## 1 Introduction
The study makes a significant contribution to the field of multi-objective and adaptable optimization of Z-bar mechanisms, employing a fully parameterized kinematic model and an enhanced complex optimization algorithm. However, this work focuses solely on geometric and functional performance, without considering friction, wear, or energy losses in the joints. In contrast, our research introduces tribological parameters and a minimum power loss criterion, thereby overcoming a key limitation of previous studies and enabling a more energy-efficient and durable design. In [22], the optimization procedure for the drive mechanisms of manipulators with parallelogram kinematics is presented using the MSC Adams optimization module, based on two objective functions: minimum change in the bucket angle and maximum mechanism ratio of the manipulator drive mechanisms. The study focuses on the optimization of an eight-bar loader mechanism based on simulation, with emphasis on improving the bucket angle and transmission ratio. Its main advantage lies in the use of dynamic simulation and the functional enhancement of the mechanism's geometry. Although the optimization results are valuable for functional characteristics, the study does not include force analysis, load evaluation, or the influence of friction, which limits the broader applicability of the results. In contrast, our research integrates tribological parameters and a minimum power loss criterion, thereby contributing to the development of a more reliable and energy-efficient design. As part of the research in [23], the authors conduct a sensitivity analysis to identify the parameters with the greatest impact on the objective functions. The following objective functions are selected for the multi-criteria optimization: minimum change in the bucket angle, maximum vertical reach, and minimum horizontal reach. The integration of fuzzy logic with weighted objective evaluation represents a methodological contribution in the field of complex mechanical system optimization. Although the optimization framework is thoroughly developed, the study lacks a connection to practical operational and maintenance requirements, such as wear, reliability, or durability. In contrast, our research explicitly incorporates tribological effects and energy dissipation as optimization criteria, thereby enhancing the practical applicability and functional reliability of the mechanism design. In previous research, the authors have normalized the multi-criteria optimization problem into a single criterion by using the Weighted Sum Method and the Penalty function. The maximum mechanism ratio as an objective function of the optimal synthesis, presented in previous works, does not take into account the importance of the position of the manipulator in the working range. Research [24; 25; 26; 27; 28; 29] has shown that the manipulator drive mechanisms are most heavily loaded during the material loading operation. This phase involves high resistance forces resulting from the interaction between the bucket and the excavation material, which significantly increases the forces transmitted through the kinematic chain and, consequently, the stress on the joints, hydraulic actuators, and structural elements. Due to these demanding working conditions, it is necessary to optimize the manipulator mechanism specifically for the loading operation phase. In [30], the authors propose a directed digging force criterion that defines the normalized limit digging force, determined on the basis of the loader stability conditions, with the aim of achieving maximum digging forces in the zone of the manipulator's working range, in which the material loading operation is most often performed. Therefore, the existing literature in the field of working mechanism optimization for construction machinery primarily focuses on kinematic characteristics, geometric parameters, and multi-objective approaches that do not include a detailed analysis of actual energy losses.