Designing an outer toothed gear whose wheel teeth are outlined by the logarithmic spiral arcs

Toothed gears are the most common mechanical gears in machine building, which are characterized by high reliability and durability, a constant transfer number, and which can transmit high torque. During toothed gear operation, the surfaces of the teeth slide, which gives rise to friction forces and wears their working surfaces. To prevent this, the surfaces of the teeth need constant lubrication. This paper considers the design of a gear tooth engagement, which does not have friction between the surfaces of the teeth since they roll over each other without slipping. The profile of the tooth of such a gear is outlined by congruent arcs, symmetrical relative to the line that connects the center of rotation of the toothed wheel with the top of the tooth. These symmetrical curves at the top of the tooth intersect at the predefined angle. In the depressions of the wheel, adjacent teeth also intersect at the same angle. Such a condition can be ensured by a curve that at all its points crosses the radius-vector emanating from the coordinate origin, also at a stable angle equal to half of the given one. This curve is a logarithmic spiral. If the number of teeth of the drive and driven wheels is the same, then their teeth are congruent. Otherwise, the profiles of the teeth would differ but they could be outlined by congruent arcs of the same logarithmic spiral of the same length taken from different areas of the curve. The minimum possible angle at the top of the teeth is straight. At acute angle, the toothed gear operation is impossible. To build gear wheels with a right angle at the top of the tooth, it would suffice to set the number of teeth of the drive and driven wheels. The center-to-center distance is calculated using the derived formula. The transfer number of such a gear is variable but, with an increase in the number of teeth, the range of its change decreases. The algorithm of wheel construction is given.

Application of Virtual Reality Human-Computer Interaction Technology Based on the Sensor in English Teaching

In order to improve the online English teaching effect, the paper applies the sensor and human-computer interaction into the English teaching. The paper improves the sensor information by applying Kalman Filter, combines sensor positioning algorithm to trace the students in the English teaching online, and turns the kernels by the skeleton algorithm into corresponding coordinates of space rectangular coordinate system taking the waist as a coordinate origin to get a human-computer interaction skeleton model in the virtual reality. According to the actual needs of English teaching human-computer interaction, the paper builds a new English teaching system based on the sensor and the human-computer interaction and tests its performance. The experiments suggest that the smart system in the paper can effectively improve English teaching effects.

Comparative assessment of drought monitoring indices susceptibility using geospatial techniques

There are two main categories of dryness monitoring indices based on spectral feature space. One category uses the vertical distance from any point to a line passing through the coordinate origin, which is perpendicular to a soil line, to monitor the dryness conditions. The most popular indices are the Perpendicular Dryness Index (PDI) and the modified perpendicular dryness index (MPDI). The other category uses the distance from any point in feature space to the coordinate origin to represent the dryness status, for instance, the soil moisture (SM) monitoring index (SMMI) and the modified soil moisture monitoring index (MSMMI). In this study, the performances and differences of these four indicators were evaluated using field-measured SM (FSM) data based on Gaofen-1 (GF-1) wide field of view (WFV), Landsat-8 Operational Land Imager (OLI), and Sentinel-2 Multi-Spectral Instrument (MSI) sensors. Performance evaluations were conducted in two study areas, namely an arid and semi-arid region of northwest China and a humid agricultural region of southwest Canada. We employed gradient-based structural similarity (GSSIM) to quantitatively assess the similarity of the structural information and structural characteristics among these four indicators. Monitoring SM in bare soil or low vegetation-covered areas in the semi-arid region, the SMMI, PDI, MSMMI, and MPDI from Near-infrared (NIR)-Red had significantly negative linear correlations with the FSM at 0-5 cm depth (P < 0.01). However, SMMI was better than PDI in estimating SM in bare soil, which was better than MSMMI and MPDI for GF-1. Moreover, the PDI and SMMI had similar SM evaluation abilities, which were better than those of MPDI and MSMMI for Landsat-8. The GSSIM map of the SMMI/PDI and the MSMMI/MPDI showed that the low change areas accounted for 99.89% and 98.89% for GF-1, respectively, and 95.78% and 94.45% for Landsat-8, respectively. This result indicated that the SMMI, PDI, MSMMI, and MPDI values from NIR-Red in low vegetation cover were similar. In monitoring SM in agricultural vegetation areas, the accuracy of the four indices from Short-wave Infrared (SWIR) feature space was higher than that from NIR-Red feature space for Sentinel-2. The SM monitoring effect of MSMMI and MPDI was better than that of SMMI and PDI. Due to the lack of SWIR band, GF-1 was limited in monitoring SM in vegetation-covered areas. The SMMI and MSMMI, which do not rely on the soil line, were more suitable than PDI and MPDI for retrieving SM in the complex surface environment depending on the soil line and the number of parameters. GF-1 with 16 m resolution had higher accuracy in SM assessment than Landsat-8 with 30 m resolution and had almost the same accuracy as Sentinel-2 with 20 m.

