Background: A precise three-point shot (3S) is considered a key parameter of success in a basketball game, and therefore the factors that affect its success have always attracted the attention of researchers. Aim: The aim of this research was a biomechanical-mathematical analysis of 3S in basketball, in order to determine the key parameters for performing a 3S. Results: The research shows a model of shooting a basketball player from the central position of the shot with 6.75 m. The modeling led to the conclusion that the height of the throw, the speed and the angle of the throw of the ball have a positive and direct relationship with the angle at which the ball falls into the basket when it comes to a shot for three points. Conclusion: The height of the throw, the speed and the angle of the ball have a positive and direct relationship with the angle at which the ball hits the basket when it comes to a shot for three points. Anthropometric characteristics of the player, such as the length of the arm, and the height of the player, directly lead to a positive relationship with the throwing angle.

Aim To determine the effect of the load on the meniscus in relation to a different angle, and to present the impact of force on eventual injury of menisci. Methods Research included 200 males with average height of 178.5 cm, mass 83.5 kg, and average age of 22 years. The simulation of treadmill that was used in the evaluation of ischemic heart disease was made. Effects on the knee were evaluated by measuring at different inclinations (5°70', 6°80', 7°90', 9°10', 10°20', 11°30' and 12°40'). Results With increasing ascent of treadmill the load on the meniscus also increased. Each increase in ascent after 22% (which corresponded to the angle of 12°40' and seventh degree of load according to the Bruce protocol) at given anthropological values was an etiological factor for meniscus injury. Conclusion The seventh degree of load according to the Bruce protocol can lead to the meniscus injury.

© The Author(s) 2020. Published by ARDA. Abstract Background: The subject of this research is the creation of an optimal school bench design with the aim of determining the most favorable posture of students while sitting, taking into account the relevant ergonometric and biomechanical characteristics of the human body. For the proposed model of the school bench which allows adjusting the different slopes of its surface, the corresponding computer model of the student and the table was first created, and then biomechanical and RULA analysis was performed in order to determine the maximum load in the lumbar part. Next, for each test subject of given weight, it was necessary to determine the amount of maximum load in lumbar zone L3/L4 for different slope angles and to determine the critical angles at which the maximum permissible load of 3400 N is reached.

Background: The problem of heavy school bags is a global problem recognized in many countries in Europe and the world, including in Bosnia and Herzegovina. In addition to poor posture habits, "sedentary lifestyles" and insufficient physical activity, school bags is one of the main causes of low back pain and deformity in pupils. The recommendation of the World Health Organization (WHO) is that the weight of the school bag should not exceed 10% of the student's weight. However, in practice these limitations are far from reality with the obvious problems caused by too heavy bags. The aim of the paper is to identify and analyze the backbone load caused by the overweight school backpacks in real school work conditions and eliminate them by creating new solutions that are in line with ergonomic and biomechanical principles, as well as the recommendation given by WHO. Methods: The research included first grade primary school students at the age of seven, including their parents. The research began by interviewing parents with relevant questions, as well as measuring the students’ height and weight and the weight of their school backpacks. The analysis was performed in CATIA v5 software package (Dassault Systemes, Velizy-Villacoublay, France) using its advanced biomechanical modules. By knowing the anthropometric and work environment data with ergonomic design and analysis, the biomechanical analysis, rapid upper limb assessment (RULA) and carry analysis were performed. Results: The conducted survey showed that 84% of students walk from home to school nineteen minutes on average and that 77% of them carry their school backpacks independently. Based on the measurements, it has been shown that, on average, the weight of the school backpacks is well above the WHO recommendation. A study conducted on a representative sample of students confirmed the relation between fatigue and spinal pain caused by carrying a heavy school bag. Computer analysis showed excessive loads on the spinal segment of L4/L5 that were outside the normal range of 3,400 N. Conclusions: A simulated computer analysis using RULA and biomechanical analysis with calculations of maximum loads in the lumbar segment of students found that school backpacks carried by students were too heavy for their age and well beyond the normal limits and WHO recommendations. The analysis showed that it is necessary to reduce the weight of the bag by about 30%.

