## 1 Introduction  
The human hand is a highly complex masterpiece with 23 degrees of freedom (DOF) [1,2] (Figure 1a). The thumb, which has three joints and 5 DOFs, plays a vital role in the functional integrity of the human hand and has been widely studied [3, 4, 5]. The other four fingers each have three joints and 4 DOFs. These joints can be named the distal interphalangeal (DIP) joint, proximal interphalangeal (PIP) joint, and metacarpophalangeal (MCP) joint, respectively, from fingertip to bottom. The DIP and PIP joints are 1-DOF joints, while the MCP joints are 2-DOF joints with a condyloid shape, which enables a large workspace of the fingers [6]. However, the contribution of this type of joint to grasp manipulations is rarely studied, and in developing a prosthetic hand, the dexterity of the MCP joints is frequently ignored. Relevant research has focused on the mechanical and kinematic properties of MCP joints. [PERSON] et al. analytically and experimentally investigated the kinematic behavior of the human MCP joint [7]. Then, they analyzed the biomechanical characteristics of MCP joint prosthesis design with fresh cadaver finger rays in later work [8]. [PERSON] et al. analyzed the move independence of the MCP joint by a series of grasp experiments and hand gestures [9]. [PERSON] et al. presented time-varying synergies that were observed during reach and grasp experiments in angular velocity profiles of MCP joints and PIP joints in [10]. However, these works only studied the characteristics of the joint itself and did not take the task into consideration. The grasping operation is a critical aspect in evaluating the impact of joints on the human hand. [PERSON] et al. analyzed the load distribution and contact area in four common grasp types used in daily living activities, and the results demonstrated that the surface of the MCP joint was one of the main components of the maximum contact area [11]. [PERSON] et al. explored the actual contribution of independent fingers while performing activities of daily living, including grasping different objects under three hand configurations achieved using custom built orthoses [12]. The results suggested that the remarkable grasping skills of the human hand rely more on the independent abduction/adduction (ab/d) of the MCP joints than on their independent flexion/extension (flex/ex). [PERSON] et al. evaluated the correlations of coordinated movements in human hands during 23 grasp tasks, and they found that the ab/d motion of the hand fails to show either strong coordination or group coupling with other joint movements [13]. In this study, we mainly expanded the research in two aspects: (1) the constraint condition of MCP joints is further divided into four different situations for research, and (2) we explore multiple aspects of grasping, namely grasping size, grasping force, grasping quality and grasping success rate. In general, in the development of prosthetic hands, a key point is the number of active DOFs that the hand has, which means the number of actuators. Some robotic hands have achieved a high number of DOFs close to the human hand, such as the Shadow Hand [14], and the Anatomically Correct Testbed Hand (ACT hand) [15]. However, these prosthetic hands are expensive, weighty, and sophisticated in design and control. Therefore, there is often a trade-off between complexity and accessibility in most scenarios of hand design, such as the most advanced commercially available prosthetic hands (Bebionic Hand, i-Limb Hand, and Michelangelo Hand) [16; 17]. These hands have only 5-6 active DOFs with the four fingers that can merely produce flex/ex motion; namely, the MCP joints of these hands are 1-DOF joints [18]. Similar circumstances can be seen in the design of most anthropomorphic soft robotic hands, such as [19; 20; 21; 22; 23; 24]. The MCP joints of these soft hands are all 1-DOF joints incapable of producing ad/b motion. Some exceptions of reducing hand DOFs are given as follows: [PERSON] et al.