Endmember Estimation with Maximum Distance Analysis

Endmember estimation plays a key role in hyperspectral image unmixing, often requiring an estimation of the number of endmembers and extracting endmembers. However, most of the existing extraction algorithms require prior knowledge regarding the number of endmembers, being a critical process during unmixing. To bridge this, a new maximum distance analysis (MDA) method is proposed that simultaneously estimates the number and spectral signatures of endmembers without any prior information on the experimental data containing pure pixel spectral signatures and no noise, being based on the assumption that endmembers form a simplex with the greatest volume over all pixel combinations. The simplex includes the farthest pixel point from the coordinate origin in the spectral space, which implies that: (1) the farthest pixel point from any other pixel point must be an endmember, (2) the farthest pixel point from any line must be an endmember, and (3) the farthest pixel point from any plane (or affine hull) must be an endmember. Under this scenario, the farthest pixel point from the coordinate origin is the first endmember, being used to create the aforementioned point, line, plane, and affine hull. The remaining endmembers are extracted by repetitively searching for the pixel points that satisfy the above three assumptions. In addition to behaving as an endmember estimation algorithm by itself, the MDA method can co-operate with existing endmember extraction techniques without the pure pixel assumption via generalizing them into more effective schemes. The conducted experiments validate the effectiveness and efficiency of our method on synthetic and real data.

A Soil and Impervious Surface Adjusted Index for Urban Impervious Surface Area Mapping

Index-based methods are widely applied to urban impervious surface area (ISA) mapping, but the confusion between ISA and soil remains unsolved. In this article, the near-infrared (NIR)-blue bands were selected as feature space by analyzing the spectra from the US Geological Survey spectral library, and a simple impervious surface ratio index (ISRI) was developed by shifting the NIR-blue coordinate origin toward the convergence point of the fitting lines of ISA and soil. The ISRI was then validated for threshold simulation, separability, and correlation analysis. Results demonstrated that ISRI had a good performance for ISA mapping in four cities in China with different geographic environments, with all extraction accuracies all above 90%. ISRI had a high separability between ISA and soil and was better than other indices (normalized difference built-up index and biophysical composition index). Further, ISRI has a close relationship with the ISA proportion. Therefore, ISRI would be a simple and reliable index for urban ISA mapping.

Evaluation of surface energy for formation of multiple edge cracks using Medg-integral

A novel contour integral approach termed Medg is introduced for computation of the surface energy required for the formation of multiple edge cracks. The method is developed by reinterpretation of the conventional M-integral with deliberate delimitation of integration contour and selection of coordinate origin. Due to path independence, this method is efficient, easy to implement by using finite elements, and does not require a complicated mesh around the crack tips for good accuracy. Attention is also addressed to discussion of the size effects on proper interpretation of its physical meaning. The adequacy of the numerical results computed for the finite size corrections has been validated by using some of the available empirical formulations. It is observed that the size effect can be neglected when the crack size remains under one-tenth of the structure size. The results of a specific multi-cracked geotechnical structure suggest that, the damage state such as degradation of the structural stiffness due to the presence of edge cracks can be properly inspected by using Medg.

