Angle Α0 Research Articles

Geometric Model for the Postural Characterization in the Sagital Plane of Lumbar Raquis.

The individual's posture is the physical expression of his body. It is modified throughout life and it is determined by the particular anatomical characteristics that directly affect the biomechanics of the spine. The typing of the spinal curvature is important for the knowledge of body posture. The possibility of having a method for the systematic postural characterization of the spine is an essential objective resource in order to obtain normal or control patterns of the spinal morphology of the population. A widely accepted methodology of morphological characterization of the spine is a necessary requirement for the establishment of preventive criteria for spinal pathologies based on epidemiological population studies. It also represents a necessary requirement for the classification of individuals, based on the biomechanical, orthopaedic or ergonomic criteria necessary for disciplines such as sports, industrial design or sports performance. The present study proposes the development of a morphological postural model of the spine in the lumbar region. The model is based on a system of measurement of objective and comparable parameters by means of X-ray analysis, in order to characterize its morphology in the sagittal plane. The comparison of the results in a population of 47 individuals allowed the possibility to carry out a statistical study on three morphological parameters: sacral angle (α1); reversal angle (α2) and degree of lordosis (DL). The statistical hypothesis that the results behave according to a normal distribution with p < 0.05 is relevant and allows the systematization and postural modelling of the individual.

Mixed Convection in an Inclined Nanofluid Filled-Cavity Saturated With a Partially Layered Porous Medium

The contribution of the current study is to investigate the mixed convection in an inclined nanofluid filled cavity saturated with a partially layered non-Darcy porous medium. Moreover, due to the advantage of the particle-based methods, we presented the improved version of an incompressible smoothed particle hydrodynamics (ISPH) method. The current ISPH method was improved in boundary conditions treatment using renormalization kernel function. In the current investigation, we assumed that the inclined cavity is filled with a Cu-water nanofluid. The upper half of the cavity is saturated with a non-Darcy porous medium. Here, one domain approach is used for coupling the nanofluid and the porous medium layer. The cooled top wall of the cavity is carrying a tangential unit velocity and the bottom wall is heated. The other two wall sides are adiabatic at zero velocity. Here, we investigated the effects of the Richardson parameter Ri0.0001–100, Darcy parameter Da 10−5–10−2, an inclination angle α0–90deg and a various solid volume fraction ϕ0–0.05 on the heat transfer of a Cu-water nanofluid. The obtained results showed that the average Nusselt number decreases as the Richardson number increases. An addition of 1–5% Cu nanoparticles slightly increased the overall heat transfer rate.

Observations and Fokker‐Planck Simulations of the L‐Shell, Energy, and Pitch Angle Structure of Earth's Electron Radiation Belts During Quiet Times

AbstractThe evolution of the radiation belts in L‐shell (L), energy (E), and equatorial pitch angle (α 0) is analyzed during the calm 11‐day interval (4–15 March) following the 1 March 2013 storm. Magnetic Electron and Ion Spectrometer (MagEIS) observations from Van Allen Probes are interpreted alongside 1D and 3D Fokker‐Planck simulations combined with consistent event‐driven scattering modeling from whistler mode hiss waves. Three (L, E, α 0) regions persist through 11 days of hiss wave scattering; the pitch angle‐dependent inner belt core (L ~ &lt;2.2 and E &lt; 700 keV), pitch angle homogeneous outer belt low‐energy core (L &gt; ~5 and E~ &lt; 100 keV), and a distinct pocket of electrons (L ~ [4.5, 5.5] and E ~ [0.7, 2] MeV). The pitch angle homogeneous outer belt is explained by the diffusion coefficients that are roughly constant for α 0 ~ &lt;60°, E &gt; 100 keV, 3.5 &lt; L &lt; L pp ~ 6. Thus, observed unidirectional flux decays can be used to estimate local pitch angle diffusion rates in that region. Top‐hat distributions are computed and observed at L ~ 3–3.5 and E = 100–300 keV.

