Product design and manufacturing leverage 3D scanning for various applications. This study aims to investigate the effectiveness of 3D scanning in furniture production by surveying the literature and showcasing four real-world case studies. The literature review reveals that 3D data acquired from real-world objects have applications in research, rapid prototyping, restoration, and preservation of antique furniture, optimizing CNC machining processes, and measuring furniture components for quality control. The case study descriptions demonstrated the circumstances, rationale, and methodology for 3D scanning. All the case studies analyzed stem from the collaboration between the Laboratory for Product Development and Design at the Faculty of Mechanical Engineering at the University of Sarajevo and various furniture production enterprises from Bosnia and Herzegovina. The conclusions highlight that 3D scanning in the furniture sector is advantageous for developing computer-aided design models from early-stage design prototypes, validating the dimensional accuracy of manufactured components by comparing with CAD models, safeguarding and reconstructing vintage furniture, and remanufacturing formerly produced goods that lack complete technical records (reverse engineering).

The current paper investigates the effects of geometric design parameters on the fatigue failure of the drive axle housing using the Finite Element Method (FEM). The study examines the effects of various factors on the fatigue life of the drive axle housing, such as axle housing wall thickness, housing cross-sectional rounding radius, and rounding radius of the central part of the housing. Based on the known material properties and dynamic loads, a CAD/FEM model of the drive axle housing was developed, and a structural analysis was carried out. Based on the results of the structural analysis, critical places on the housing were determined, and fatigue analysis and lifetime prediction were performed. Through a series of simulations, the study reveals that increasing housing wall thickness can significantly improve fatigue performance. Similarly, increasing the rounding radius at the housing cross-section, as well as the rounding radius at the central part of the housing can also lead to improved fatigue performance. However, the effect of increasing the value of these two radii is not as significant as the effect of the wall thickness. These findings give useful information regarding the design and manufacture of drive axle housings for vehicles, intending to reduce the likelihood of fatigue failure.

In this paper we present a local dynamics and investigate the global behavior of the following system of difference equations$x_{n+1}=ax_{n}^{3}+by_{n}^{3}$ $y_{n+1}=Ax_{n}^{3}+By_{n}^{3}$ $n\in\mathbb{N}_0$ with non-negative parameters and initial conditions $x_{0}$ and $y_{0}$ that are real numbers. We establish the relations for local stability of equilibriums and necessary and sufficient conditions for the existence of period-two solution(s). We then use this result to give global behavior results for special ranges of parameters and determine the basins of attraction of all equilibrium points.

Bridge crane is exposed to dynamic loads during its non-stationary operations (acceleration and braking). Analyzing these operations, one can determine unknown impacts on the dynamic behavior of bridge crane. These impacts are taken into consideration using selected coefficients inside the dynamic model. Dynamic modelling of a bridge crane in vertical plane is performed in the operation of the hoist mechanism. The dynamic model is obtained using data from a real bridge crane system. Two cases have been analyzed: acceleration of a load freely suspended on the rope when it is lifted and acceleration of a load during the lowering process. Physical quantities that are most important for this research are the values of stress and deformation of main girders. Size of deformation at the middle point of the main crane girder is monitored and analyzed for the above-mentioned two cases. Using the values of maximum deformation, one also obtains maximum stress values in the supporting construction of the crane.

We study the local dynamics and global character of third-order polynomial difference in the first octant of initial conditions with infinite number of prime period-three solutions (three cycles). It is also presented the case when the observed difference equation may be extended to the whole ℝ𝟑.

This study performed a mechanical stability analysis for the impact of axial pressure on an Ultra X external unilateral fixation device applied to a tibia with an open fracture. The real construction of the fixation device was used to create a 3D geometric model using a Finite Element Method (FEM) model, which was made to perform structural analysis in the CATIA V5 (Computer Aided Three-dimensional Interactive Application) CAD/CAE system. Specific stresses and displacements were observed at points of interest using structural analysis. The focus was on the relative displacements of the proximal and distal bone segments in the fracture zone. These displacements were used to calculate the stiffnesses of the bone in the fracture zone and the fixation device itself. The results obtained provide the necessary information regarding the stability of the Ultra X fixation device.

In this paper, we observed the ordinary differential equation (ODE) system and determined the equilibrium points. To characterize them, we used the existing theory developed to visualize the behavior of the system. We describe the bifurcation that appears, which is characteristic of higher-dimensional systems, that is when a fixed point loses its stability without colliding with other points. Although it is difficult to determine the whole series of bifurcations that lead to chaos, we can say that it is a common opinion that it is precisely the Hopf bifurcation that leads to chaos when it comes to situations that occur in applications. Here, subcritical and supercritical bifurcation occurs, and we can say that subcritical bifurcation represents a much more dramatic situation and is potentially more dangerous than supercritical bifurcation, technically speaking. Namely, bifurcations or trajectories jump to a distant attractor, which can be a fixed point, limit cycle, infinity, or in spaces with three or more dimensions, a foreign attractor.

