## 2 Materials and Methods
### Mathematical Methods  
A simplified mathematical model was employed for this research, primarily focusing on simplifying shoulder anatomy for moment calculations. It assumes a single point of shoulder contact, consistent with similar studies where moments are estimated [18; 19]. The neck kinetic chain is open, and it consists of one main segment--the head. The most significant factor influencing neck moment is overall position of the head, which is defined by an angle. All ergonomic angles may affect head's angle, and while flexion and extension are biggest contributors to shoulder moment arm, it is important to be able to evaluate all angles. Figure 3A presents the principal schematic for head moment calculation in this model. Figure 2: The experiment lifting procedure environment and schematical view: (**A**)—patient transfer motion capture setup; (**B**)—patient load evaluation: (**B.1**)—patient reaction force estimation; and (**B.2**)—patient leftover reaction force estimation [20]. Based on the head moment calculation schematic (Figure 3A), the head moment arm is determined as the projection of the distance between the C7 vertebra and the head's center of gravity. The calculation for this moment is expressed as follows:  
\[S_{N}=F_{h}\cdot D_{h}=(m_{h}\cdot g)\cdot(\cos\delta\cdot L_{h}), \tag{2}\]  
Here, \(S_{N}\) represents the neck moment, \(F_{h}\) denotes the gravitational force at the center of mass, and \(D_{h}\) is the shoulder arm of head. \(m_{h}\) is mass, \(g\) is gravitational constant, and \(L_{h}\) signifies the distance between C7 and mass center of the head. This representation is applicable to both 2D and 3D environments, depending on how \(L_{h}\) and \(\delta\) are defined in the calculation. In this case, 3D vectors were defined in Rhino Grasshopper computational model to obtain representative values based on the marker positions. Figure 3B illustrates principal schematics for shoulder and elbow moment calculation. An additional simplification assumes the lower arm is a conjunction of the wrist and forearm. The load center of mass is calculated to be 10 cm closer than end of lower arm segment, based on approximated trunk size of the patient. Center of mass and other parameters are calculated accordingly. Center of mass calculation schematics are shown in Figure 4 and described in Expression (3) based on the Pamula, H. center of mass calculator [21]. The hand position is assumed to be clenched, as the patient is held during lifting. All the other dimensions and masses are calculated based on individual data. \[X_{la}=\frac{m_{d}\cdot X_{d}+m_{p}\cdot X_{p}}{m_{d}+m_{p}}, \tag{3}\]  
Here, \(X_{la}\) is the lower arm COG distance from elbow side. Other parameters are masses and COG distances, accordingly, with \(d\) representing lower arm and \(p\) representing hands. Figure 4: Unified forearm and hand center of mass schematics. Figure 3: Neck moment (**A**) and shoulder moment (**B**) calculation principal schematics. Purple outline represents patients body. The mathematical expression for shoulder moment is given in Expression (4). It comprises three separate moments: upper arm, lower arm, and load. Each component is the gravitational force multiplied by the shoulder arm distance from shoulder joint to center of mass of a calculated segment. The elbow moment is expressed with two components, the lower arm and the load, as presented in Expression (5). \[S_{S}=s_{S-ua}+s_{S-la}+s_{S-load}=F_{ua}\cdot D_{sua}+F_{la}\cdot Q_{sla}+F_{ load}\cdot Q_{sl}, \tag{4}\]  
\[S_{E}=s_{E-la}+s_{E-load}=F_{la}\cdot D_{ela}+F_{load}\cdot D_{el}, \tag{5}\]  
Since some of the data are not directly available in the output of the MVN system, those moments can be expressed using known metrics, primarily limb lengths and ergonomic angles. Schematic overview of further mathematical expressions is given in Figure 5A.