Design and Enhancement of Thermal Flow Characteristic in an Annular Diffuser under Turbulent Flow

The annular diffuser is an expansion area, which, despite its simple structure, is very important in some engineering and thermal applications. In the present research, numerical simulations were performed to investigate the temperature field and flow structure characteristics in an annular diffuser. The hub of the annular diffuser consisted of a straight semi-dimpled tube SSDT. Three different diffuser wall angles (α) 1.8°, 3.6° and 5.4° with inlet Reynolds number 1.5 × 104 were studied in details with air as a working fluid. The computational fluid dynamics CFD was used to simulate the model in a turbulent flow. The standard k-ε turbulence model was used to complete the governing equations. The numerical results, mainly the temperature distribution, pressure drop and velocity distribution for the airflow in the annular diffuser fitted with SSDT for different diffuser wall angles α were obtained and compared. It was observed that as the wall diffuser angle α increases, the enhancement of the temperature distribution and the velocity distribution decrease while the pressure drop rate increases. The maximum temperature distribution and velocity distribution were completed by diffuser wall angle α1 = 1.8° whereas, the highest pressure drop achieved by diffuser wall angle α3 = 5.4°.

Influence of Incidence Angle in the Correlation of C-band Polarimetric Parameters with Biophysical Variables of Rain-fed Crops

A multi-temporal field experiment was conducted within the Soil Measurement Stations Network of the University of Salamanca (REMEDHUS) in Spain in order to retrieve useful crop information. The objective of this research was to evaluate the potential of polarimetric observations for crop monitoring by exploiting a time series of 20 quad-pol RADARSAT-2 images at different incidence angles (i.e. 25°, 31°, and 36°) during an entire growing season of rain-fed crops, from February to July 2015. The time evolution of 6 crop biophysical variables was gathered from the field measurements, whereas 10 polarimetric parameters were derived from the images. Thus, a subsequent correlation analysis between both datasets was performed. The study demonstrates that the backscattering ratios (HH/VV and HV/VV), the normalized correlation between HH and VV (γHHVV), and the dominant alpha angle (α1), showed significant and relevant correlations with several biophysical variables such as biomass, height, or leaf area index (LAI) at incidence angles of 31° or 36°. The joint use of data acquired with different beams could be exploited effectively to increase the refresh rate of information about crop condition with respect to a single incidence acquisition scheme.

Optical Bessel tractor polarized beams on a charged sphere of arbitrary size

Optical tractor beams can reel in an object towards the source, and are becoming a topic of significant worldwide research. Previous works considered the axial and transverse radiation pressure cross-sections (RPCSs) of optical tractor Bessel polarized beams on a dielectric sphere. However, most particles are charged, and it is important to investigate the tractor beam effect on charged particles. The aim of this work is therefore directed toward this goal, where the axial and transverse RPCSs for a charged sphere illuminated by a vector Bessel beam are computed in the framework of generalized Lorenz-Mie theory (GLMT). Numerical computations of the RPCSs are performed, with emphasis on the emergence of a negative pulling force and its dependence on the half-cone angle α0, the order l, and the polarization. A higher-order (l ≠ 0) Bessel beam possesses a hollow core and is of vortex nature, while the fundamental mode (l=0) is of non-vortex type and has a bright maximum intensity at the center of the beam. In our calculation, both l=0 and l=1 are considered. The axial PRCSs versus ka and α0 are first calculated, and the negative axial forces can arise. Moreover, the axial and transverse RPCSs in the plane perpendicular to the beam axis are computed. However, numerical results show that the RPCSs are same to that for a neutral particle. To explain this, the ratios of axial RPCSs for charged and neutral spheres are investigated taking ka as a parameter. The results show that charges only affect the RPCSs for small particles. Finally, the RPCSs for a charged sphere of relatively small are considered. The charge can affect the magnitude of the RPCSs, however, it does not affect the direction of axial optical forces. These results are of great importance in the development of novel optical tweezers and tractor beams.

