## 3 Analysis of Joint Loading Under Different Drive Mechanism Variants  
A comprehensive analysis has been conducted to evaluate how variations in drive mechanism parameters affect the tribological behavior and friction-induced power loss in the revolute joints of a loader manipulator. The generation of variant solutions and the application of design constraints represent the first stage in the procedure for optimal synthesis of loader manipulator mechanisms. This process is based on a previously developed mathematical model of the loader. However, it is not the primary focus of this paper and is discussed in more detail in [12]. The process of generating variant solutions begins with the definition of a set of design parameters \(D_{p}\):  
\[D_{p}=\left[V,X_{i},Y_{i},Y_{d},Y_{t},t_{p},t_{i},t_{s},F_{d},p_{max}\right] \tag{14}\]  
where \(V\) is the bucket volume, \(X_{i}\), \(Y_{i}\), \(Y_{d}\), \(Y_{t}\) are the working area of the manipulator, \(\alpha_{t}\), \(\alpha_{i}\) are the angles of the bucket position during transport and unloading, \(t_{p}\), \(t_{i}\), \(t_{s}\) is the time of operation for the manipulation task, \(F_{d}\) is the declared bucket breaking force, and \(p_{max}\) is the maximum pressure of the manipulator hydrostatic drive system. The design (optimization) space is defined by the permissible variations of the transmission parameters of the mechanisms within the range:  
\[\varepsilon_{3j}^{min}\leq e_{3j}\leq\varepsilon_{3j}^{max}\ \forall\ j=1, \ldots,4;\quad e_{4j}^{min}\leq e_{4j}\leq e_{4j}^{max}\ \forall\ j=1,\ldots,10 \tag{15}\]  
where, \(e_{3j}^{min}\), \(e_{4j}^{min}\), \(e_{3j}^{max}\), \(e_{4j}^{max}\) represent the minimum and maximum values of the transmission parameters, defined on the basis of the available installation space and the requirement for undisturbed relative motion between the components of the manipulator drive mechanisms and the members of the loader's kinematic chain. In the synthesis of manipulator drive mechanisms, two types of variables are considered:Transmission parameters (continuous variables): include the coordinates of the joints and the lengths of the levers within the mechanism. These parameters define the geometric configuration and are optimized using a genetic algorithm. Possible variant solutions for the transmission part of the mechanism are selected on the basis of a set of geometric constraints that account for the relative positions of the mechanism's members in specific manipulator configurations. * Transformation parameters (discrete variables): refer to the diameters of the pistons and piston rods in the hydraulic cylinders that actuate the manipulator. As discrete design choices, they are selected on the basis of performance requirements, manufacturing constraints, and compatibility with the overall kinematic characteristics of the mechanism. As an example, various drive mechanism solutions were proposed for a loader manipulator with a \(Z\)-kinematics linkage system, a mass of 15,000 kg and a bucket capacity of 2.7 m\({}^{3}\). The selected parameters are based on the Komatsu WA320-6 loader, a typical mid-sized wheel loader which is widely used in construction, mining, and material handling applications. This configuration reflects standard industry practice and provides a realistic foundation for evaluating the performance of various drive mechanism solutions. The optimization was conducted within a defined search space and included specific design constraints. This procedure generated 300 design variants for the transmission components of the manipulator's drive system. After applying additional constraints related to the hydraulic cylinder characteristics, 26 feasible configurations were selected. These configurations exhibited notable differences in transmission and transformation parameters, as shown in Tables 1 and 2. Selected variants of the manipulator mechanisms have different transmission parameters. The variants V.001 and V.135 share the same transformation parameters (piston/piston