Kinematics as a science of geometry of motion describes motion by means of position, orientation, and their time derivatives. The focus of this article aims screw theory approach for the solution of inverse kinematics problem. The kinematic elements are mathematically assembled through screw theory by using only the base, tool, and workpiece coordinate systems-opposite to conventional Denavit-Hartenberg approach, where at least n þ 1 coordinate frames are needed for a robot manipulator with n joints. The inverse kinematics solution in Denavit-Hartenberg convention is implicit. Instead, explicit solutions to inverse kinematics using the Paden-Kahan subproblems could be expressed. This article gives step-by-step application of geometric algorithm for the solution of all the cases of Paden-Kahan subproblem 2 and some extension of that subproblem based on subproblem 2. The algorithm described here covers all of the cases that can appear in the generalized subproblem 2 definition, which makes it applicable for multiple movement configurations. The extended subproblem is used to solve inverse kinematics of a manipulator that cannot be solved using only three basic Paden-Kahan subproblems, as they are originally formulated. Instead, here is provided solution for the case of three subsequent rotations, where last two axes are parallel and the first one does not lie in the same plane with neither of the other axes. Since the inverse kinematics problem may have no solution, unique solution, or many solutions, this article gives a thorough discussion about the necessary conditions for the existence and number of solutions.

Automated Fiber Placement (AFP) is a relatively new technology that has revolutionized the production of composite structures in the aerospace and space industries for more than two decades and is nowadays increasingly used in new industries such as the wind energy. Generally, the AFP machine consists of an automatic manipulator (robot) on which a layup head is fixed for laying multiple individual composite strips at once (certainly not excluding the possibility of laying a single wider tape when it comes to Automatic Tape Placement). The layup process is performed on a mandrel or tool with a certain geometric shape. The laying head should at least include a feeder, a cutting mechanism, a compaction mechanism (usually roller) and a certain type of heater (depending on the material type). Conventionally, three types of composite materials are used in combination with AFP technology: continuous fibers reinforced with thermoset resin (usually epoxy resin), same continuous fibers reinforced with thermoplastic resin as well as bonded continuous carbon fibers. Depending on the type of material this technology uses various types of heat sources in order to achieve a good adhesion to the individual fibers that are deposited in the laying process and the pre-laid composite layers. Thermoplastic pre-impregnated material requires high temperature to reach degree of melting of the resin used to achieve complete 'welding' with the previous layers. The melting temperature varies for different materials and ranges from 130°C to 200°C for low melting thermoplastics (such as Polyamide PA and Polypropylene PP), 280°C to 350°C for Polypropylene Sulfide (PPS) up to 400°C - 450oC for Polyether Ether Ketone (PEEK). For more than two decades, hot gas torches have been used for thermoplastic layup - not a very expensive system but very difficult to control. One of the newer sources of heat close to infrared radiation (λ = 0.9-1.1 μm) is diode laser heating. This research presents a simple thermal model of the process which correlates the heater power and the layup speed with the temperature of the heating area. The deposition temperature was measured over a range of heater powers and layup speeds. The experimental data is used to define and validate a thermal model for thermoplastic material used in conjunction with a diode laser: carbon fibre reinforced thermoplastics PEEK. This enables open-loop, speed dependent heater power control, based on defining and programming the speed dependent heater power function in the machine controls. Obtained functional dependency was implemented in the AFP machine control system and tested for production of several plates with different layup angles. The achieved temperature during layup process is monitored on the thermal camera and through several pyrometers.

This paper presents a comprehensive pedagogical research related to mathematics instruction at the tertiary, university-level. Developed educational materials in electronic format, using the Matlab software package are integrated into instruction. The impact of using ICT on the essential knowledge related to the multivariate calculus, intensive use of 3D static and dynamic visualization tools has been statistically investigated. Some of students (experimental group) involved in the research study have individually created Matlab programs. Part of the research study is focused on the potential impacts of programming skills on learning mathematical concepts.

Composites as multiphase materials offer the possibility to influence their properties or to add new functionalities by a proper choice and combination of the different phases. In addition to get best properties for the composite design numerous calculations for different combination of the fibers winding angles should be done. This paper targets the design of a composite laminate structure used for production of high pressure vessel. The application developed in this research manages to design a composite with most effective elastic modules, in a time shorter than the usual composite designing time, taking into account filament winding process, materials price as well as the purpose of the final product. This application uses a database of available materials in order to point out which combination creates a pressure vessel of cheaper composite material with the best strength, bulk modulus and load level of failure.