Multi-objective optimization of process parameters of multi-step shaft formed with cross wedge rolling based on orthogonal test

In order to achieve reasonable process parameters in forming multi-step shaft by cross wedge rolling, the research studied the rolling-forming process multi-step shaft on the DEFORM-3D finite element software. The interactive orthogonal experiment was used to study the effect of the eight parameters, the first section shrinkage rate φ1, the first forming angle α1, the first spreading angle β1, the first spreading length L1, the second section shrinkage rate φ2, the second forming angle α2, the second spreading angle β2 and the second spreading length L2, on the quality of shaft end and the microstructure uniformity. By using the fuzzy mathematics comprehensive evaluation method and the extreme difference analysis, the influence degree of the process parameters on the quality of the multi-step shaft is obtained: β2>φ2L1>α1>β1>φ1>α2L2. The results of the study can provide guidance for obtaining multi-stepped shaft with high mechanical properties and achieving near net forming without stub bar in cross wedge rolling.

Coordinating bracket torque and incisor inclination : Part1: The development of widely applicable equations.

The objective of this investigation was to develop equations to describe the geometric relations among "targeted incisor inclinations" (tU1, tL1) accommodating different cephalometric norms (Ricketts, Bergen, etc.) with the "expected inclinations" (eU1, eL1), as they can be generated by bracket torque values according to Andrews, Roth, Ricketts, and MBT. In its key parts, the present study is a theoretical work in which structural relationships are described using standard mathematical and geometric methodologies. The "targeted norm-inclinations" (tU1, tL1) were calculated relative to a single reference plane (BOP according to Downs), thus, allowing for a direct comparison of different cephalometric values. Referring to the "expected inclinations" (eU1, eL1), it was found that in addition to bracket torque (BT) morphological and structural parameters also have to be taken into account. These are the "torque coordination angle" (TCA) representing the variation in dental morphology and, the correction angles between BOP and the upper (uOP) (α1) or the lower (lOP) occlusal plane (β1). Moreover, the angles α2 between an upper (uBPP) and β2 between a lower bracket positioning plane (lBPP) and the occlusal planes (uOP, lOP) have to be considered. As a consequence, suitable equations were developed (eU1(BOP) = 90° - BT(U1) - TCA(U1) + α1 - α2, and eL1(BOP) = 90° - BT(L1) - TCA(L1) + β1 - β2), allowing the calculation of expected torque-dependent inclinations (eU1, eL1) and representing the prerequisite for a comparison with the cephalometric targeted values (tU1, tL1). By developing suitable equations, it became possible to name and quantify those parameters that are responsible for incisor inclinations and enable a comparison with targeted cephalometric values.

Effects of Upstream Weir Slope on Local Scour at Submerged Weirs

The variation of upstream slope of a submerged weir could significantly alter the local flow pattern and sediment transport. This paper presents an experimental investigation into local scour at submerged weirs with different upstream weir slope angles. In this study, 62 tests are carried out in a tilting recirculating flume, including 38 tests using coarse sand and 24 tests using fine sand, to investigate the effects of upstream weir slope on the local scour at a submerged weir. The tests of each sand use four weirs with different upstream weir slopes. For clear-water scour, no upstream scour depth is observed at the sloped weirs, and downstream scour depth is independent of the upstream weir slope. For live-bed scour, a flatter upstream weir slope reduces upstream scour depth for both sands. The results for fine sand show that when the slope is gentler than a critical angle α0, the effects of upstream weir slope on upstream scour depth are minimized, such that the upstream scour depth no longer decreases with decreasing weir slope angle. The existence of upstream weir slope slightly reduces the downstream scour depth when the sediment is transported as bedload. When the sediment transport mode is suspension load, the downstream scour depth is independent of the weir slope. New predictors for the average scour depth including the effects of upstream weir slope are developed. A relationship between the average and maximum scour depth is also proposed.

