Step by step, one foot in front of the other – the easiest thing in the world, right? In reality, the human gait is one of the most complex movements we perform. How can we describe it, and what can gait analysis tell us?

This work is an analysis of fabrication of a prior-designed wind turbine blade using the CAM system software. The presented research was realized on a 5-axis CNC machine.

This work is an analysis of construction and creation of a 3D model of a wind turbine blade in a CAD environment, using SOLIDWORKS on the basis of forces influencing the blade, which were determined using WIATRAK 1.1 software. The presented process is related to the issues of 3D modelling of a wind turbine blade and simulation of fabrication process in the CAM environment.

In order for a quadruped robot to be able to move on wheels while keeping its platform in horizontal position, and to walk, the kinematic system of its limbs should be so designed that each of the wheels has at least four degrees of freedom. Consequently, the designed system will have many DOFs and many controlled drives. This paper presents a novel solution in which, thanks to a suitable limb kinematic system geometry, the number of drives for the robot travel function, i.e. travelling on an uneven surface with the robot platform kept horizontal, has been reduced by four which are used only for walking. The robot structure, the required geometry of the limb links and the driving torque characteristics are presented. Moreover, an idea of the control system is sketched. Finally, selected results of the tests carried out on the robot prototype are reported.

In the design of asphalt mixtures for paving, the choice of components has a remarkable importance,as requirements of quality and durability must be assured in use, guaranteeing adequate standardsof safety and comfort.

In this paper, an approach of analysis on the aggregate materials using fractal geometry is proposed. Following an analytical and an experimental approach, it was possible to find a correlation betweencharacteristics of the asphalt concrete (specific gravity and porosity) and the fractal dimension ofthe aggregate mixtures.

The studies revealed that this approach allows to draw the optimal fractal dimension and, conse-quently, it can be used to choose an appropriate aggregate gradation for the specific application;once the appropriate initial physical parameters are finalized.

This fractal approach could be employed for predicting the porosity of mixed asphalt concretes,given as input the fractal characteristics of the aggregate mixtures of the concrete materials.

Hørbyebreen surged in the 19th or early 20th century, as suggested by geomorphological evidences and looped medial moraines. In this study, we investigate its wide−spread geometry changes and geodetic mass balance with 1960 contour lines, 1990 and 2009 digital elevation models, in order to define the present−day state of the glacier. We also study its thermal structure from ground−penetrating radar data. Little is known about the glacier behaviour in the first part of the 20th century, but from its surge maximum until 1960 it has been retreating and losing its area. In the period 1960–1990, fast frontal thinning (2–3 m a −1 ) and a slow mass build−up in the higher zones (~0.15 m a −1 ) have been noted, resulting in generally negative mass balance (−0.40 ± 0.07 m w. eq. a −1 ). In the last studied period 1990–2009, the glacier showed an acceleration of mass loss (−0.64 m ± 0.07 w. eq. a −1 ) and no build−up was observed anymore. We conclude that Hørbyebreen system under present climate will not surge anymore and relate this behaviour to a considerable increase in summer temperature on Svalbard after 1990. Radar soundings indicate that the studied glacial system is polythermal, with temperate ice below 100–130 m depth. It has therefore not (or not yet) switched to cold−bedded, as has been suggested in previous works for some small Svalbard surge−type glaciers in a negative mass balance mode.

Real objects in horizontal projection often have a complex geometry. Their irregular shape causes issues during analyses and calculations that consider their geometry. The paper proposes the replacement of real-world objects with equivalent rectangles (ER). The paper also defines the geometric criteria of ER as well as ER parameters and methods for calculating them. The paper also demonstrates the difference in the duration of calculations for different types of rectangles (equivalent rectangle with the same area, surrounding rectangle with the smallest area, inscribed rectangle with the largest area). The presented approach has been illustrated with three case studies. The first one is the application of ER to underground mining cavities to determine post-mining deformations of the ground surface. In the second study, an ER was applied to analyse the geometry of agricultural parcels in a selected part of a rural settlement. ER can help assess whether the spatial layout is faulty and if a planning intervention is necessary. The third example describes a building’s geometry with an ER. Regarding the simplification of building’s geometry, it is crucial to replace a simplified building with a model that has the same centroid location and the same area. It is the perfect solution for rapid analyses of displaying objects on maps in various scales.

