Development of a Wearable Finger Exoskeleton for Rehabilitation

: This research work shows a new architecture of a novel wearable ﬁnger exoskeleton for rehabilitation; the proposed design consists of a one degree of freedom mechanism that generates the ﬂexion and extension movement for the proximal, medial and distal phalange of the ﬁngers to assist patients during the rehabilitation process, after neurological trauma, such as a stroke. The anatomy and anthropometric measures for the hand were used to deﬁne the design of the mechanism. In the analytic part, the representative equations for the forward and inverse kinematic analysis of the ﬁngers are obtained, also a dynamic analysis is presented. The position and displacement continued for the structural analysis, were developed by following a static analysis, to know the deformation that the structure links show when an external load is applied in the mechanism. As result, a prototype was manufactured with acrylonitrile butadiene styrene (ABS) using an additive manufacturing machine.


Introduction
Nowadays, due to technological advances, robotics are present in different places, such as hospitals, factories, schools, and houses [1]. One of the areas where robotics has a large presence is in healthcare, where its applications are focused on rehabilitation, helping people with disease or disability to perform daily activities, or provide therapies to improve physical or cognitive functions [1].
There are several diseases, which affect physical functions of the human hand, generating limitations in performing activities like grasping objects or opening a tin or a bottle of water. Many robotic systems specifically intended for hand rehabilitation have been reported in the literature, where two different hand exoskeleton systems exist: singlephalanx devices, in which the robot exerts forces to the hand only at the fingertips, and multi-phalanx ones, where the device can directly control each phalanx of the hand.
The single-phalanx solution has a rigid mechanism and a cable-driven architecture; there are a few examples found in the literature and most of them use actuation systems separated by the device (usually the device is located on the hand and the motors are placed on the ground) [2,3]. Only a narrow part of these examples directly use motors placed on the back of the hand (extraordinary portability but limited in terms of device performance due to the weight and high cost). An example of such a system is WaveFlex, which is a commercial continuous passive movement device for physical therapy of the finger exoskeleton [20] provides independent control of all three joints of the index finger. HEXORR [17] is a device that provides a full range of motion (ROM) for all of the hand's digits. A hand exoskeleton system for index finger rehabilitation [34] uses both active and passive rehabilitative motions. Finally, the novel exoskeleton robotic system for hand rehabilitation [35] is a novel hand exoskeleton rehabilitation device that facilitates tendon therapy exercises. Table 1 presents a comparative review of exoskeletons developed for hand rehabilitation. Not all of the exoskeletons can be applied effectively to daily life, e.g., only a few can be used alone without a large drive device. Some are too complex, bulky, and unwearable, with many active DOF, or are too expensive for home and personal use. By following this approach, inspired by extreme portability and affordability, this work presents a new finger mechanism based on linkage approximation, using only one active degree of freedom per finger to obtain full actuation and it was assembled using a 3D printing machine from a thermoplastic polymer, acrylonitrile butadiene styrene (ABS); the structure of the proposed exoskeleton presented in this paper is based on human hand capabilities, with the ranks of motion and physical length as important criteria. This paper is organized as follows: In Section 2, the design of the finger exoskeleton is presented. Section 3 develops the kinematics and dynamics for the proposed exoskeleton with one DOF. Section 4 presents experimental results for the exoskeleton kinematics and dynamics, followed by proper structural analysis. Section 5 presents the discussion on the proposed exoskeleton and, finally, in Section 6, some important conclusions and suggestions for future research are presented.

Structure Design for the Finger Exoskeleton
The proposed material design consists of a one-DOF mechanism that allows the flexion and extension of finger movements of the hand; it is made up of different links that adhere to the proximal phalanx and the middle phalanx of fingers L 1 and L 2 , respectively, see Figure 1. According to the configuration of the links, the mechanism transforms linear movement from the actuator into a rotational type, allowing the movement of finger joints, which are represented as θ 1 , θ 2 , and θ 3 . The forces resulting from these movements are called F 1 and F 2 . These forces are present on the first two phalanges of the fingers (proximal phalanx and middle phalanx), which in turn generate rotational movements of the metacarpophalangeal (MCP), proximal interphalangeal (PIP), and distal interphalangeal (DIP) joints. It is important to note that the distal phalanx has a sub-acted movement with respect to the middle phalanx, so it moves in coordination with it. For this reason, the proposed mechanism only applies rotational movements on the proximal phalanx and the middle phalanx. The sub-acted finger movements mentioned above are also contemplated for the subsequent studies carried out in the present investigation.