Validation and Analysis of Bounce Resonance Diffusion Coefficients

AbstractTheoretical bounce resonance diffusion coefficients for waves generated near the equatorial plane are analyzed theoretically and validated numerically using guiding‐center test particle simulations. A previous study demonstrated numerically the sensitivity of the diffusion coefficients to the peak wave normal angle and the maximum wave latitude for electrons in bounce resonance with equatorially confined magnetosonic waves. We demonstrate analytically that the sensitivity of the diffusion coefficients to the peak wave normal angle is due to the narrow width of the wave normal angle distribution of the particular wave model used by the previous study. We also show that there is no dependence on the maximum latitude if particle's mirroring points are located within the wave boundary. By analyzing the contribution of each harmonic resonance to the total diffusion coefficients, we show that the discontinuities of the diffusion coefficients as a function of the equatorial pitch angle (α0) occur when the contribution of a harmonic resonance goes to 0. Using a two‐dimensional pitch angle and energy diffusion simulation, we demonstrate that bounce resonance with magnetosonic waves can cause pitch angle scattering of equatorially mirroring electrons, leading to a smooth variation of flux with α0 for α0∼90∘. We conclude that bounce resonance with magnetosonic waves might be an important mechanism in pitch angle scattering and acceleration of electrons in the radiation belt.

Chalcogenide optical fiber couplers made by FBT method

We report on developing and characterization of chalcogenide FBT single mode fiber coupler for Mid-IR fiber optics applications. Single mode 6.3μm core/123μm cladding chalcogenide fibers of IHPS RAS with homemade polishing and standard PC/AFC connectors were utilized. Two fiber coupler geometries with angles α1=70° and α2=40° between the fibers were investigated and nature of excess loss has been studied. Excess loss and coupling ratios on time for both geometries were determined. Excess losses were measured to be 7dB and 5dB for α1 and α2 geometries respectively. For α1 geometry 70:30 and for α2 geometry 55:45 coupling ratios were achieved. For α2 geometry coupling ratio at wavelength 2.64μm was 63:37.

Modeling radiation belt dynamics using a 3‐D layer method code

AbstractA new 3‐D diffusion code using a recently published layer method has been developed to analyze radiation belt electron dynamics. The code guarantees the positivity of the solution even when mixed diffusion terms are included. Unlike most of the previous codes, our 3‐D code is developed directly in equatorial pitch angle (α0), momentum (p), and L shell coordinates; this eliminates the need to transform back and forth between (α0,p) coordinates and adiabatic invariant coordinates. Using (α0,p,L) is also convenient for direct comparison with satellite data. The new code has been validated by various numerical tests, and we apply the 3‐D code to model the rapid electron flux enhancement following the geomagnetic storm on 17 March 2013, which is one of the Geospace Environment Modeling Focus Group challenge events. An event‐specific global chorus wave model, an AL‐dependent statistical plasmaspheric hiss wave model, and a recently published radial diffusion coefficient formula from Time History of Events and Macroscale Interactions during Substorms (THEMIS) statistics are used. The simulation results show good agreement with satellite observations, in general, supporting the scenario that the rapid enhancement of radiation belt electron flux for this event results from an increased level of the seed population by radial diffusion, with subsequent acceleration by chorus waves. Our results prove that the layer method can be readily used to model global radiation belt dynamics in three dimensions.

