## 2 Materials and Methods
### Development of a Human Body Load Evaluation Model
#### 2.3.1 Human Posture Risk Classification on Inverse Trigonometric Function  
The reference planes of the human body are defined as the sagittal, coronal and horizontal planes as shown in Figure 4, the normal direction of the sagittal, coronal and horizontal planes of the human body are defined as the X-axis, Y-axis and Z-axis of the human body coordinate system, and the projection angles of the human body limbs in the horizontal, coronal and sagittal planes are defined as torsion angles \(\theta\), deflection angles \(\varphi\) and bending angles \(\psi\). Biomechanics analysis evaluates physical workloads in terms of joint force or torque. The force between adjacent bone segments is determined by the angle of the adjacent bone segments and the applied load, therefore, the angle between the adjacent bone segments needs to be calculated first. The three joint points controlling two adjacent limbs are defined as \(\mathrm{P_{1}(x_{1},Y_{1},z_{1})}\),\(\mathrm{P_{2}(x_{2},y_{2},z_{2})}\),\(\mathrm{P_{3}(x_{3},y_{3},z_{3})}\). The relative angle, the relative torsion angle, the relative deflection angle, and the relative bending angle of two adjacent limbs are calculated from inverse trigonometric functions with the equations shown below:  
\[ \begin{split}&\gamma_{\mathrm{n}}=\cos^{-1}\frac{\left(\mathrm{P_{1} -P_{2}}\right)\left(\mathrm{P_{3}-P_{2}}\right)}{\left\|\mathrm{P_{1}-P_{2}} \right\|\left\|\mathrm{P_{3}-P_{2}}\right\|}\\ &=\cos^{-1}\frac{\left(\mathrm{x_{1}-x_{2}}\right)\left(\mathrm{ x_{3}-x_{2}}\right)+\left(\mathrm{y_{1}-y_{2}}\right)\left(\mathrm{y_{3}-y_{2}} \right)+\left(\mathrm{z_{1}-z_{2}}\right)\left(\mathrm{y_{3}-z_{2}}\right)}{ \sqrt{\left(\mathrm{x_{1}-x_{2}}\right)^{2}+\left(\mathrm{x_{3}-x_{2}}\right) ^{2}}\sqrt{\left(\mathrm{y_{1}-y_{2}}\right)^{2}+\left(\mathrm{y_{3}-y_{2}} \right)^{2}}\sqrt{\left(\mathrm{z_{1}-z_{2}}\right)^{2}+\left(\mathrm{z_{3}- z_{2}}\right)^{2}}}\end{split}  \tag{1}\]  
\[ \begin{split}&\psi_{\mathrm{n}}=\cos^{-1}\frac{\left(\mathrm{P_{1} ^{\mathrm{T}}-P_{2}^{\mathrm{T}}}\right)\left(\mathrm{P_{3}^{\mathrm{T}}-P_{2 }^{\mathrm{T}}}\right)}{\left\|\mathrm{P_{1}^{\mathrm{T}}-P_{2}^{\mathrm{T}}} \right\|\left\|\mathrm{P_{3}^{\mathrm{T}}-P_{2}^{\mathrm{T}}}\right\|}\\ &=\cos^{-1}\frac{\left(\mathrm{x_{1}-x_{2}}\right)\left(\mathrm{ x_{3}-x_{2}}\right)\left(\mathrm{z_{1}-z_{2}}\right)\left(\mathrm{z_{3}-z_{2}} \right)}{\sqrt{\left(\mathrm{x_{1}-x_{2}}\right)^{2}+\left(\mathrm{x_{3}-x_{2 }}\right)^{2}}\sqrt{\left(\mathrm{z_{1}-z_{2}}\right)^{2}+\left(\mathrm{z_{3} -z_{2}}\right)^{2}}}\end{split}  \tag{2}\]  
\[\begin{split}&\varphi_{\mathrm{n}}=\cos^{-1}\frac{\left(\mathrm{y_{1} -y_{2}}\right)\left(\mathrm{y_{3}-y_{2}}\right)+\left(\mathrm{z_{1}-z_{2}} \right)\left(\mathrm{z_{3}-z_{2}}\right)}{\sqrt{\left(\mathrm{y_{1}-y_{2}} \right)^{2}+\left(\mathrm{y_{3}-y_{2}}\right)^{2}}\sqrt{\left(\mathrm{z_{1}- z_{2}}\right)^{\[\theta_{\rm n}=\cos^{-1}\frac{\left({\rm x_{1}-x_{2}}\right)\left({\rm x_{3}-x_{2} }\right)+\left({\rm y_{1}-y_{2}}\right)\left({\rm y_{3}-y_{2}}\right)}{\sqrt{ \left({\rm x_{1}-x_{2}}\right)^{2}+\left({\rm x_{3}-x_{2}}\right)^{2}}\sqrt{ \left({\rm y_{1}-y_{2}}\right)^{2}+\left({\rm y_{3}-y_{2}}\right)^{2}}} \tag{4}\]  
Advances in aircraft maintenance technology and equipment have allowed maintenance personnel to often work straight during the process of the maintenance work, with each joint working within a defined range, greatly reducing the risk of WMSD associated with abnormal body postures. For example, the likelihood of the upper limb during maintenance is almost non-existent, so this situation should be ignored. The risk level coding table (Table 2) is established based on the RULA and REBA theories for assessing the risk level of limb joint angles based on real repair situations. The evaluation of human posture risk level is affected by temporal overlap in dynamic job analysis. The posture risk level score should be determined by the sum of the individual joint scores under the time series.