## Appendix A Deflection Terms and Non-linear Equations of Motion of the 7-DOF Human Body Model  
The derived expression for deflection terms, \(\delta_{ij}\) are as follows:  
\[\delta_{32}=\Big{(}z_{h}-z_{h}^{*}\Big{)}\text{cos}\,\theta_{3}^{*}-\Big{(}x_{ h}-x_{h}^{*}\Big{)}\text{sin}\,\theta_{3}^{*}-\frac{T_{3}}{2}\text{cos}\, \Big{(}\theta_{3}-\theta_{3}^{*}\Big{)}+d_{32}\text{sin}\Big{(}\theta_{3}- \theta_{3}^{*}\Big{)}+\frac{T_{3}}{2}+z_{b}\text{cos}\,\theta_{3}^{*}\]  
\[\delta_{21}=\Big{(}x_{h}-x_{h}^{*}\Big{)}\text{sin}\,\theta_{2}^{*}-\Big{(}z_ {h}-z_{h}^{*}\Big{)}\text{cos}\,\theta_{2}^{*}-\frac{T_{2}}{2}\text{cos}\, \Big{(}\theta_{2}-\theta_{2}^{*}\Big{)}-d_{21}\text{sin}\Big{(}\theta_{2}- \theta_{2}^{*}\Big{)}+\frac{T_{2}}{2}-z_{b}\text{cos}\,\theta_{2}^{*}\]  
\[\delta_{22}=\Big{(}x_{h}-x_{h}^{*}\Big{)}\text{sin}\,\theta_{2}^{*}-\Big{(}z_ {h}-z_{h}^{*}\Big{)}\text{cos}\,\theta_{2}^{*}-\frac{T_{2}}{2}\text{cos}\, \Big{(}\theta_{2}-\theta_{2}^{*}\Big{)}-d_{22}\text{sin}\Big{(}\theta_{2}- \theta_{2}^{*}\Big{)}+\frac{T_{2}}{2}-z_{b}\text{cos}\,\theta_{2}^{*}\]  
\[\delta_{51}=\big{(}z_{h}-z_{h}^{*}\big{)}\text{cos}\,\theta_{5}^{*}-\big{(}x_ {h}-x_{h}^{*}\big{)}\text{sin}\,\theta_{5}^{*}-\frac{T_{5}}{2}\text{cos}\, \big{(}\theta_{5}-\theta_{5}^{*}\big{)}+d_{51}\text{sin}\,\big{(}\theta_{5}- \theta_{5}^{*}\big{)}+\frac{T_{5}}{2}+z_{b}\text{cos}\,\theta_{5}^{*}\]  
\[+\frac{T_{3}}{2}\big{[}\text{cos}\,\big{(}\theta_{3}^{*}-\theta_{5}^{*}\big{)} -\text{cos}\,\big{(}\theta_{3}-\theta_{5}^{*}\big{)}\big{]}-L_{3}\big{[}\text{ sin}\,\big{(}\theta_{3}^{*}-\theta_{5}^{*}\big{)}-\text{sin}\,\big{(}\theta_{3}- \theta_{5}^{*}\big{)}\big{]}\]  
\[+L_{4}\big{[}\text{sin}\,\big{(}\theta_{4}^{*}-\theta_{5}^{*}\big{)}-\text{sin} \,\big{(}\theta_{4}-\theta_{5}^{*}\big{)}\big{]}\]  
and the elements of **C** are as follows:  
\[C_{11}=(c_{31}+c_{32}){\sin}^{2}\theta_{3}^{*}+(c_{21}+c_{22}){\sin}^{2}\theta_{2 }^{*}+c_{51}{\sin}^{2}\theta_{5}^{*},\]  
\[C_{12}=-(c_{31}+c_{32}){\cos}\theta_{3}^{*}{\sin}\theta_{3}^{*}-(c_{21}+c_{22}) {\cos}\theta_{2}^{*}{\sin}\theta_{2}^{*}-c_{51}{\cos}\theta_{5}^{*}{\sin} \theta_{5}^{*},\]  
\[C_{13}=-(c_{31}d_{31}+c_{32}|3_{2}){\sin}\theta_{3}^{*}+\frac{T_{3}}{2}c_{51}{ \sin}\left(\theta_{3}^{*}-\theta_{5}^{*}\right)+L_{3}c_{51}{\cos}\left(\theta _{3}^{*}-\theta_{5}^{*}\right),\]  
\[C_{15}=-(c_{21}d_{21}+c_{22}d_{22}){\sin}\theta_{2}^{*},\ \ C_{16}=c_{51}L_{4}{ \sin}\theta_{5}^{*}{\cos}\left(\theta_{4}^{*}+\theta_{5}^{*}\right),\]  