Application of CFD on the optimization by response surface methodology of a micromixing unit and its use as a chemical microreactor

The optimization of a mixing unit by means of CFD (computational fluid dynamics) and RSM (response surface methodology) is presented in this work. The starting geometry is the one studied by Fang and co-workers [14] consisting in a T-type microchannel with the mixing unit inserted in the straight main channel. The mixing takes place at a very low Reynolds number and is promoted by means of two bars at 69° each with respect to the mixing unit walls. These angles are the input parameters of the optimization process while the output ones are the mixing efficiency, the needed pumping power to run the channel and the mixing energy cost. Fang and co-workers found numerically an efficiency of around 22% when one mixing unit was employed, while an almost perfect mixing could be reached by using 28 of them. However, they did not carry out a grid convergence study and their results were got for just one mesh. Due to this, before the optimization tasks and thanks to the Grid Convergence Index, it is shown that Fang and co-workers’ mixing efficiency has an uncertainty of around 40%. This is due to the fact that, with the optimal grid, the mixing efficiency is around 12.5% which is quite far from what Fang and co-workers said. Additionally, with the RSM and by using the optimal mesh, it is found that the optimal angles α1 and α2 are: ∼76° and ∼62° to get the highest efficiency which is around 14%; and ∼72° and ∼74° to get both the lowest pumping power to run the channel and the lowest mixing energy cost. The performing of the micromixer as a microreactor, where a basic reaction must take place, is finally assessed.

Experimental and numerical investigation of the cylindrical blade tube inserts effect on the heat transfer enhancement in the horizontal pipe exchangers

In this experimental and numerical study an attempt to enhance the heat transfer rate by cylindrical blade that form turbulence flow inside the exchanger pipe is carried out. The effects of the blade geometry are also examined to investigate heat transfer rate in experimented tube inserts. Experiments are performed in different blade spacing (Sy1,2,3 = 101–216–340 mm) and various blade angles (α1,2,3 = 0°–45°–90°). The water flow rate inside the tube is adjusted in three different ranges to approach intended Reynolds numbers (Re1,2,3 = 6000–11,000–17,000). Nusselt number, Reynolds number and effect of friction factor are investigated separately. For all experiments, the increase in Nu number due to used tube inserts is recorded and compared to each other and plain tube in the related profiles. It is concluded that installed tube inserts in the heat exchanger tube, led to a significant increase in Nu number and energy saving. Among different experimented cases, using mean value in various Re numbers, the highest Nusselt number was obtained at Sy1 = 101 mm which was 24% more than that of plain tube. This value was 18.7 and 8.3% for Sy2 = 216 and Sy3 = 340 mm respectively. By this way, according results for friction factor were 0.30, 0.19 and 0.14. The presented study has been simulated by ANSYS Fluent 16 software to analyze flow behavior and heat transfer characteristics.

Accurate Compensation of Attitude Angle Error in a Dual-Axis Rotation Inertial Navigation System.

In the dual-axis rotation inertial navigation system (INS), besides the gyro error, accelerometer error, rolling misalignment angle error, and the gimbal angle error, the shaft swing angle and the axis non-orthogonal angle also affect the attitude accuracy. Through the analysis of the structure, we can see that the shaft swing angle and axis non-orthogonal angle will produce coning errors which cause the fluctuation of the attitude. According to the analysis of the rotation vector, it can be seen that the coning error will generate additional drift velocity along the rotating shaft, which can reduce the navigation precision of the system. In this paper, based on the establishment of the modulation average frame, the vector projection is carried out, and then the attitude conversion matrix and the attitude error matrix mainly including the shaft swing angle and axis non-orthogonal are obtained. Because the attitude angles are given under the static condition, the shaft swing angle and the axis non-orthogonal angle are estimated by the static Kalman filter (KF). This kind of KF method has been widely recognized as the standard optimal estimation tool for estimating the parameters such as coning angles (α1 , α2), initial phase angles (ϕ1,ϕ2), and the non-perpendicular angle (η). In order to carry out the system level verification, a dual axis rotation INS is designed. Through simulation and experiments, the results show that the amplitudes of the attitude angles’ variation are reduced by about 20%–30% when the shaft rotates. The attitude error equation is reasonably simplified and the calibration method is accurate enough. The attitude accuracy is further improved.

