## 1 Introduction  
Robots play an important role in the industrial production and human life and most of them require corresponding efficient end effectors to interact with the environments. Robot hands can mimic the basic functions of human hands and are a kind of popular end effector in the industrial sector, they are widely used in aerospace [1; 2], agriculture [3], medical devices [4; 5], and industrial sectors [6]. In the past 30 years, researchers have paid great attention to the development of robot hands [7] and made many outstanding achievements. According to the relationship of degree of freedom (DOF) and degree of the actuator (DOA), the robot hands can be divided into three categories, which include the redundant hand, full-actuated hand, and underactuated hand. As for the redundant hand and full-actuated hand, each joint DOF is driven by at least one actuator, and the gesture and movement of the finger joints can be controlled in a precise way. The redundant and full-actuated design methodology are widely used in the field of dexterous hands and many outstanding dexterous hands have been developed and studied, such as Utah/MIT hand [8], NTU hand [9], BCL-13 hand [10], and TUAT/Karlsruhe hand [11]. These dexterous hands can perform complex gestures and accomplish complex grasping tasks. However, they require as many actuators as the number of their DOF and often have complex or bulky control and sensing system to manage the whole device, as a result, the redundant and full-actuated hands are often expensive and difficult to build [12]. These disadvantages restrict the application possibilities of these hands. To maintain good performance and a relatively simple control, researchers propose the concept of the underactuated hand. By optimizing the structure design, the hands can perform the same functions with fewer actuators. The underactuated hand often means the DOA is smaller than the DOF,therefore it can simplify the control system of the robot hand due to the small number of actuators [13]. In the past decades, researchers have made many achievements in the study of the underactuated hand. The examples of the underactuated hands are SDM hand [14], PASA-GB hand [15], and SARAH hand [16]. These underactuated hands take advantages of springs or coupled linkages to achieve the underactuated grasping function. Besides, many researchers have proposed some method to optimize the design of the underactuated hand system, [PERSON] et al. designed an underactuated hand based on a maximum grasping space [17; [PERSON] et al. proposed the modular design solution for the underactuated hand [18], and [PERSON] et al. proposed a method for optimizing the fingertip trajectories of the underactuated hand [19]. Their studies help improve the performance in different aspects, but there is still no solution to optimize the pinching grasping mode and achieve the underactuated linear-parallel pinching function. The traditional underactuated hands make a combination between the multifunction and simple control system, and some of them can even perform parallel pinching and self-adaptive grasping modes to enlarge the usage. They can meet most application requirements, however, the end of robot hand executes a circle trace under the parallel grasping mode, which has a relatively small workspace and is not suitable for grasping thin objects on tables without manipulation of other devices. To overcome this bottleneck of the traditional underactuated hands, the linear-parallel pinching grasping mode was proposed in previous research [20]. This paper proposes a novel straight-line mechanism, based on the mechanism a robot finger with a variable geometrical structure (called VGS finger) was designed and analyzed. The robot finger has hybrid grasping modes by using the variable geometrical structure, it can perform both the linear-parallel pinching and self-adaptive grasping mode. The VGS hand consists of two fingers and a palm, and can meet most application requirements.