Experimental Studies of Microchannel Tapering on Droplet Forming Acceleration in Liquid Paraffin/Ethanol Coaxial Flows

The formations of micro-droplets are strongly influenced by the local geometries where they are generated. In this paper, through experimental research, we focus on the roles of microchannel tapering in the liquid paraffin/ethanol coaxial flows in their flow patterns, flow regimes, and droplet parameters, i.e., their sizes and forming frequencies. For validity, the non-tapering coaxial flows (the convergence angle α = 0 ∘ ) are investigated, the experimental methods and experimental data are examined and analyzed by contrasting the details with previous works, and consistent results are obtained. We consider a slightly tapering microchannel (the convergence angle α = 2.8 ∘ ) and by comparison, the experiments show that the tapering has significant effects on the flow patterns, droplet generation frequencies, and droplet sizes. The regimes of squeezing, dripping, jetting, tubing, and threading are differentiated to shrink toward the coordinate origin of the C a c – W e d space. The closer it is to the origin, the less variations will occur. For the adjacent regimes of the origin, i.e., dripping and squeezing, slight changes have occurred in both flow patterns, as well as the droplet characters. In the dripping and squeezing modes, the liquid droplets are generated near the orifice of the inner tube. Their forming positions (geometry) and flow conditions are almost the same. Therefore, the causes of minute changes in such regimes are physically understandable. While in the jetting regimes, the droplets shrink in size and their forming frequencies increase. The droplet sizes and the frequencies are both linearly related to those of the non-tapering cases with the corresponding relations derived. Furthermore, the threading and the tubing patterns almost did not emerged in the non-tapering data, as it seemed easier to form elongated jets, thinning or widening, in the tapered tubes. This can be explained by the stable analysis of the coaxial jets, which indicates that the reductions in the microchannel diameters can suppress the development of the interface disturbances.

Neither past nor present : Authenticity and late twentieth-century architectural heritage

It was the present moment. No one need wonder that Orlando started, pressed her hand to her heart, and turned pale. For what more terrifying revelation can there be than that it is the present moment? That we survive the shock at all is only possible because the past shelters us on one side and the future on another. But we have no time now for reflections.(Virginia Woolf, Orlando)How long does the present moment last? Where and when does the past begin and how does the present end? In physics – or more precisely in the special theory of relativity – the present can be defined as the coordinate origin in a spacetime diagram – an unextended point that separates an observer’s past and future light cones. From that point of view, the present has no duration at all; the past instantly assimilates the future without any hesitation in between. However, time perception tells us that we actually experience a ‘here and now’. Psychologists believe that the time range we perceive as the present, the socalled specious present, lasts about three seconds – the interval duration after which the brain may be said to reset its attention. This is already infinitely more than no duration at all but this recognition is still not enough to explain concepts like the present time or ‘today’ as an indicator of the contemporary. In the domain of history, the present seems to be a much more complex construction. When we speak of phenomena as contemporary, we place them in an extended present. We concede that the present encompasses the recent past and the near future – a temporal range that provides a stage for the actions and reactions that shape our world.

Energy and Work

This chapter discusses the work–energy theorem, which is developed from Newton’s second law, and defines the kinetic and potential energies of the system. While there is some vector calculus involved, it has been kept to the bare minimum and the reader should not require in-depth knowledge to understand the salient points. If there is a net force on the particle, it accelerates in the direction of the unbalanced force. The force is a central force if it depends only on the distance between the point on which the force acts and the coordinate origin. Using Stokes’s theorem, potential energies are thoroughly discussed. The chapter also discusses spherically symmetric potentials, isotropic force, force on systems of particles, centre of mass coordinates and rigid bodies.

A Sparse Modulation Signal Bispectrum Analysis Method for Rolling Element Bearing Diagnosis

Modulation signal bispectrum (MSB) analysis is an effective method to obtain the fault frequency for rolling bearing, but harmonics make fault frequency dense and even frequency aliasing. Carrier frequency of bearing is generally determined by its structure and inherent characteristics and changes with the increase of the damage degree, so it is hard to be accurately found. To solve these problems, this paper proposes a sparse modulation signal bispectrum analysis method. Firstly the vibration signal is demodulated by MSB analysis and its bispectrum is obtained. After the frequency domain filtering, the carrier frequency is computed based on the characteristics of energy concentration at the carrier frequency on MSB. By shift-frequency MSB (SF-MSB), the carrier frequency is moved to the coordinate origin, the entire MSB is shifted for the same distance, and SF-MSB is obtained. At last, the bispectrum is shifted to the frequency zero point and diagonal slices are performed to obtain a sparse representation of MSB. Experimental results show that sparse MSB (S-MSB) method can not only eliminate the interference of harmonic frequency, but also make the extracted characteristic frequency of fault more obvious.