## 3 Results and Discussion
### Design Process
#### 3.2.2 Detailed Design  
Significant modifications were made to the selected conceptual design, mainly in the regulation of the force of the gripper, which was originally based on the rotation of a worm gear mechanism (Figure 3a). Since this concept had an exposed mechanism, it was vulnerable to dust damage, requiring a greater number of parts and a higher geometric tolerance. Therefore, a simpler \"tubular band mechanism concept\" was proposed by using a tubular band to regulate the gripper's force (Figure 3b). As a result, 16 parts were eliminated, including screws, gears, bushings, as well as the spring and shaft. The elimination of the gears increased the required geometric tolerances. The mechanism and its dimensions were designed within the range of the measures presented by various commercial VO hand and hook prostheses [14]. Mechanically, the device has an opening of 50\({}^{\circ}\) \(\theta\) (Figure 4), which allows a maximum clamp opening of 84 mm (from K to D point in Figure 4). In this way, the user is able to hold various objects. The maximum cable excursion of 42 mm shows that the device can be manipulated by the user through shoulder abduction. The design has the capacity to regulate grip force when adding tension to or releasing the tubular band. Figure 4: Kinematic diagram. Figure 3: (**a**) Worm gear crown mechanism concept, (**b**) tubular band mechanism concept. Figure 2: Conceptual design: gripper and hook with force regulation. A kinetic study was performed using a tubular band with a design specification \(k\) of 5.0 N/mm and a unstretched length of 31 mm, 43 mm, and 47 mm, attached from point C to point H (Figure 4), which has an initial distance of 52 mm at 0\({}^{\circ}\) \(\theta\). The activation and pinch force were determined by static equilibrium equations; that is, the principle that the sum of moments resulted by each force equals zero, as shown in Equation (1):  
\[\sum\overset{\rightarrow}{M}_{A}=\overset{\rightarrow}{M}_{c}-\overset{ \rightarrow}{M}_{E}-\overset{\rightarrow}{M}_{D}= \tag{1}\]  
where \(\sum\overset{\rightarrow}{M}_{A}\) stands for the moment that resulted in point A, while \(\sum\overset{\rightarrow}{M}_{c}\), \(\sum\overset{\rightarrow}{M}_{E}\), and \(\sum\overset{\rightarrow}{M}_{D}\) stand for the moments generated by the pinch, the cable, and the elastic band, respectively. Then, each moment was decomposed into its components, as in: \(\overset{\rightarrow}{M}_{i}=\overset{\rightarrow}{r}_{i}\times\overset{ \rightarrow}{F}_{i}\). Where \(\overset{\rightarrow}{r}_{i}\) represents the distance from the applied force to the point of rotation and \(\overset{\rightarrow}{F}_{i}\) represents the actual force. Finally, each force was determined separately by considering one term equal to zero at a time. For \(\overset{\rightarrow}{F}_{E}\), \(\overset{\rightarrow}{M}_{D}=0\), when the cable is excursed, as shown in Equation (2):  
\[\sum\overset{\rightarrow}{M}_{A}=\overset{\rightarrow}{M}_{c}-\overset{ \rightarrow}{M}_{E}=0\ \rightarrow\ \overset{\rightarrow}{M}_{C}=\overset{\rightarrow}{M}_{E}\ \rightarrow\ \overset{\rightarrow}{r}_{C}\times\overset{ \rightarrow}{F}_{c}=\overset{\rightarrow}{r}_{B}\times\overset{ \rightarrow}{F}_{E}\rightarrow\ \overset{\rightarrow}{F}_{E}=\frac{\overset{ \rightarrow}{r}_{C}\times\overset{\rightarrow}{F}_{C}}{\overset{ \rightarrow}{r}_{B}} \tag{2}\]  
And \(\overset{\rightarrow}{M}_{E}=0\) for \(\overset{\rightarrow}{F}_{D}\), as seen in Equation (3):  
\[\sum\overset{\rightarrow}{M}_{A}=\overset{\rightarrow}{M}_{c}-\overset{ \rightarrow}{M}_{D}=0\ \rightarrow\ \overset{\rightarrow}{M}_{C}=\overset{\rightarrow}{M}_{D}\ \rightarrow\ \overset{\rightarrow}{r}_{C}\times\overset{ \rightarrow}{F}_{c}=\overset{\rightarrow}{r}_{D}\times\overset{ \rightarrow}{F}_{D}\rightarrow\ \overset{\rightarrow}{F}_{D}=\frac{\overset{ \rightarrow}{r}_{C}\times\overset{\rightarrow}{F}_{C}}{\overset{ \rightarrow}{r}_{D}} \tag{3}\]  
Now, \(\overset{\rightarrow}{r}_{C}\) stands for the distance from points A to C; it is equal to 36.77 mm.