## 3 Results
### Prosthetic Hand Design
#### 3.2.1 Motion Transmission Mechanism  
The performance of an underactuated prosthetic hand depends on how its actuators provide motion to the active joints. The degree of underactuation is determined by the number of actuators, and minimizing this number is crucial in prosthetic hand design. Fewer actuators offer several advantages: (i) reduced weight, (ii) lower battery requirements for extended use, (iii) simplified control architecture with fewer biosignal inputs, and (iv) reduced cost, as motors are the priciest components. However, fewer motors limit individual finger control and dexterity, influencing the design of the motion transmission system. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Objects**} & \multirow{2}{*}{**Human Hand (mm3)**} & **Parallel Finger Design** & **Current Design** \\  & & **(mm3)** & **(mm3)** \\ \hline \(\phi\)50 mm Sphere & 109.3 & 51.8 & 66.9 \\ \(\phi\)70 mm Sphere & 2066.9 & 77.7 & 1950.3 \\ \(\phi\)100 mm Sphere & 236.2 & 85.5 & 216.7 \\ \(\phi\)40 mm; \(h=100\) mm Cylinder & 10.5 & 5.5 & 6.5 \\ \(\phi\)60 mm; \(h=120\) mm Cylinder & 208.2 & 15.5 & 50.1 \\ \(30\) mm side Cube & 43.9 & 32.3 & 34.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Simulation results indicating volume of manipulability ellipsoid. Figure 10: (a) CAD model of the fingers also showing the finger orientation, (b) 3D printed prototype of the finger used in the prosthetic hand. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{} & **Human Hand** & **Parallel Finger Design** & **Current Design** \\ \hline IF & 7.7 & 4.7 & 5.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Result of finger interactivity index for human hand, prosthetic hand with parallel fingers, and current design. In the current work, a novel motion transmission mechanism (MTM) has been developed to control the prosthetic hand. Given the emphasis on the novel finger configuration analysis, it is essential to design an MTM capable of efficiently actuating the proposed prosthetic hand while maintaining its functional versatility and precision. The hand is chosen to be actuated by three input motors--one DC motor (N20 Motor, 12V, 60 RPM, 1.6 Nm of Rated Stall Torque) and two servo motors (Tower Pro SG90 with continuous rotation, 0.12 Nm of Stall Torque). The DC motor is used to actuate the flexion motion of all five fingers. The two servo motors individually control the Ab/Ad motion of the thumb. All three motors are placed in the forearm region of the designed hand. The single DC motor input is distributed to the four fingers through a whippletree-based differential mechanism. A modified whippletree-based differential mechanism is used here for motion transmission to generate adaptive grasping. It is generally used in the design of prosthetic hands to provide uniform force output to the fingers [40; 41]. The other advantage of using a Whippletree mechanism is that, when properly designed, it enables complete flexion of those fingers that do not contact the object being grasped. The input motion through the differential mechanism halts once all the fingers reach maximum flexion or have contacted the object. The overall motion transmission mechanism involving motors and the differential mechanism is shown in Figure 11.  
The mechanism consists of three links (AB, CD, and EF), as shown in Figure 11b. It typically features symmetric links to distribute the input to all the outputs evenly. However, in this prosthetic hand design, the pivot points of the links are acentric. This acentricity is intended to create the stable 3-fingered tripod as the initial pose. Grasping studies show that most daily objects can be effectively manipulated using only a tripod grasp [21]. In the current design, the link lengths of the differential mechanism are set such that the fingers have anthropomorphic behavior. Link AB has an uneven fulcrum point with \(l_{1}<l_{2}\). The index finger and the thumb make preliminary contact with the object.