Mechanical Design
The proposed design was developed in SolidWorks, and is shown in Figure 2a, where is possible to see the isometric exoskeleton. The proposed exoskeleton is formed by four parts, where part 1 is the exoskeleton base, part 2 is the selected linear actuator (Actuonix model L12-50-100 [37]), the main function of the actuator is to transmit linear-type movements towards the mechanisms that move the proximal phalanges and the middle phalanges. Part 3 is the mechanism that transmits the movement of the actuator towards the proximal phalanx and, finally, part 4, is the mechanism that transmits the movement of the actuator towards the middle phalanx and the distal phalanx through the same sub-acted movement.
The motion transmission is based on a linkage mechanism that allows the possibility of coupling the motion of phalanxes so that natural hand movements are achievable using only one active DOF driven using one linear actuator per finger. Additionally, bars can transmit both tensile and compressive loads, so the same mechanism can perform extension and flexion movement of the fingers. Each phalange element is attached to the human phalange using Velcro straps. As shown in Figure 2b, the mechanism is formed as a base mechanism (element 1), the linear actuator is used to transmits the force to mechanisms (elements 2 and 3). The pushing force allows the flexion movement, and the pulling force allows the extension movement. The proximal phalanx movement is generated by elements 4 and 5, and elements 6, 7, and 8 generate a rotational movement for the mechanism that moves the middle phalanx. The movement of the distal phalanx is generated through the mechanism that moves the middle phalanx since these two have a sub-acted motion with respect to each other.

Design Parameters
The finger parameters for the development of the proposed design are shown in Table 2 [38]. Each finger on the hand has different lengths as do the phalanges that compose them. However, due to design issues, and as a starting point for this research, the mechanisms used for each finger's movement have the same dimensions, starting from the lengths of the phalanges of the middle finger. The proposed ranges of motion were taken from the range of each of the finger phalange's natural motion.

Position Analysis
In several mechanisms, position analysis has the goal to determine the position of all the links in different phases of an operative cycle [39].
The position analysis of exoskeleton components is developed using an analytic method through a geometric approach. In Figure 3a, a schematic diagram is shown, where the lengths of the exoskeleton links are known. L 1 represents the element that joins the linear actuator with element L 2 . The length of L 1 is variable according to the linear displacement of the actuator; L 2 represents the section of the mechanism that moves the proximal phalanx; L 3 is the element that allows the angular displacement of link L 4 -L 5 ; L 4 -L 5 is the element that moves to link L 8 ; L 9 is the element linked to link L 4 -L 5 with link L 8 ; L 8 represents the section of the mechanism that moves the middle phalanx; F 1 is the force applied by the linear actuator to move the mechanism. Figure 3b, represents the final position achieved after the linear actuator reaches its final position. To solve for θ 2 , from Figure 3a, the initial position of element L 2 is obtained, using the values of L 2 , L 1 , D 2 , and d 1 the input data are: where atan2 is the inverse tangent function. The atan2 function is different from the conventional arctangent function. The major difference is that the atan2 function also determines the quadrant of an angle, which is not the case for the arctangent function.
In the same way, using L 2 and R 1 gets initial the position for θ 1i where L 1i and θ 3i represent the initial position for the linear actuator and link L 1 , respectively. The final position for the same elements, when the linear actuator has its maximum length, can be obtained as: where i and f represent the initial and final positions, and θ 3T is the angular position for link L 2 .
Using L 1 , L 2 , and R 1 the θ 24 equation can be obtained as: and Using L 2 and θ 3 , the distance between centers of rotation are C 5 and C 2 . Angular displacement β of element L 3 is expressed by: where θ 11 is the angle between the center of rotation C 2 C 3 and C 3 C 5 . Using the value of Equation (16), the value of R 5 is expressed as: where Equation (16) describes the angular displacement of element L 3 . Using R 5 , L 3 and L 4 the angular displacement for the link L 3 and L 4 can be obtained as: where θ 21 is the angle between segments C 2 C 3 and C 3 C 5. Using the triangle formed by elements R 8 , d 4 , and L 5 , the angular position for links L 8 and L 9 can be expressed by:

Inverse Kinematics
This section is concerned with finding the solution to the inverse kinematics problem, which consists in determining the joint variables in terms of the end-effector position and orientation. It is commonly known from the literature, that, for open kinematic chains, the determination of closed-form equations for inverse kinematics represents a greater challenge than the forward kinematics [1]. Figure 4 shows a simplified sketch in the XY plane, where the base coordinate is at the center of the proximal phalange joint. The local frames (Xi, Yi) are assigned to each joint, d i denotes the length of link i, q i is the articular angle, ω represents the angle between medial phalange and R 1 and β represent the angles between the medial and distal phalanges. The approach followed in this paper for finding the inverse kinematics solution of the exoskeleton consists in determining joints angles q 1 , q 2 , and q 3 given the global position distal phalange.
Using Figure 4, results in where, applying the cosines law to the triangle bounded by d 2 and d 3 , the solution for β is expressed by:

