In addition to other things, a robot’s design also determines its singularity configurations and points in the workspace. In designing the robot’s working trajectory, one of the main issues of robot steering is avoiding singularities. The article proposes a different approach to calculating the inverse task, which lies in the random mapping of the robot mechanism’s workspace through searching for points closest in proximity to the trajectory in question. The new methodology of mapping and detecting the states of singularity in the workspace is actually based on Monte Carlo analysis, since we were also interested in the number of occurrences. In terms of mathematical analysis, this method is less demanding, because in searching for joint variables suitable for the given trajectory, it does not use inverse calculation. It is important that the method is chosen appropriately. The method is sufficiently illustrative in the form of a graph, making, e.g., programming optimization simpler. The ultimate effect is the reduced time needed for computing joint variables and the availability of an option to select a robot configuration suitable for carrying out the required work. The paper offers an example of an analysis concerning three different robots.

This paper deals with a modified methodology for measuring the static stiffness of the machine tool. Inspiration to modify the commonly used expanded method of static stiffness measurement resulted from considerably different experimentally measured static stiffness values in the simulated process of load application under laboratory conditions compared to the standard method. An important takeaway from the measurements is that the measured static stiffness of the table depends greatly on the previous work performed thereon and on the method of the load application onto the table. This modified view of the static stiffness of the machine can have an impact on the increased emphasis on eliminating the phenomena related thereto. It is applicable in engineering practice, in particular in the field of machine tool design, where it will ensure higher machining precision under comparable conditions. In the experiments performed, deformations and displacements were measured with a laser interferometer.

The input of this paper lies in displaying possibilities how to determine the condition of a coordinate measuring machine (CMM) based on a large number of repeated measurements. The number of repeated measurements exceeds common requirements for determining positioning accuracy. The total offset in the accuracy of spatial positioning consists of partial inaccuracies of individual axes. 6 basic errors may be defined at each axis. In a triaxial set, that translates into 18 errors, to which an offset from the perpendicularity between the axial pairs must be added. Therefore, the combined number of errors in a single position is 21. These errors are systemic and stem from the machine’s geometry. In addition, there are accidental errors to account for as well. Accidental errors can be attributed to vibrations, mass inertness, passive resistance, and in part to fluctuations in temperature. A peculiar set of systemic errors are time-varying errors. The nature of those errors may be reversible, for instance if they result from influence of temperature or elastic deformation. They can be also irreversible, for example as a result of wear and tear or line clogging, due to loosened connection or permanent deformation of a part post collision. A demonstration of thermal equalizing of the machine’s parts may also be observed in case of failure to adhere to a sufficient time interval from the moment the air-conditioning is turned on. Repeated measurements done on a selected axis with linear interferometer can provide complex information on the CMM condition and also on the machine’s interaction with the given technical environment.

The paper describes the original robotic arm designed by our team kinematic design consisting of universal rotational modules (URM). The philosophy of modularity plays quite an important role when it comes to this mechanism since the individual modules will be the building blocks of the entire robotic arm. This is a serial kinematic chain with six degrees of freedom of unlimited rotation. It was modeled in three different environments to obtain the necessary visualizations, data, measurements, structural changes measurements and structural changes. In the environment of the CoppeliaSim Edu, it was constructed mainly to obtain the joints coordinates matching the description of a certain spatial trajectory with an option to test the software potential in future inverse task calculations. In Matlab, the model was constructed to check the mathematical equations in the area of kinematics, the model’s simulations of movements, and to test the numerical calculations of the inverse kinematics. Since the equipment at hand is subject to constant development, its model can also be found in SolidWorks. Thus, the model’s existence in those three environments has enabled us to compare the data and check the models’ structural designs. In Matlab and SolidWorks, we worked with the data imported on joints coordinates, necessitating overcoming certain problems related to calculations of the inverse kinematics. The objective was to compare the results, especially in terms of the position kinematics in Matlab and SolidWorks, provided the initial joint coordinate vector was the same.

Static stiffness is determined by one-sided loading and unloading of machine parts relative to the selected base. For each structure, there will be some loss of potential energy due to the dissipative forces that occur during the loading inside the structure. This loss is manifested in hysteresis in the stiffness diagram. A new approach to the assessment of static stiffness consists in gradual, bilateral loading and unloading of the structure through the effect of static forces of different magnitude. In this process, the stiffness hysteresis varies, depending on the intrinsic nature of the dissipative forces, a specific property suitable for assessing the condition of machines.

Topology optimization is a dynamically developing area of industrial engineering. One of the optimization tasks is to create new part shapes, while maintaining the highest possible stiffness and reliability and minimizing weight. Thanks to computer technology and 3D printers, this path of development is becoming more and more topical. Two optimization conditions are often used in topology optimization. The first is to achieve the highest possible structure stiffness. The second is to reduce the total weight of the structure. These conditions do not have a direct effect on the number of elements in the resulting structure. This paper proposes a geometric method that modifies topological structures in terms of the number of truss elements but is not based on the optimization conditions. The method is based on natural patterns and further streamlines the optimization strategies used so far. The method’s efficiency is shown on an ideal Michell truss.