Contents I. Introduction
The human hand is the most versatile gripper created by the nature. It is able to firmly grasp objects with different and complex shape thanks to the kinematics of its five fingers, powerful muscles, and a complex biological motor control system. From the kinematic point of view, the hand is composed by a ground part (the palm), four fingers with 4 dofs each, and a thumb. The thumb is the unique finger in the human hand with 5 dofs. Therefore, it is able to perform spatial movements such as its opposition to the other fingers of the hand, which is the basic movement of the grasping action. Because of its incredible complexity, in the last decades, the hand and in particular the human thumb have been widely studied from the kinematic point of view, and many kinematic models able to perform natural motions have been developed. In 1995 Giurintano et al. [1] proposed one of the first 5 link thumb model which entails non orthogonal and non incident axis for the carpo-metacarpal joint (CMC) and metacarpo-phalangeal (MCP) joint. Previous 3 link models use universal joints to model the CMC and MCP joints, leading to a non anatomically correct motion. The comparison between the error produced in the position of the trapeziometacarpal joint by using a 3 link model and a 5 link model has been investigated by Cerveri et al. in [2]. Other studies have been conducted in order to measure muscles arms at the thumb joints [3], or to define some kinematic properties, such as the kinematic parameters of the thumb carpo-metacarpal joint in [4]. An interesting study about the kinematic parameter of the thumb has been performed by Santos et al. in [5]. They investigate the anatomical variability in the Denavit-Hartenberg (D-H) parameaters of the human thumb. As results they clustered 3550 D-H parameters sets in four types of five links thumb models. Moreover, the distribution and the representative value for every D-H parameter for each type are provided. Since hand exoskeletons are developed in order to work combining their kinematics with the kinematics of the hand, the study of the human hand kinematics, especially of the thumb, is of particular interest for the development of effective devices. An example of hand-exos design based on both a hand model and a thumb motion analysis is presented in [6]. Hand exoskeletons can find their application in many different fields, ranging from the rehabilitation to the virtual reality interaction, therefore, in recent years, many hand-exoskeletons have been developed. Some devices have been designed in order to allow full posture control of the finger, therefore, they are able to control all the finger joints independently and provide full mobility during the grasping tasks [7], [8]; however, they mostly suffer from the heavy, bulky and high-cost design, sacrificing the wearability. In alternative one single actuator can be used to control the finger position as proposed in [9], or to control the pose of the fingers constraining the movement of one phalanx to the others, as shown in [10], [11]. Concerning the design of thumb exoskeletons, in literature it is possible to find different solutions proposed for the control of the 5 dofs human thumb. A 2 dofs device for controlling the CMC and MCP joints has been described in [12], whereas in [13], a full 5 dofs device able to control independently all the thumb joints is presented. Finally, in [14] a 4 dof cable driven underactuated thumb-exos device is proposed. In [14] two different actuators are used to independently drive the flexion-extension thumb motion and the adduction-abduction (AA) motion of the CMC joint of the thumb, whereas the AA motion of the MCP joint has been locked. Both the movements are guided by an underactuated cable driven kinematics. Recently, authors have developed an underactuated hand exoskeleton for all the fingers but the thumb [15], characterized by one actuator per finger, full mobility of the fingers, automatic hand size adaptability, possibility of grasping objects with different shape and size, efficient transmission of forces between the device and the fingers. In this work a novel thumb exoskeleton with the same characteristics but adjusted to the higher complexity of the thumb kinematics is presented ( Fig. 1). Moreover, data reported in [5] has been used within the design process to create a human thumb model integrated with the designed hand-exos device. The presented device is able to combine the advantages given by a powerful single motor actuation placed on the back of the hand, with a 5 dof kinematics able to guarantee the full mobility of the users thumb while wearing the device. The single actuation solution allows to reduce the weight and the volume occupied by the actuation system, whereas in order to guarantee the kinematic specifications the proposed device is based on a parallel kinematics featured by a high degree of underactuation. Furthermore such a parallel kinematics is designed to be able to adapt to different hand sizes. To the best of the authors knowledge, thumb-exoskeletons with such a high degree of underactuation has not been presented in previous works. In the following sections the requirements for the design of the thumb-exoskeleton are listed and the adopted design solutions are described. Successively, the solutions of both the inverse kinematics and the statics are described for the mechanical system composed by the thumb exos attached to the thumb finger. Those solutions have been implemented in a Genetic Algorithm (GA) in order to define the optimized link lengths for the kinematics. Finally, the experimental validation results obtained by testing the realized device on eight subjects with different hand size are presented.
