## 1 Introduction  
Prosthetic hands that have been developed to date can primarily be categorized into two types: Fully actuated [1; 2; 3; 4] and under-actuated [5; 6; 7]. The former type is usually equipped with actuators corresponding to every moving joint, which can achieve dexterous motions similar to those performed by a human being owing to its multiple degrees of freedom (DoFs). However, a multiple actuator configuration exhibits disadvantages such as the increased weight, bulky packaging, high power requirements, and complex control strategy. The weight of a prosthetic hand remains one of the most distinguishing factors limiting its adoption by amputees [8]. Therefore, research and design related to prosthetic hands have trended towards the under-actuated mechanism, which can significantly reduce the weight and packaging size, and much more easily realize human-like appearance, low power consumption, and simple control architecture compared to the fully actuated type. The under-actuated mechanism involves greater DoFs than degrees of actuation, usually including one to six actuators (compared to the 34 muscles of a human hand) [9]. The data from 1983 to 2016 have demonstrated that the majority of prosthetic hands are under-actuated [10]. However, even these under-actuated handsexhibit a trade-off between dexterity and light weight. That is, increasing the hand motion functions increases the weight, while reducing the weight leads to a simple mechanism that cannot achieve diversiform hand motions. Figure 1 presents a comparison between the achievable hand motion types and the entire weight of several under-actuated anthropomorphic prosthetic hands, covering a range of commercial to experimental uses. The comparison is based on the Cutkosky taxonomy as it is currently the most widely used approach in the field of robotics [11]. As illustrated in Figure 2, the human hand grasp motions are mainly categorized into power and precision grasps in the Cutkosky taxonomy, for a total of 16 types of grasp motions (labeled from 1 to 16). In Figure 1, it is clear that as the number of achievable types of motion increases, the entire weight increases. All of the hands that could achieve 13 types of motion weigh more than 600 g. Whereas, even though some of the light weight hands weigh under 400 g, they cannot achieve more than 6 types of motion. Therefore, there are mainly two inclinations: The focus is on reduced weight at the expense of fewer hand motions, or the focus is on diversiform motions at the expense of increased weight. This trade-off problem implies that combining dexterity and light weight will be a great challenge. It is of great importance to consider both dexterity and light weight when designing a prosthetic hand, owing to two factors: (1) Amputees consider that the weight is important to relieve their burden [8; 19], and (2) grasping is the most important task to restore the lost hand function as far as possible [10]. Therefore, the design objective of this study is to achieve a trade-off that can meet both dexterity and light weight requirements. Therefore, two design restrictions exist for the prosthetic hand: (1) Limited weight to reduce the burden of the user, and (2) realizing as many hand motions as possible. Firstly, the maximum weight of the prosthetic hand should not be more than 370 g. However, three different prosthetic hand weight limits exist, namely 370, 400, and 500 g, as presented by three different reports [20]. Here, the lightest weight limitation is adopted to minimize the influence of weight. Secondly, the scope of the target hand motions needs to be defined, because it is impossible to mimic every human hand motion for a prosthesis with the state of the art. As mentioned before, in this study, the Cutkosky taxonomy is followed to realize the grasp motion as much as possible, because it is the most widely used.