## 4 Minimum Power Loss Criterion  
Based on the previously established mathematical model and the conducted analysis, a custom software was developed to calculate the minimum power loss criterion based on joint angular velocities and maximum reaction forces obtained from the stability analysis of the loader that represents a worst-case scenario. Using the derived equations, the program computed the frictional power losses at each joint according to the defined mathematical model of the loader.  
The optimization criterion was defined for the optimal synthesis of the drive mechanisms of the loader manipulator. The goal was to minimize the power \(N_{li}\) required to overcome the resistance caused by friction in the joints of the kinematic pairs of the manipulator mechanisms during manipulation tasks.  
The objective function, which represents the minimum power loss, is defined by the following equation:  
\[f_{t}=min\frac{1}{n_{p}}\sum_{i}^{n_{p}}N_{li} \tag{16}\]  
where \(n_{p}\) represents the number of manipulator positions throughout the manipulation task.  
A program was developed to determine tribological criterion indicators for evaluating the generated variant solutions of manipulator mechanisms. The criterion indicator was determined based on an analytical estimation of power losses due to friction under a constant worst-case load.  
The program receives as input a file containing variant solutions of the loader, which includes parameters of the kinematic chain members and manipulator mechanisms, and the simulation conditions, i.e., the parameters of the manipulation task:  
\[U_{st}=\left\{\theta_{31},\theta_{35},\theta_{41},\theta_{43},\alpha_{i},t_{ z},t_{p},t_{i}\right\} \tag{17}\]  
here, \(\theta_{31}\), \(\theta_{35}\) are the angles of the arm position during the material loading and unloading operations, respectively, \(\theta_{41}\), \(\theta_{43}\) are the angles of the bucket's relative position at the beginning and end of the loading operation, respectively; \(\alpha_{i}\) is the bucket angle during the unloading of material, while \(t_{z}\), \(t_{p}\), and \(t_{i}\) are the durations of the loading, material transfer and unloading phases, respectively.  
When determining the tribological parameters in the manipulator joints, the possible loading resistance force, derived from the loader's stability conditions, acts on the manipulator mechanism throughout the entire manipulation task.  
By iteratively varying the duration \(t_{c}\) of the manipulation task, the program determines the positions of the kinematic chain and drive mechanisms. At each position, it calculates the tribological parameters of the revolute joints in the manipulator's kinematic pairs: angular velocity \(\omega_{i}\), normal forces \(F_{n}\), frictional resistance moments \(M_{tt}\), and the power \(N_{li}\) required to overcome frictional resistance between joint elements.  
The results obtained (Table 3) show that the generated variants of the manipulator mechanisms exhibit significantly different values of the objective functions \(f_{t}\), i.e., the indicators \(\rm p_{t}\) of the tribological criterion. It is notable that the variants of the manipulator mechanisms with smaller transformation parameters (smaller diameters of the piston/piston rod of the hydraulic cylinder) have lower values of the objective functions \(f_{t}\), and consequently higher indicators \(p_{t}\), than the variants with larger transformation parameters. For example, the variant V.271 (\(D_{3}/d_{3}=110/80\) mm, \(D_{4}/d_{4}=140/100\) mm) has the highest indicator (\(p=1\)), while the variant V.108 (\(D_{3}/d_{3}=150/100\) mm, \(D_{4}/d_{4}=180/125\) mm) has the lowest (\(p_{t}=0.532\)).