## 3 Results and Discussion  
Progress of the topology optimization is shown in Figure 13. It is confirmed that contact pressure concentration level corresponded to a minimum value at the seventh iteration. The element density distribution at the seventh iteration when the optimal result is obtained is shown in Figure 14. As shown in the figure, low element density is identified at the parts where contact with the fingertips of the index finger and middle finger occurs. Conversely, high element density is identified at the part where contacts with the proximal region of the palm occurred. Figure 12: Relationship between the gripping comfort score and contact pressure concentration level. Figure 13: Changes in the value of objective function during the optimization process. The result of topology optimization indicated that the parts where contact with the fingertips of the index finger and middle finger tended to exhibit low element density, and this decreased Young's modulus. Thus, it also implies that the parts should be sufficiently soft to allow a user to perceive a better gripping comfort. The highest contact pressure was confirmed to occur in region 2 in the simulation. Therefore, low element density (low Young's modulus) in the region is required to minimize the contact pressure concentration level. Low element density (low Young's modulus) absorbed forces were generated by the index finger and middle finger to push the column FE model, and thus they did not significantly transmit to region 2 on the opposite side. The contact pressure on the index finger and middle finger was reported as important for evaluating gripping comfort [6]. Furthermore, the index finger and middle finger were also reported to contribute more than the ring finger and little finger while gripping an object [33; 34; 35]. The result of the optimization study indicated that the response caused by the two fingers was crucial in obtaining a gripping part design with high gripping comfort. Conversely, the ring finger was reported to contribute more than the index finger based on the handle diameter [36; 37; 38]. The differences in findings were assumed to be caused by the position of the thumb during gripping of an object. The contact pressure on the index finger is considered to increase when the thumb is on the opposite side of the index finger whereas the contact pressure on the ring finger is considered as higher when the thumb is on the opposite side of the ring finger or little finger while gripping an object. Hence, it is necessary to consider grasp type [39; 40; 41] including the position of the thumb given that grasp type varies among users. A new shape of the column where elements with low element density (0.5 or below) are removed is shown in Figure 15. The elements for which low element density was unnecessary were considered as another interpretation of the topology optimization result, as also recommended in other studies, that elements with element density below the threshold can be removed [32]. The optimized shape should be gripped with larger flexion in the index finger and middle finger joints when compared to the initial shape. Handle shape that reflects human-hand anthropometry was proposed to improve a handles' ergonomics [18; 42]. The shape obtained from the study was in good agreement with the shape proposed in a previous study in terms of the concave surface on the object. However, in the study, only the parts in contact with the index finger and middle finger exhibit concave surfaces. However, in a previous study [18; 42], all parts in contact with fingers exhibit concave surfaces. The inconsistency  
Figure 14: Element density (\(-\)) distribution of the column FE model after the 7 th iteration. Red color denotes high element density and the blue–black color denotes low element density. The hand model is in the initial posture. is caused by the difference in the methodology to obtain an optimal shape and which fingers were referenced in the study.