The processing of cartographic data demands human involvement. Up-to-date algorithms try to automate a part of this process. The goal is to obtain a digital model, or additional information about shape and topology of input geometric objects. A topological skeleton is one of the most important tools in the branch of science called shape analysis. It represents topological and geometrical characteristics of input data. Its plot depends on using algorithms such as medial axis, skeletonization, erosion, thinning, area collapse and many others. Area collapse, also known as dimension change, replaces input data with lower-dimensional geometric objects like, for example, a polygon with a polygonal chain, a line segment with a point. The goal of this paper is to introduce a new algorithm for the automatic calculation of polygonal chains representing a 2D polygon. The output is entirely contained within the area of the input polygon, and it has a linear plot without branches. The computational process is automatic and repeatable. The requirements of input data are discussed. The author analyzes results based on the method of computing ends of output polygonal chains. Additional methods to improve results are explored. The algorithm was tested on real-world cartographic data received from BDOT/GESUT databases, and on point clouds from laser scanning. An implementation for computing hatching of embankment is described.

It is shown that decrease and damping of the traction force at the end of the plunger move is possible not only due to application of a special keeper design, but also due to change of the plunger shank geometric form. The computer modeling with the use of finite element method is used to analyze the influence of system geometry on force distribution along plunger movement. The damping effect is confirmed when special shape plunger shanks are used.

The paper analyzes, from the geometrical aspect, the quality of the new flux cored wire intended for cladding process in function of changes in cladding parameters such as welding speed, coefficient of thermal conductivity, power source setting, the length of projecting portion of the electrode. The results of bead geometry analysis allows to illustrate the nature of the impact of the examined input variables on parameters of generated surface. The most important parameters here are the depth of penetration and the height of clad. The experimental data were processed using the Plackett-Burman experiment, which describes the impact of technological parameters on the main parameters used during production of resisting panels. It shows mathematical relations describing correlations between the input parameters and the value of depth of penetration and hight of bead made by Flux Cored Arc Welding (FCAW).

A new double stator permanent magnet machine having two sets of alternating current (AC) windings in separate stators is proposed in this study. The proposed machine is appropriate for low-speed direct-drive applications. 2D- and 3D-finite element analysis (FEA) is adopted in the result predictions. The considered machine elements are: coil and phase flux linkage, coil and phase induced-electromotive force (EMF), copper loss, current density and torque characteristics. The analysis shows that the studied permanent magnet (PM) machine has better electromagnetic performance than its single-stator equivalent. Moreover, the proposed machine has potential for higher reliability if the separate stators are used independently. The effect of design parameters on open-circuit flux linkage and induced-electromotive force, as well as on the average electromagnetic torque of the proposed double stator machine is also presented. It is observed that for each of the investigated design variables, there is a need to select the optimal value in order to achieve the best average torque. The investigated design parameters are: the split ratio, magnet thickness, rotor radial thickness, inner stator tooth-width, rotor inner and outer iron-width/pitch ratio, and stator yoke size.

Products of complex geometry, aerodynamic shape and high quality surface finishes are among the most difficult to produce by using stamping methods. When additionally materials with special properties are intended, the task of determining their technological character becomes difficult to solve without the use of physical and numerical methods of process modeling. The paper presents the results of modeling the process of producing a single tube of the jet engine tubular diffuser subassembly. This is a product representative of such a complex geometry one. The charge material for this element requires resistance to operating conditions at elevated temperature and high durability. Therefore, an Inconel type nickel superalloy was proposed for the charge material. In the solution of designing the method of producing a single diffuser tube task, the capabilities of the AutoGrid automatic strain analyzer and the FEM simulation software Eta / Dynaform 5.9 were combined. Numerical simulations of different variants of the manufacturing process of the diffuser tube were made using the Eta / Dynaform 5.9 software. The results of forming simulations became the basis for the alternative technological cycle design of this drawpiece.

