Electromagnetic calculation and kinematics analysis of multi-DOF motor with air-floation

In view of the fact that the transmission mode of the multi-DOF motor hinders its further development, the gas bearing is applied to the multi-DOF motor to form a new structure of the multi-DOF motor with air-floation (AMM). AMM not only improves the motor’s motion characteristics and transmission performance, but also basically does not cause environmental pollution. AMM uses porous static pressure gas bearing as the support structure, and completes the multi-DOF movement by controlling the energizing strategy of the coils. This paper introduces the structure of AMM, analyzes the basic working principle of AMM, and solves the air gap magnetic field; the kinematics model of the motor is established, the motion of the motor is controlled with the help of virtual simulation software, and the motion trajectory of the motor is obtained through the marked points of the output shaft. Finally, the AMM was verified by experiments, the error of experiment and simulation was controlled at 5%, and the kinematics characteristics of the motor met the design requirements. The research results provide a new idea for the development of multi-DOF motor.

Determination of the Accuracy of Linear Height Bone for Implant Placement in Panoramic Radiography Relative to CBCT in the Posterior Areas of the Jaws

Purpose: In the levels of implant treatment in the posterior region, determining the height of the bone has particular importance. The aim of the study was to compare the accuracy of linear bone height measurement for implant placement on panoramic view compared to CBCT in posterior jaw area. Materials and Methods: The study was performed on 20 patients. In each of the posterior edentulous areas, a surgical guide for each patient was marked with gutta-percha (a total of 70 points). Panoramic radiographs and CBCTs were obtained from the patients and then the distance between the marked points in the maxilla to the maxillary sinus and in the mandible to the upper border of the alveolar canal was measured by Romaxis software and analyzed by Statistical software Stata 14. The obtained measurements of panoramic view were compared to CBCTs using t-test. P≤0.05 was considered significant. Results: The mean difference between the sizes obtained from panoramic radiography and CBCT radiography in the maxilla was 0.34 mm (P = 0.57) and the mean difference between the sizes obtained from panoramic radiography and CBCT radiography in the mandible was 0.86 mm (P = 0.004). Conclusion: According to the results of study, it is logical panoramic radiography just used to pre-assessment of implant procedures in posterior area of mandible were as it could be more reliable in maxilla.

Kinematics of steam film wetting while quenching cylindrical samples in thermal oils

The paper presents the determination of the velocity of the vapor front along the outer wall of a cylindrical specimen in the process of two-dimensional axisymmetric quenching of the samples in thermal oils. One thermal oil is Isorapid 277 HM heated to 40°C and the other thermal oil is Marquench 722 heated to 90°C. The experimental setup of the work consists of heating to a temperature of 850°C, then quenching three dimensionally different cylindrical probes. The dimensions of the probe were: ϕ25x100 ϕ50x150 and ϕ75x225 mm. All quenchings were done in strictly controlled conditions of the flow rate of the quenchant around the cylinder as well as maintaining the temperature of the quenchant within the maximum 40±2.5°C or 90d3°C, during the quenching of the samples. The velocity of movement of the steam front on the outer surface of the cylinder was determined from the time-measured values of temperatures at the marked points of each sample. The analysis of the steam front movement velocity along the cylinder wall starts from the moment the lower base of the probe touches the quenchant. During the process of immersing the test probe in the quenchant, in addition to measuring the temperatures in time, the time of lowering the probe to contact with the quenchant sample was also measured. The approximate average velocity of the vapor front was determined based on the indications of the lower and middle thermocouples located 1.5 mm below the outer surface of the cylinder wall. Based on the distance of one half the height of each probe and time, the velocity of the steam film movement or the kinematics of the steam film wetting was obtained. The obtained results were compared with the results of quenching in water and aqueous solutions of the same probes under the same strictly controlled conditions.

Logarithmic Connections, WZNW Action, and Moduli of Parabolic Bundles on the Sphere

Moduli spaces of stable parabolic bundles of parabolic degree 0 over the Riemann sphere are stratified according to the Harder–Narasimhan filtration of underlying vector bundles. Over a Zariski open subset $$\mathscr {N}_{0}$$ N 0 of the open stratum depending explicitly on a choice of parabolic weights, a real-valued function $$\mathscr {S}$$ S is defined as the regularized critical value of the non-compact Wess–Zumino–Novikov–Witten action functional. The definition of $$\mathscr {S}$$ S depends on a suitable notion of parabolic bundle ‘uniformization map’ following from the Mehta–Seshadri and Birkhoff–Grothendieck theorems. It is shown that $$-\mathscr {S}$$ - S is a primitive for a (1,0)-form $$\vartheta $$ ϑ on $$\mathscr {N}_{0}$$ N 0 associated with the uniformization data of each intrinsic irreducible unitary logarithmic connection. Moreover, it is proved that $$-\mathscr {S}$$ - S is a Kähler potential for $$(\Omega -\Omega _{\mathrm {T}})|_{\mathscr {N}_{0}}$$ ( Ω - Ω T ) | N 0 , where $$\Omega $$ Ω is the Narasimhan–Atiyah–Bott Kähler form in $$\mathscr {N}$$ N and $$\Omega _{\mathrm {T}}$$ Ω T is a certain linear combination of tautological (1, 1)-forms associated with the marked points. These results provide an explicit relation between the cohomology class $$[\Omega ]$$ [ Ω ] and tautological classes, which holds globally over certain open chambers of parabolic weights where $$\mathscr {N}_{0} = \mathscr {N}$$ N 0 = N .