Experimental verification of a CFD model intended for the determination of restitution coefficients used in erosion modelling

Erosion caused by solid particles transported with the steam or flue gas has a negative impact on the power unit reliability and availability. The erosion rate depends inter alia on the restitution of the particle velocity upon impact. The restitution coefficients determine the angle of the particle reflection off the tube surface and the particle post-impingement velocity, i.e., they determine the direction of the particle path, which has a substantial impact on the erosion phenomenon inside the tube. An attempt is made herein to develop a method of determination of restitution coefficients by means of numerical modelling assisted by experimental testing on physical models that will be implemented further in the Ansys Fluent code. Such a numerical procedure will verify the model of erosion caused by particles of iron oxides. The erodent impingement angle α1, the impingement velocity w1, and the reflection velocity w2 are measured using the Casio High-Speed Exilim EX-F1 camera, which enables filming at a high rate. The film is then processed graphically for “frame-by-frame” tracking. The following erodents were used in the testing: iron oxides, quartz sand with a different grain size (490, 1000, 1500, 2000 μm), and 1000 μm-diameter steel balls. The steel balls, due to their ideal shape, were treated as the comparative analysis reference standard. Erosion of three types of 5x10 cm plates was tested: a plasma-coated plate with an anti-erosion layer, an aluminium plate; and a steel sheet plate. Based on the restitution coefficient testing results, numerical simulations were performed of the particle reflection off the surface.

Optical tractor Bessel polarized beams

Axial and transverse radiation force cross-sections of optical tractor Bessel polarized beams are theoretically investigated for a dielectric sphere with particular emphasis on the beam topological charge (or order), half-cone angle and polarization. The angular spectrum decomposition method (ASDM) is used to derive the non-paraxial electromagnetic (EM) field components of the Bessel beams. The multipole expansion method using vector spherical harmonics is utilized and appropriate beam-shape coefficients are derived in order to compute the radiation force cross-sections. The analysis has no limitation to a particular range of frequencies such that the Rayleigh, Mie or geometrical optics regimes can all be considered effectively using the present rigorous formalism. The focus of this investigation is to identify some of the tractor beam conditions so as to achieve retrograde motion of a dielectric sphere located arbitrarily in space. Numerical computations for the axial and transverse radiation force cross-sections are presented for linear, right-circular, radial, azimuthal and mixed polarizations of the individual plane waves forming the Bessel beams of zeroth- and first-order (with positive or negative helicity), respectively. As the sphere shifts off the beam׳s axis, the axial pulling (tractor) force is weakened. Moreover, the transverse radiation force cross-section field changes with the sphere׳s size factor ka (where k is the wavenumber and a is the sphere radius). Both stable and unstable equilibrium regions around the beam׳s axis are found, depending on the choice of ka and the half-cone angle α0. These results are particularly important in the development of emergent technologies for the photophoretic assembly of optically-engineered (meta)materials with designed properties using optical tractor (vortex) beams, particle manipulation, levitation and positioning, and other applications.

Determination of kinematic indices corresponding to a solid particle on a flat oscillating surface

This articles presents a mathematical analysis having as purpose the understanding of the behaviour of a solid particle on a flat oscillating surface. The starting point of the analysis is the initial identification of the actions direction of forces on a solid particle placed on a flat oscillating surface, in a 3D reference system. Following the distribution of forces, for different specific cases of the behaviour of the solid particle, the general equations of kinematic indices could be determined, ks and kj. Due to achieving the 3D distribution model of forces acting on a solid particle, a new kinematic index could be determined, index corresponding to the sideways moving of the solid particle kl. Moreover, a series of graphical representations have been carried out, having as purpose the emphasis of the variation mode of the newly determined kinematic indices, as following: friction coefficient µ = 0.4; the angle of the inertial force to the flat oscillating surface, Φ = 0 - 180°; the angle between the projection of the inertial force on XOY plane and OX axis, α2, = 0 - 80o. After analyzing the graphical representations for the new calculation forms of the kinematic indices, kl variation has the same rate and trend as kj. If angle α2 = 0o, the variation curve of ki index coincides with the variation curve of kj, and as we increase the value of angle α2, the variation curve of kl index moves away from the kj curve.