Usually, cellular networks are modeled by placing each tier (e.g macro, pico and relay nodes) deterministically on a grid. When calculating the metric performances such as coverage probability, these networks are idealized for not considering the interference. Overcoming such limitation by realistic models is much appreciated. This paper considered two- tier twohop cellular network, each tier is consisting of two-hop relay transmission, relay nodes are relaying the message to the users that are in the cell edge. In addition, the locations of the relays, base stations (BSs), and users nodes are modeled as a point process on the plane to study the two hop downlink performance. Then, we obtain a tractable model for the k-coverage probability for the heterogeneous network consisting of the two-tier network. Stochastic geometry and point process theory have deployed to investigate the proposed two-hop scheme. The obtained results demonstrate the effectiveness and analytical tractability to study the heterogeneous performance.

The article presents the use of computer graphics methods and computational geometry for the analysis on changes of geometrical parameters for a mixed zone in resistance-heated samples. To perform the physical simulation series of resistance heating process, the Gleeble 3800 physical simulator, located in the Institute for Ferrous Metallurgy in Gliwice, was used. The paper presents a description of the test stand and the method for performing the experiment. The numerical model is based on the Fourier-Kirchoff differential equation for unsteady heat flow with an internal volumetric heat source. In the case of direct heating of the sample, geometrical parameters of the remelting zone change rapidly. The described methodology of using shape descriptors to characterise the studied zone during the process allows to parametrise the heat influence zones. The shape descriptors were used for the chosen for characteristic timing steps of the simulation, which allowed the authors to describe the changes of the studied parameters as a function of temperature. Additionally, to determine the impact of external factors, the remelting zone parameters were estimated for two types of grips holding the sample, so-called hot grips of a shorter contact area with the sample, and so-called cold grips. Based on the collected data, conclusions were drawn on the impact of the process parameters on the localisation and shape of the mushy zone.

The relationships between the conditions that describe the shape of the flow and power consumption characteristics and the pump design and performance parameters are described. These relations concern: - flow characteristics (throttling curves) described with a fourth-order polynomial, - non-overloading power consumption characteristics of the pump. The pumps that have to exhibit such characteristics are these designed to operate in an arbitrary installation. These pumps must also be characterised by cavitation-free operation in the whole range of discharge variability. In the relations presented, the condition of cavitation-free operation is considered as well.

castings. The possibility of reducing the total volume of machining allowances, reducing the wear of cutting tools, shortening machining time and eliminating idle machining passes was considered. The tests were carried out on two batches of castings supplied by two independent foundries. Casting geometry measurements were made using a structured light scanner. The analysis included machining with cemented carbide tools and tool ceramics at two machining centers: DMC200U and DMC270U. It has been shown that as a result of eliminating idle machining passes, it is possible to reduce machining time by 12% for the first and by 44% for the second casting supplier. The estimated annual savings for the production volume of 500 pcs of these castings can range from € 7388 to even € 23 346. The actual cost of cheaper casts was also calculated, taking into account the difference in machining cost resulting from larger machining allowances.

Andrzej Białynicki-Birula, Professor at the University of Warsaw died on April 19, 2021 at the age of 85. He was an outstanding mathematician, who made important contributions to algebra and algebraic geometry. He published many important articles in most prestigious journals such that Annals of Mathematics, Inventiones mathematicae, Topology, American Journal of Mathematics. Professor Białynicki graduated from the University of Warsaw and obtained Ph.D. from the University of California at Berkeley in 1960. After his return to Poland he initiated and played a major role in modernization of research and university curricula in a broad spectrum of mathematical disciplines related to algebra. He has published several textbooks on linear algebra, algebra, algebraic geometry and cryptography, which are currently used at the University of Warsaw and many other Polish universities. Professor Białynicki-Birula served as the dean of the Faculty of Mathematics, Informatics and Mechanics (1977–1981) and as the vice-rector of the University of Warsaw (1985–1987). He was an ordinary member of the Polish Academy of Sciences, and a member of the Academia Europea. In recognition of his achievements Professor Białynicki-Birula received several prizes and distinctions, among them the Officers Cross of the Order Polonia Restituta. Professor Białynicki-Birula was also an art collector, particularly interested in a gothic sculpture, on which he was an expert. In his summerhouse near Belorussian border he was renovating and collecting ethnographic objects related to everyday life and work of peasants. He left a wife, Magdalena Borsuk-Białynicka, a professor of palaeontology, two daughters, a son and 11 grandchildren.