This article explores a possibility to improve mathematical teaching by using 3D printing technology. The question is whether it is possible to use low cost additive manufacturing technology to develop and manufacture real physical prototypes of complex mathematical surfaces and volumes and on that way improve mathematics education. Five mathematical problems were chosen as case studies. Visualization of this problems was done using professor hand drawing, using computer visualization and using development and manufacturing of real physical prototypes. To find out how much better is understanding of these problems, survey with 57 students is carried out. Results showed significant improvements of understanding and better visualization of selected mathematical problems.

In this paper we observed the global dynamics and the occurrence of a certain bifurcation for the corresponding values of a certain rational difference equation of the second order with analyzed quadratic terms. The analysis of the local stability of the unique equilibrium point, as well as the unique periodic solution of period two, was performed in detail. The constraint of the equations on both sides for the corresponding values of the parameters is proved and on this basis the global stability is analyzed. The existence of Neimark-Sacker bifurcation with respect to the arrangement of equilibrium points has been proven. Thus, the basins of attraction have been determined in full for all the positive values of the parameters and all the positive initial conditions.

In this paper we proved the existence and local stability of prime period-two solutions for the equation 𝐱𝐧􀬾𝟏 􀵌 𝛂𝐱𝐧 𝟐 􀬾𝛃𝐱𝐧􀬾𝛄𝐱𝐧􀰷𝟏 𝐀𝐱𝐧 𝟐 􀬾𝐁𝐱𝐧􀬾𝐂𝐱𝐧􀰷𝟏 , for certain values of parameters ,,,A,B,C0, where ++>0 , A+B+C>0, and where the initial conditions x₋₁, x₀>0 are arbitrary real numbers such that at least one is strictly positive. For the obtained periodic solutions, it is possible to be locally asymptotically stable, saddle points or nonhyperbolic points. The existence of repeller points is not possible.

The goal of this research is development, design and manufacturing of CNC milling machine prototype using standard aluminium profiles. Machine is a three axis’s machine and it is developed primarily for education in the field of wood machining. It can be used also for machining of light metal parts. Main initial goal of the machine development was the low cost for its manufacturing. To achieve this goal, rapid prototyping technology was used to manufacture most of the machine parts. In addition, a lot of standard parts are used. The detail methodology for machine development, design and manufacturing are shown in this paper. Design process includes development of CAD models, calculation of all necessary critical parts, selections of materials and development of machine subassemblies and assemblies.

This paper describes comparative analysis of the biomechanical performances conducted on the external fixation devices whose frames are made out of two different material (stainless steel and composite material). Biomechanical properties were determined with experimental and FEM (finite element method) models which are used to study the movement of the fracture crack, establish stiffness of the design solutions and monitor generated stresses on the zones of interest. Geometric modeling of two fixation devices configurations B50 and C50 is used as a basis for structural analysis under the impact of axial load. Structural analysis results are confirmed with an experimental setup. Analyzed deflection values in the load and fracture zones are used to define the exact values of the stiffness for the construction design and fracture, respectively. The carbon frame device configuration has 28% lower construction stiffness than the one with the steel frame (for B50 configuration), i.e., 9% (for C50 configuration). In addition, fracture stiffness values for the composite frame application are approximately 23% lower (B50 configuration), i.e., 13% lower (C50 configuration), compared to steel frame. The carbon frame device has about 33% lower stresses at the critical zones compared to the steel frame at the control zone MM+ and, similarly, 35% lower stresses at the control zone MM-. With an exhausting analysis of the biomechanical properties of the fixation devices, it can be concluded that steel frame fixation device is superior, meaning it has better biomechanical characteristics compared to carbon frame fixation device, regarding obtained data for stresses and stiffnesses of the frame construction and fracture. Considering stresses at the critical zones of the fixation device construction, the carbon frame device has better biomechanical performances compared to steel frame devices.

UDK: 630*52:519.233.5]:582.475(497.6) As the result of sporadic afforestation of not-grown forest land in the past, today in B&H we have significant areas of even-aged forest plants of Scots pine of different ages. Estimate of yield capabilities of habitats/sites of these stands is one of very real issues in even-aged management planning for this tree species. In order to get the clear idea on the value of yield of even-aged stands, it is necessary to conduct long-term researches on permanent experimental plots. Considering that for the results of those researches it is necessary to wait approximately for the duration of production periods for specific tree species, to gain orientation solutions of the problem we can apply short-term researches – using temporary experimental plots set in stands of different ages. Members of the Forest Management Department of Forestry Faculty in Sarajevo in a period from 1985 to 1990 gathered data on temporary experimental plots in existing even-aged forest plantations of spruce, Scots pine and black pine in order to research their growth, structural and production characteristics. Part of those data for Scots pine is used for making of this document. Objective of this research was, based on data on measurement of 77 experimental plots positioned in even-aged not-tended plantations of Scots pine Bosnia-wide, to reach relevant information on the value of wood volume depending on their age and site quality, and to create the most favourable regression model for assessment of volume of large wood value based on known values of the stand taxation elements that could be easily and quickly determined. Besides this, in this document by comparing gained results with appropriate data from other authors we have evaluated productivity of even-aged not-tended forest plantations of Scots pine in B&H.

In this paper, a polynomial system of plane differential equations is observed. The stability of the non-hyperbolic equilibrium point was analyzed using normal forms. The nonlinear part of the differential equation system is simplified to the maximum. Two nonlinear transformations were used to simplify first the quadratic and then the cubic part of the system of equations.