## 1 Introduction  
The complexity of production processes and the variety of products in small and medium-sized businesses with high-mix, low-volume production require relatively high investment costs in the case of conventional industrial robotization [1]. This has resulted in a shortage of robotic work processes within small-scale production companies. Thus, most production processes are still performed manually, which often cannot ensure optimal and competitive production. The development of collaborative robotic systems in combination with other technologies offers more and more [2] opportunities for the automation of jobs, even in companies with custom production such as the toolmaking industry. A collaborative robotic system aims to achieve more flexible execution of even highly complex tasks. It can also help to increase the adaptability of robotic systems by incorporating humans into the work process [3, 4] when full automation is not viable or financially justifiable. Collaborative robots assist humans to achieve a more efficient work process by relieving them of monotonous and physically demanding tasks, while the humans use their abilities of flexibility, adaptability, and intelligence. As a result, improved productivity and market competitiveness could be achieved by this approach. To attain greater flexibility and adaptability of collaborative robotic systems, and thus shorten the time required to implement a specific robotic task solution, some algorithms have recently been developed to enable more autonomous trajectory planning [5]. To make such robotic tasks feasible,a thorough understanding of the robot's moving abilities within its working space is essential for planning and executing more complex robotic tasks, such as robotic surface machining [6]. In the case of complex robotic tasks, where simultaneous tracking of the tool tip along the surface of the workpiece at a constant tool speed is required, such as milling [7; 8], welding [9], composite laying [10; 11] or hammer peening, it is not always necessary that such a task will be feasible with the required technological parameters for arbitrary workpiece placement in the robot's workspace. The available motion capabilities are reduced significantly if we compare collaborative robots to traditional industrial robots, due to the size of the integrated actuators [6]. The predefined robot's surface machining path will be executable successfully according to the required technological parameters only if we determine the appropriate placement of the workpiece. To ensure that the collaborative robot's capabilities will not be exceeded during the execution of the robotic task, it is necessary to determine the workpiece placement for which the robot's movement capabilities are the best possible. Moreover, this ensures the robotic task can be accomplished with increased tool speed, which results in significant time savings during the usually time-consuming surface machining process. In the past, researchers have searched for the optimal position of the workpiece based on different kinematic criteria. Due to the reduced stiffness of robots compared to conventional CNC machines, optimal workpiece placement was determined to optimize the stiffness of the robot along a trajectory, and thereby increase the accuracy of robotic machining, such as robotic milling [8; 12; 13]. By optimizing workpiece placement, the improved accuracy of robot-based additive manufacturing can be achieved, particularly for applications such as robotic 3D printing [14]. The primary goal of determining the optimal placement of the workpiece for other authors has been to minimize energy consumption [15; 16].