\[\delta_{21}=\Big{(}x_{h}-x_{h}^{*}\Big{)}\text{sin}\,\theta_{2}^{*}-\Big{(}z_ {h}-z_{h}^{*}\Big{)}\text{cos}\,\theta_{2}^{*}-\frac{T_{2}}{2}\text{cos}\, \Big{(}\theta_{2}-\theta_{2}^{*}\Big{)}-d_{21}\text{sin}\Big{(}\theta_{2}- \theta_{2}^{*}\Big{)}+\frac{T_{2}}{2}-z_{b}\text{cos}\,\theta_{2}^{*}\]0  
\[\delta_{21}=\Big{(}x_{h}-x_{h}^{*}\Big{)}\text{sin}\,\theta_{2}^{*}-\Big{(}z_ {h}-z_{h}^{*}\Big{)}\text{cos}\,\theta_{2}^{*}-\frac{T_{2}}{2}\text{cos}\, \Big{(}\theta_{2}-\theta_{2}^{*}\Big{)}-d_{21}\text{sin}\Big{(}\theta_{2}- \theta_{2}^{*}\Big{)}+\frac{T_{2}}{2}-z_{b}\text{cos}\,\theta_{2}^{*}\]1  
\[\delta_{21}=\Big{(}x_{h}-x_{h}^{*}\Big{)}\text{sin}\,\theta_{2}^{*}-\Big{(}z_ {h}-z_{h}^{*}\Big{)}\text{cos}\,\theta_{2}^{*}-\frac{T_{2}}{2}\text{cos}\, \Big{(}\theta_{2}-\theta_{2}^{*}\Big{)}-d_{21}\text{sin}\Big{(}\theta_{2}- \theta_{2}^{*}\Big{)}+\frac{T_{2}}{2}-z_{b}\text{cos}\,\theta_{2}^{*}\]2  
\[\delta_{21}=\Big{(}x_{h}-x_{h}^{*}\Big{)}\text{sin}\,\theta_{2}^{*}-\Big{(}z_ {h}-z_{h}^{*}\Big{)}\text{cos}\,\theta_{2}^{*}-\frac{T_{2}}{2}\text{cos}\, \Big{(}\theta_{2}-\theta_{2}^{*}\Big{)}-d_{21}\text{sin}\Big{(}\theta_{2}- \theta_{2}^{*}\Big{)}+\frac{T_{2}}{2}-z_{b}\text{cos}\,\theta_{2}^{*}\]3  
\[\delta_{21}=\Big{(}x_{h}-x_{h}^{*}\Big{)}\text{sin}\,\theta_{2}^{*}-\Big{(}z_ {h}-z_{h}^{*}\Big{)}\text{cos}\,\theta_{2}^{*}-\frac{T_{2}}{2}\text{cos}\, \Big{(}\theta_{2}-\theta_{2}^{*}\Big{)}-d_{21}\text{sin}\Big{(}\theta_{2}- \theta_{2}^{*}\Big{)}+\frac{T_{2}}{2}-z_{b}\text{cos}\,\theta_{2}^{*}\]4  
\[\delta_{21}=\Big{(}x_{h}-x_{h}^{*}\Big{)}\text{sin}\,\theta_{2}^{*}-\Big{(}z_ {h}-z_{h}^{*}\Big{)}\text{cos}\,\theta_{2}^{*}-\frac{T_{2}}{2}\text{cos}\, \Big{(}\theta_{2}-\theta_{2}^{*}\Big{)}-d_{21}\text{sin}\Big{(}\theta_{2}- \theta_{2}^{*}\Big{)}+\frac{T_{2}}{2}-z_{b}\text{cos}\,\theta_{2}^{*}\]5  
\[\delta_{21}=\Big{(}x_{h}-x_{h}^{*}\Big{)}\text{sin}\,\theta_{2}^{*}-\Big{(}z_ {h}-z_{h}^{*}\Big{)}\text{cos}\,\theta_{2}^{*}-\frac{T_{2}}{2}\text{cos}\, \Big{(}\theta_{2}-\theta_{2}^{*}\Big{)}-d_{21}\text{sin}\Big{(}\theta_{2}- \theta_{2}^{*}\Big{)}+\frac{T_{2}}{2}-z_{b}\text{cos}\,\theta_{2}^{*}\]6  
\[\delta_{21}=\Big{(}x_{h}-x_{h}^{*}\Big{)}\text{sin}\,\theta_{2}^{*}-\Big{(}z_ {h}-z_{h}^{*}\Big{)}\text{cos}\,\theta_{2}^{*}-\frac{T_{2}}{2}\text{cos}\, \Big{(}\theta_{2}-\theta_{2}^{*}\Big{)}-d_{21}\text{sin}\Big{(}\theta_{2}- \theta_{2}^{*}\Big{)}+\frac{T_{2}}{2}-z_{b}\text{cos}\,\theta_{2}^{*}\]7  
The stiffness matrix, **K** is composed of:  
\[\textbf{K}=