Gaps of saddle connection directions for some branched covers of tori

We compute the gap distribution of directions of saddle connections for two classes of translation surfaces. One class will be the translation surfaces arising from gluing two identical tori along a slit. These yield the first explicit computations of gap distributions for non-lattice translation surfaces. We show that this distribution has support at zero and quadratic tail decay. We also construct examples of translation surfaces in any genus $d>1$ that have the same gap distribution as the gap distribution of two identical tori glued along a slit. The second class we consider are twice-marked tori and saddle connections between distinct marked points with a specific orientation. These results can be interpreted as the gap distribution of slopes of affine lattices. We obtain our results by translating the question of gap distributions to a dynamical question of return times to a transversal under the horocycle flow on an appropriate moduli space.

Legendrian skein algebras and Hall algebras

We compare two associative algebras which encode the “quantum topology” of Legendrian curves in contact threefolds of product type $$S\times {\mathbb {R}}$$ S × R . The first is the skein algebra of graded Legendrian links and the second is the Hall algebra of the Fukaya category of S. We construct a natural homomorphism from the former to the latter, which we show is an isomorphism if S is a disk with marked points and injective if S is the annulus.

On the unirationality of moduli spaces of pointed curves

We show that$$\mathcal {M}_{g,n}$$Mg,n, the moduli space of smooth curves of genusgtogether withnmarked points, is unirational for$$g=12$$g=12and$$2 \le n\le 4$$2≤n≤4and for$$g=13$$g=13and$$1 \le n \le 3$$1≤n≤3, by constructing suitable dominant families of projective curves in$$\mathbb {P}^1 \times \mathbb {P}^2$$P1×P2and$$\mathbb {P}^3$$P3respectively. We also exhibit several new unirationality results for moduli spaces of smooth curves of genusgtogether withnunordered points, establishing their unirationality for$$g=11, n=7$$g=11,n=7and$$g=12, n =5,6$$g=12,n=5,6.

A computer vision-based, in-situ springback monitoring technique for bending of large profiles

Bending processes have various advantages, such as less processing time, lower number of tooling parts, and cost compared to other manufacturing processes. However, one of the disadvantages of a bending process is the inevitable springback problem, which entails geometrical inaccuracy. Many researchers have made attempts to effectively measure springback in-line to control product quality and compensate for variability. While measurement tools and machines are available to measure springback, they might not be able to accommodate large products due to the size limit of measurement devices. Nevertheless, sensor-based monitoring is becoming critical to control product quality and to move towards Industry 4.0. In this paper, an in-situ springback monitoring technique for bending of large-size profiles is proposed to overcome the measurement restrictions for such profiles. A computer vision technique with the circular Hough transform was used to evaluate springback. The marked points on a profile were used to track the deformation of the workpiece. However, a weakness with image processing is to recognize the points from the complex background. Instead of employing global search for the points in an image frame, the marked points were detected by locally setting regions based on forming parameters such as a bending angle and stretching level. Springback was calculated by the change of position of those points. The results of springback monitoring were validated with the physically measured data from experiments. Based on this measurement technique, the feasibility of a computer vision-based springback monitoring in large-size profile bending is discussed in detail.

Defects, nested instantons and comet-shaped quivers

We introduce and study a surface defect in four-dimensional gauge theories supporting nested instantons with respect to the parabolic reduction of the gauge group at the defect. This is engineered from a $$\mathrm{{D3/D7}}$$ D 3 / D 7 -branes system on a non-compact Calabi–Yau threefold X. For $$X=T^2\times T^*{{\mathcal {C}}}_{g,k}$$ X = T 2 × T ∗ C g , k , the product of a two torus $$T^2$$ T 2 times the cotangent bundle over a Riemann surface $${{\mathcal {C}}}_{g,k}$$ C g , k with marked points, we propose an effective theory in the limit of small volume of $${\mathcal C}_{g,k}$$ C g , k given as a comet-shaped quiver gauge theory on $$T^2$$ T 2 , the tail of the comet being made of a flag quiver for each marked point and the head describing the degrees of freedom due to the genus g. Mathematically, we obtain for a single $$\mathrm{{D7}}$$ D 7 -brane conjectural explicit formulae for the virtual equivariant elliptic genus of a certain bundle over the moduli space of the nested Hilbert scheme of points on the affine plane. A connection with elliptic cohomology of character varieties and an elliptic version of modified Macdonald polynomials naturally arises.