## Materials and Methods
### Establishment of Grasping Motion Simulation
#### 2.1.2 Material Properties  
Material properties were defined via FEA software Radioses (Altair Engineering Inc., Troy, MI, USA). The material properties of each component were based on extant studies [19; 24; 25] as shown in Table 2. The material of the cylinder FE model was defined as Acrylonitrile Butadiene Styrene resin and was the same as that of the cylinder used in the experiment. The material properties of the skin and cylinder showed linearly elastic behavior. Bones were defined as a rigid body since the deformation can be neglected and have low computational cost. Moreover, the rigid bones allowed more accurate finger motions because they were used in the construction of local coordinate systems that were utilized for modelling the finger joint characteristics and applying joint torques to the joints, as will be described in Section 2.1.3.  
Furthermore, Ogden hyperelastic material model was utilized for the subcutaneous soft tissue. The Ogden hyperelastic material model was expected to adequately simulate the deformation behavior of subcutaneous soft tissue. This material model exhibited a good record in the FE simulation of the deformation of soft tissue, as shown in previous studies [8; 26]. Based on the expression of the strain energy density \(W\), the Ogden hyperelastic material model is formulated in Equation (1) in Radioss as follows:  
\[W(\lambda_{1},\lambda_{2},\lambda_{3})=\sum_{p}\frac{\mu_{p}}{\alpha_{p}} \Big{(}\overline{\lambda_{1}}^{\alpha_{p}}+\overline{\lambda_{2}}^{\alpha_{p} }+\overline{\lambda_{3}}^{\alpha_{p}}-3\Big{)}+\frac{K}{2}(J-1)^{2} \tag{1}\]  
\[\lambda_{i}=1+\varepsilon_{i} \tag{2}\]  
\[J=\lambda_{1}\cdot\lambda_{2}\cdot\lambda_{3} \tag{3}\]  
\[\overline{\lambda_{i}}=J^{-\frac{1}{3}}\lambda_{i} \tag{4}\]  
where \(\lambda_{i}\) denotes the \(i\)th principal stretch (Equation (2)); \(\varepsilon_{i}\) denotes the \(i\)th principal engineering strain, \(J\) denotes the relative volume (Equation (3)); and \(\overline{\lambda_{i}}\) denotes the deviatoric stretch (Equation (4)). Specifically, \(K\) denotes the bulk modulus related to [PERSON]'s ratio \(\
u\) and is expressed in Equation (5) as follows:  
\[K=\mu\cdot\frac{2(1+\
u)}{3(1-2\
u)} \tag{5}\]  
where, the shear modulus \(\mu\) is calculated by using material parameters \(\mu_{p}\), \(\alpha_{p}\) (Equation (6)).  
\[\mu=\frac{\sum_{p}\mu_{p}\cdot\alpha_{p}}{2} \tag{6}\]  
The material parameters for subcutaneous soft tissue are identified from the result of compression test using porcine fat tissue [26] as listed in Table 3. The appropriate number of parameters was determined via a parametric study. In the study, \(p=4\) was considered as the appropriate number of parameters that optimally fitted the result of the compression test.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Density [kg/mm\({}^{3}\)]** & **Young’s Modulus [GPa]** & **Poisson’s Ratio** & **Literature** \\ \hline Skin & \(0.90\times 10^{-6}\) & \(8.00\times 10^{-5}\) & 0.48 & [19; 25] \\ Subcutaneous soft tissue & \(0.90\times 10^{-6}\) & - & 0.48 & [25] \\ Bones & \(1.80\times 10^{-6}\) & - & - & [25] \\ Cylinder & \(1.04\times 10^{-6}\) & 2.00 & 0.39 & [24] \\ \hline \hline \end{tabular}
\end{table}
Table 2: Mechanical properties used in the hand FE model and cylinder FE model.  
The contact between the skin and the cylinder was defined as surface-to-surface contact using the penalty method with a friction coefficient of 0.3 [27; 28; 29]. In addition, nodes at the boundary between the bones and the subcutaneous soft tissue as well as nodes at the boundary between the subcutaneous soft tissue and the skin were shared between the two parts.