Geometry and head loss in Venturi injectors through computational fluid dynamics

ABSTRACT To determine the influence of geometry on the hydrodynamic behavior of Venturi injectors, using computational fluid dynamics techniques, we studied, at the Universitat Politècnica de València, Valencia, Spain, the geometric parameters that exert the most influence on head losses: the relationship between throat diameter and nozzle (β), nozzle angle (α1) and diffuser angle (α2). In addition, three throat morphologies (B1: nozzle-throat and throat-diffuser with a sharp edge; B2: nozzle-diffuser with a zero-length, sharp-edge throat; B3: nozzle-throat and throat-diffuser with rounded edge). We analyzed their influence on the velocity distribution and differential pressure between inlet and throat (DP/γ), throat and outlet (Δhv/γ), and outlet and throat ((P3-P2)/γ). The development of the velocity profile from the throat is slower the greater β is and the lower α2 is. DP/γ decreases with β, increases with α1 and varies little with α2. Δhv/γ decreases with β and increases with α1 and α2. (P3-P2)/γ decreases with β and increases with α1 and α2. Geometry B3 decreases the losses and delays the onset of cavitation. Thus, the lower β and the higher α2, the greater the losses; however, the influence of α1 is less clear. The rounded edges produce lower head losses.

3D-printed upper cervical models: accuracy validation and feasibility study into anterior occiput-to-axis screw fixation on them

Objective To validate the accuracy of 3D-printed upper cervical models and investigate the feasibility of use of the models in anterior occiput-to-axis screw fixation, in an attempt to provide a protocol of pre-operative plan for surgeons. Methods Forty-five adult atlantoaxial CT scans were obtained, imported into Mimics software for 3D reconstruction, successively imported into 3D printer to print the 3D models. Fourteen parameters were measured on both imaging system and 3D-printed models to validate the accuracy of 3D-printed models. Thirty upper cervical CT data were obtained and imported into Mimics software for 3D reconstruction. Cylinders in 1.75 mm radius were drawn to simulate the trajectory of anterior occiput-to-axis screw fixation. Anteroposterior view of the minimum lateral angle (α1) and maximum lateral angle (α2) and lateral view of the minimum posterior angle (β1) and maximum posterior angle (β2) were measured. Mean value of α1 and α2 was calculated as α3 and mean value of β1 and β2 as β3. Meanwhile, the 3D models were printed, and an angle guide device was used to introduce the anterior occiput-to-axis screws into the 3D models in reference to the angles of α3 and β3. Anteroposterior view of lateral angle (α4) and lateral view of posterior angle (β4) were measured. Differences in α3 vs. α4 and β3 vs. β4 were compared. Results All above 14 parameters did not differ significantly between radiographic images and 3D-printed models (P>0.05). Intraclass correlation coefficient (ICC) values of 13 parameters were >0.800. On the 3D digital models, the α3 was (12.6±3.7)° (left) and (12.0±4.2)° (right), and the β3 was (23.9±4.8)° (left) and (23.4±4.9)° (right). On the 3D-printed models, the α4 was (12.0±4.1)° (left) and (12.3±4.1)° (right), and β4 was (23.4±4.2)° (left) and (22.8±4.4)° (right). There were no significant differences in both comparisons of α3 vs. α4 and β3 vs. β4 (P>0.05). Conclusions The 3D printing technique enables accurate fabrication of upper cervical spine. Aided by the 3D reconstruction with screw trajectory simulation and angle guide device, the anterior occiput-to-axis screws are introduced on the 3D-printed models successfully. Key words: Imaging, three-dimensional; Spine; Computer-assisted design