Dynamics Analysis
The approach followed in this paper applies the Newton-Euler dynamic formulation to solve the dynamics of the exoskeleton hand. The main advantages of this technique are the facility of implementation and obtaining models with a reduced number of operations. The Newton-Euler formulation is derived by the direct interpretation of Newton's second law of motion, which describes system dynamics in terms of force and momentum. The equations incorporate all the forces and momentum acting on individual exoskeleton links, including the coupling forces and momentum between the links. The equations obtained from the Newton-Euler method include the constraint forces acting between adjacent links. Thus, additional arithmetic operations are required to eliminate these terms and obtain explicit relations between the joint torques and the resultant motion in terms of joint displacements.
For the development of dynamic analysis through the Newton-Euler formulation, the finger exoskeleton mechanism is simplified and shown in Figure 5. The diagram represents only the links of the proximal phalanx and middle phalanx of the fingers; the main reason why only these two phalanxes are contemplated is because of the type of movement that the distal phalanx performs concerning the middle phalanx, which is an underactuated type, which, when exerting a force on the middle phalanx in the same way will generate movement in the distal phalanx. d 1 and d 2 are the lengths of the section of the mechanism that moves the proximal phalanx and the middle phalanx; d c1 and d c2 are the lengths of each joint of the phalanges (MCF, IFP) with its center of mass; m 1 and m 2 are the masses of each section of the mechanism; q 1 and q 2 are the joint coordinates of the proximal phalanx and the middle phalanx, respectively, and I 1 and I 2 represent the inertia tensor for each link.
Using Figure 5, the Newton-Euler equations for the dynamic model for link d 1 are: where f i−1,i , and −f i,i+1 are the coupling forces applied to link i by links i − 1 and i + 1. Note that all vectors are 2 × 1, so that moment N i−1,i and the other vector products are scalar quantities. Similarly, for link d 2 : ω 2 = 0 (34) where V i represents the velocity of the centroid for each link, ω i represents the angular velocity for link i, . ω i represents the angular acceleration for link i. To obtain a closed-form for dynamic equations, first, eliminate the constraint forces and separate them from the joint torques, to explicitly involve the joint torques in the dynamic equations. For Figure 5, joint torques τ 1 and τ 2 are equal to the coupling moments: V c2 + r 0,c1 × m 1 g + r 0,1 × m 2 g − I 1 .

Experiment Results
This work used MATLAB to produce numerical examples of the analytical solutions for the exoskeleton kinematics and dynamics. In addition to this, the paper uses SolidWorks and the SimMechanics toolboxes from MATLAB to model and simulate mechanical systems that use standard Newtonian laws.

Position Analysis
In this simulation, the positions of the main links of the proposed mechanism with respect to the position of the driving link (linear actuator) were determined using the closed equations, Equations (1)- (24), developed in Section 3.1. With the help of these data, the range of the motion structure that moves to the proximal phalanx and the middle phalanx were determined, see Table 3.  Figure 6 presents the result of simulation in SimMechanics, which was carried out in a time horizon of 21 s. For the first 10 s of the simulation, the MCP joint generated a θ 1 = 26 • movement and PIP generated θ 1 = 43 • . After 11 s, the MCP and PIP joints returned to their initial position in a time window of 11-21 s.

Inverse Kinematics
Taking the parameters d 1 = 0.0203 m, d 2 = 0.0187 m, and d 3 = 0.0202 m for the length of proximal, middle, and distal phalanges, respectively, as shown in Table 1, and Equations (25)- (30), the results are shown in Table 4. It can be seen that the values of joint coordinates q 1 , q 2 , and q 3 for rotation angles of MCP, PIP, and DIP joints coincide with the range of motion obtained for the position analysis in Section 4.1.

Dynamics
For dynamic simulations, parameters, such as mass, moment of inertia, and center of mass of the elements to be analyzed for the proximal and middle phalanges, were taken from the CAD design proposed in Solidworks, as shown in Table 5. To first validate the dynamics, a sinusoidal function was developed to represent the movement of each joint as = 13π sin(πt/90)/90 and = 43π sin(πt/90)/180 for the proximal and middle phalanxes, see Figure 7. According to the algorithm described in Section 3.3, using Equations (31)-(39) and implementing the values from Table 5, the values shown in Figure 8 and Table 6 were obtained.