When Zamość was being built the Fortress was in a close connection with the geometry of view. This was reflected both in the utilitarian and aesthetic sphere and concerned the urban scale as well as the scale of long exposure. The visual study conducted within the Study of the shaping of postfortress areas of Zamość Fortress allowed for assessing the contemporary state of exposure and for identification of the correction opportunities. The effect of the study has become the essential element of the design concept in both the compositional and in the part related to the tourist access.

Spitsbergen glaciers react rapidly to changes in the polar environment, which is expressed in differences in extent of their fronts and surface geometry. The Scott Glacier, which is situated in the NW part of Wedel Jarlsberg Land, is an example of the glacier that has undergone almost continuous recession since the Little Ice Age, interrupted by surges. The variations in recession are characterised based on multiannual data with particularly consideration of the period 1990–2005 and the season 2005/2006. Acceleration of front recession and lowering the surface was found only within the tongue up to a height of about 220 m a.s.l. Whereas, in the area situated in the zone of rock steps and above in the ablation zone, the change of glacier surface ablation (Dh) has been recorded compared to the mean annual recession for the period 1990–2005. Moreover, for the upper firn field, the positive surface ablation (DhS7 = +0.19 m) was observed. As the result of progressive reduction of the Scott Glacier mass, with the participation of other factors (bedrock relief among others), new surfaces of roche moutonnée are uncovering particularly in the tongue zone.

Image sequences, in particular digital video sequences, are characterised by the features which result in their high potential as measurement data. However, as early as at the stage of visual assessment of digital film images, originating, in particular, from amateur cameras, occurrence of some deformations may be observed, which may highly influence the results of measurements performed using these images; such deformations differ from deformations occurred in the case of static photographic images. It results both, by the method of image recording, using an electronic shutter and interlaced or progressive scanning, as well as the method of file recording and compression. It is worth to notice the systematic nature of such deformations, which highly depend on mutual motions of a camera and recorded objects. The objective of presented research works was to develop the mathematical description of image deformations, as a function of motion parameters. This would allow for adaptation of the camera calibration process to the demands of sequential imaging, as well as for modification of algorithms of measurements using self-calibration, and, as a result, minimisation of deformations. Another objective was to analyse the influence of deformations, typical for digital film images, on the results of measurements performed using these images, by means of series of experiments, which were based on multiple calibration of static and a moving camera, also with the use of a spatial test field. The first part was made by developing formulas based on some geometric relations, using some simplifications. On the stage of experimental research a certain degree of compatibility of experimental results and theoretical assumptions were confirmed.

Various methods for steady-state and transient analysis of temperature distribution and efficiency of continuous-plate fins are presented. For a constant heat transfer coefficient over the fin surface, the plate fin can be divided into imaginary rectangular or hexangular fins. At first approximate methods for determining the steady-state fin efficiency like the method of equivalent circular fin and the sector method are discussed. When the fin geometry is complex, thus transient temperature distribution and fin efficiency can be determined using numerical methods. A numerical method for transient analysis of fins with complex geometry is developed. Transient temperature distributions in continuous fins attached to oval tubes is computed using the finite volume - finite element methods. The developed method can be used in the transient analysis of compact heat exchangers to calculate correctly the heat flow rate transferred from the finned tubes to the fluid.

A proper selection of steam reforming catalyst geometry has a direct effect on the efficiency and economy of hydrogen production from natural gas and is a very important technological and engineering issue in terms of process optimisation. This paper determines the influence of widely used seven-hole grain diameter (ranging from 11 to 21 mm), h/d (height/diameter) ratio of catalyst grain and Sh/St (hole surface/total cylinder surface in cross-section) ratio (ranging from 0.13 to 0.37) on the gas load of catalyst bed, gas flow resistance, maximum wall temperature and the risk of catalyst coking. Calculations were based on the one-dimensional pseudo-homogeneous model of a steam reforming tubular reactor, with catalyst parameters derived from our investigations. The process analysis shows that it is advantageous, along the whole reformer tube length, to apply catalyst forms of h/d = 1 ratio, relatively large dimensions, possibly high bed porosity and Sh/St ≈ 0.30-0.37 ratio. It enables a considerable process intensification and the processing of more natural gas at the same flow resistance, despite lower bed activity, without catalyst coking risk. Alternatively, plant pressure drop can be reduced maintaining the same gas load, which translates directly into diminishing the operating costs as a result of lowering power consumption for gas compression.