# Development of an Anthropomorphic Prosthetic Hand with Underactuated Mechanism
## 2 Design of the Hand Mechanism
### Mechanism Design  
Fingers are composed of two interphalangeal (IP) joints, i.e., the PIP and DIP joints, and an MCP joint, as shown in Figure 1. IP joints that make flexion and extension motions can be designed as revolute joints. Although the MCP joint in the human hand is made of a ball joint type, it was designed using two revolute joints at a right angle in this research because rotation along the length direction of the finger is almost zero. The two revolute joints produce adduction/abduction and flexion/extension. The skeleton of the thumb has two differences from those of the fingers. First, it does not have the middle phalanx (Figure 1). Therefore, the carpometacarpal (CMC) joint articulated with the carpal and metacarpal of the thumb was designed using two revolute joints at right angles. Second, in the thumb, the MCP joint was made of a revolute joint. The IP joint of the thumb was designed as a revolute joint. By designing the thumb module in the same configuration as the finger module, we have the advantage that all fingers and the thumb can be designed as identical modules. The designed finger module consists of three sections, as shown in Figure 2a: \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Cylinder Power** & **Sphere Power** & **Tip Pinch** & **Prismatic Pinch** \\ \hline \hline
**Tripod** & **Lateral Pinch** & **Hook Grip** & **Flat Hand** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Eight grasping motions of an underactuated hand. (1) The first section is the blue section from the metacarpal to the proximal phalanx. Proximal phalanx motion is produced from 0\({}^{\circ}\) to 90\({}^{\circ}\) in natural motion because the miter gear moves from 0\({}^{\circ}\) to 90\({}^{\circ}\) and the gear ratio is 24:24. By connecting a torsional spring between the metacarpal and an axis of the MCP joint, a passive motion that restricts 1 DOF during natural motion is performed. The available angle of the torsional spring is 40\({}^{\circ}\) and the angle for preload is 15\({}^{\circ}\). (2) The second section is the green section from the metacarpal to the middle phalanx. This is made of a four-bar and a torsional spring. The middle phalanx provides motion in the range from 0\({}^{\circ}\) to 180\({}^{\circ}\) in natural motion because the section has a 32:16 gear ratio. In addition, a torsional spring connects the metacarpal and an axis of the MCP joint. Therefore, a passive motion (1 DOF) is also produced in this part. The available angle and angle for preload of the torsional spring are 40\({}^{\circ}\) and 15\({}^{\circ}\), respectively, which is the same in the blue section. In these two sections, passive motions of 2 DOFs during natural motion are restricted completely. (3) The third section (red) is composed of two four-bar mechanisms. This section provides active motion (1 DOF) in which the distal phalanx moves between 0\({}^{\circ}\) and 288\({}^{\circ}\) because this section is connected with 32:16, 16:16, and 22:10 gear ratios. Figure 2: Constitution of (**a**) the finger module and (**b**) palm module. The palm module includes torsional springs, an actuator for driving the thumb, and constant-velocity (CV) joints to transfer the power produced by actuators located in the carpal. There are five torsional springs. The torsional spring installed on the thumb plays a role in the rest motion of the thumb's CMC joint. The available angle and angle for the preload are 60\({}^{\circ}\) and 10\({}^{\circ}\), respectively. The other springs were installed to realize adduction/abduction motions of the fingers, as shown in Figure 2b. The available angle of them is 20\({}^{\circ}\), and the angle for preload is 10\({}^{\circ}\). The directions of motions at the forefinger and the other fingers are opposing. In other words, the adduction/abduction motions of the forefinger are rotated in the clockwise direction, while these motions of the other fingers are rotated in the counterclockwise direction.