Structural Analysis
ANSYS software was used for finite element analysis. For this simulation, only the elements of the mechanical structure were contemplated and the CAD design from ANSYS is shown in Figure 9a. The main base of the mechanism was taken as a fixed support and the friction forces between the elements were not included. A force exerted on the bolt that joins the linear actuator with the mechanism that moves to the proximal phalanx was applied. The force exerted on that element was taken with respect to a maximum force exerted by a selected linear actuator (40 N), see Figure 9b. The average size of the mesh elements was 2.088 × 10 −4 m. The material used to make the 3D print was ABS. In the simulation of static forces, only total strain analysis was considered. Using these criteria, the feasibility of the design was evaluated, focusing on total deformation. As can be seen in Figure 10a,b, the deformation magnitudes for each part of the mechanism are defined according to the colors shown in the column on the left, where the pieces in blue are the ones that suffered less deformation; the more deformation there was the more the pieces changed color, and those presented in red were the pieces that suffered more deformation. The maximum deformation obtained was 1.41073 × 10 −5 m, and is present on the "pin slide" element, which is the bolt that joins the linear actuator with the elements that move to the proximal phalanx. As result, a one-DOF prototype mechanism for a finger was developed, where the links, together with the base, were manufactured using ABS plastic by means of a 3D printer, see Figure 11. The bolts were made of aluminum alloy using a lathe, and their dimensions are based on those of the design.

Discussion
The use of a robotic device for hand rehabilitation is a new development to support the recovery of hand functions following a stroke. Exoskeleton design in the literature requires deep knowledge of physical human-robot interactions, biomechanics, rehabilitation, actuators, sensors, and control. The main goal is to design effective, lightweight, and portable robotic devices for hand rehabilitation. However, most of the reported hand exoskeleton rehabilitation devices, with very few exceptions, lack portability, have many DOF, and, at the same time, they are voluminous, heavy, complex, and expensive [2][3][4][5][6].
The exoskeleton proposed in this work is designed to achieve a lightweight device for the hand of the patient so that it can be worn more easily. It can be manufactured with a 3D printer and its lightness allows it to be used as a splint. The exoskeleton consists of a linkage-slide mechanism with one DOF that provides extension/flexion assistance for the finger. The use of the linkage-slide mechanism not only realizes the purpose, but also makes the rotation center of the linkage structure coincide with the rotation axis of the MCP, PIP, and DIP finger joints. The structure is, therefore, more compact and lightweight than those mentioned in other works [18][19][20][21][22][23][24][25][26][27][28].
Currently, the cost of complex robotic devices makes them unsuitable for use in a domestic or local clinical setting (e.g., [2]). Developing lower-cost devices could help to address this and the development of a low-cost prototype robotic device for rehabilitation to help people to recover finger functions and practice normal daily activities would be of use.

Conclusions
As discussed in the previous sections, the CAD design of a one-DOF exoskeleton for a finger's movement was presented. The prototype was based on the anthropometric measurements of a finger, as well as the movement ranges of the joints (MCP, PIP, and DIP joints).
In the development of position and displacement analyses, the link position of the proposed design was determined concerning a driving link position, which, in this case, was the linear actuator. The analysis presented a challenge since the mechanism configuration meant that obtaining the position equations of the main elements had considerable complexity. However, the equation validation indicates a good analysis.
The inverse kinematic analysis achieved the equations that described the prototype position to determine the value of the articular coordinates with respect to the finger end coordinates. Additionally, inverse kinematic analysis was performed using the geometric approach, finding a close equation. The Newton-Euler approach was applied for dynamic analysis. As a result of the simulations, pairs were obtained, for example, for the movement of the MCP joint. The maximum obtained torque was 0.0170 N·m.
The simulation developed through SimMechanics allowed mechanism movement according to the proposed ranges of motion. Additionally, structural analysis simulation was carried out using ANSYS software. With the obtained results, it was possible to determine the link deformation that occurs in the mechanism when an external force is applied from the Actuonix linear actuator, which was applied in the bolt that joins the linear actuator with the mechanism that exerts movement on the proximal phalanx. The used force value was 40 N, which is equivalent to the maximum exerted force by the actuator. The obtained results indicated that the maximum obtained deformation had a value of 1.41073 × 10 −5 m, generated in the bolt that joins the linear actuator with the mechanism that exerts proximal phalanx movement. With these data it could be concluded that the maximum deformation present in the mechanism elements was relatively small and that the use of ABS plastic in the prototype was viable.
In future work, improvements to the proposed design are expected to allow satisfactory functionality to be obtained. Likewise, various improvements are contemplated, which include better design parameter definitions and mechanism dimensions based on the anthropometric measurements of people of all ages, with the objective that the mechanism have a good performance for application in rehabilitation, to adapt sensor implementation designs that allows monitoring the movement of fingers phalanges. In addition, where the mechanism exerts movement, the use of another material type that allows optimal link manufacturing of the mechanism and to implement the proposed linear actuator in the prototype should be aims.