in nourishment and medicine which can be applied for many resolutions that diminish their consequence on environmental contamination.

Local stability of the web of a prestressed steel beam transport construction

A study of the local stability of the wall of a prestressed prefabricated beam of a steel bridge was carried out, which is not reflected in the technical literature. The critical normal stresses in a prestressed plate are determined by the energy method of S.P. Timoshenko. The stability of the plate in the zone of maximum shear forces is estimated under the assumption that the principal stresses on the web at the stage of fabrication of the structure and the principal stresses caused by the external load are oppositely directed and decrease when summed. The shear forces and shear stresses on the web are determined based on the theory of D.I. Zhuravsky. An experimental study was conducted on standard and prestressed beams of equal cross section to verify the theoretical conclusions. The graphs of web displacements from the plane of beam bending in the zone of maximum normal and shear stresses are presented. It was concluded that the prestressing of elements of steel beam has a positive effect on their local stability. Recommendations on the structural solution of prestressed beams and reduction of their mass were presented.

Design and Analysis of Ultra-Precise Large Range Linear Motion Platforms Using Compliant Mechanism

Double parallelogram compliant mechanism (DPCM) is extensively used to obtain precise straight-line motion. Symmetric DPCMs, used previously, traverse a straight-line path without parasitic error when gravity vector is perpendicular to the plane of bending of beams. However, when gravity vector is either in line with beams (orientation B) or in the plane of bending of beams (orientation C), asymmetry in the loading causes undesired deviation from a straight-line path. This undesired deviation called parasitic error increases, especially in beams with relatively low flexural rigidity required to obtain larger displacements with low power actuators. This paper first characterizes parasitic error, in such cases, using large deformation analysis and further proposes novel ways to minimize it. A recently developed, chained beam constraint method is used to model, characterize, and optimize DPCMs. Optimized parameters are further validated by FEA and experiments. In orientation B, after implementing the proposed method, numerical analysis and experimental results show that the undesired parasitic error of 123 μm is drastically reduced to 2 μm and 6 μm, respectively. Moreover, systematic design procedure with corresponding graphs is presented to avoid modeling and optimization steps for a user-specific case. The proposed methods pave pathways to reducing the parasitic error during large-range motion using multiple orientations of DPCMs and thus make DPCMs more employable in several precision motion applications such as 3D optical scanners, 3D micro-printers, CMM probes, and microscopy stages.