The action of forces in the back and abdomen under conditions of loading of different external forces at different bending angles is unexplored area. This paper presents a methodology that enables calculation of the magnitudes of forces in the back and abdominal muscles using the combined techniques of the CATIA software system, appropriate mathematical model and polynomial regression analysis. The person of 180cm in height and 85 kg in weight is loaded with 5 + 5 kg of cargo in both hands, and three cases of bending angles of 150, 300 and 600 relative to the vertical axis are analysed.

Introduction: Achilles tendon injuries usually occur with abrupt movements at the level of the ankle and foot, and the consequence is the overload of the Achilles tendon. Aim: Examine the Achilles tendon load as a function of the landing angle, and find the critical point at which the tendon overload begins and when a further increase in the landing angle can lead to rupture. Methods: The study has a prospective character. The input data represent the anthropometric values of the respondents, who are professional basketball players in the senior national team of Bosnia and Herzegovina and were processed in the CATIA v5-6 software solution. Software data processing analyzed the landing angles and the transfer of force to the Achilles tendon. The end result is a regression curve, which projects the angle at which the Achilles tendon is overloaded, and indicates an increased risk of possible injury to the tendon itself. Results: The onset of overloading starts at an angle of 32.28° and at an angle of 35.75° the overloaded load occurs, indicating the need for the subject to change the position of the foot to prevent damage to the tendon itself. Conclusion: An angle of 35.75° is the critical point at which the Achilles tendons are overloaded at the very landing. Prevention of injury should go in the direction of practicing the feet for a particular position at the time of the landing, and in the direction to develop adequate footwear that would mitigate the angle at the landing.

Knowing all characteristics of rotational system vibrations is most significant for a maintenance technician or engineer. Vibrations are carriers of a machine condition and by analysis of the vibration characteristics, it is possible to find what is the real cause of the vibrations. As a part of the research of rotational machinery vibrations, mathematical modeling of a rotational system is common tool before research is transferred to a real physical model. As an excellent method for this purpose, the best candidate could be a Finite Element Method. In this paper, an analysis of a Finite element model of rotational system motor – flexible coupling – rotor is presented. As a fault analyzed in this paper, misalignment and rotating looseness are modeled as external loads. For this FEM model of a rotational system is shown that it is suitable for the analysis of rotational machinery vibrations.

This paper shows a method to determine unknown angular accelerations of driving members of a planar mechanism with multiple degrees of freedom via partial mechanism reduction, assuming that driving loads are known for those driving members. Besides the partial reduction of mechanism, here we use the analysis of primary and secondary accelerations, as well as the principle of virtual displacements (virtual work). Using this method, a set of decoupled equations is obtained, which is an advantage when compared to classical methods, such as an application of generalized laws of dynamics, which result in a set of equations that are coupled. As an illustration of how to use the described method, an example is shown.

One of the most important and most challenging tasks of a mechanism analysis is the problem of mechanism kinematics. This paper shows the way to determine unknown angular accelerations of joint-bar mechanism components, by applying so-called (by authors) epsilon co-function. Using this method, the problem is reduced onto an analysis of relative angular accelerations of neighboring members within the mechanism and determination of a moment of all those vectors with respect to a point or an axis. The main contribution of this paper is that it shows the novel method how to calculate angular accelerations of mechanism members using analog form of equations that are similar to the moment balance equations in statics. Considering that the relative angular velocity vectors play role of forces in statics, this paper shows how to form a system of kinematic equations similar to moment equations in statics, which are sufficient to solve for all angular accelerations of a mechanism.

Analysis of flow around the high-speed body with an irregular shape (such as fragments/shrapnels formed after the detonation of high explosive projectiles) was performed using the method of numerical simulations. For supersonic motion regime, pressure and velocity flow fields, as well as the formation of shock waves, around an irregularly shaped body were analyzed. Also, streamlines around an irregularly shaped body moving through the atmosphere were visualized (Ansys Fluent) and analyzed.

This paper presents an analysis of beam elon-gation influence on the postbuckling displacements in case of axial compression by a force depending on axial deformation of the beam. It is performed both numerical and experimental analysis of this effect. Numerical analysis is done by using finite elements method. Nonlin-ear equilibrium equation is derived and solved using the method of simultaneous iterations. Verification of numeri-cal results is done by experimental analysis. Both numeri-cal and experimental results show significant influence of the beam elongation on postbuckling displacements.