A Hand Prosthesis with an Under-Actuated and Self-Adaptive Finger Mechanism

One of the major problems faced by hand amputees is the unavailability of a lightweight and powered multi-functional hand prosthesis. Under-actuated finger designs play a key role to make the hand prosthesis lightweight. In this paper, a hand prosthesis with an under-actuated and self-adaptive finger mechanism is proposed. The proposed finger is capable to generate passively different flexion/extension angles for a proximal interphalangeal (PIP) joint and a distal interphalangeal (DIP) joint for each flexion angle of metacarpophalangeal (MCP) joint. In addition, DIP joint is capable to generate different angles for the same angle of PIP joint. Hand prosthesis is built on the proposed finger mechanism. The hand prosthesis enables user to grasp objects with various geometries by performing five grasping patterns. Thumb of the hand prosthesis includes opposition/apposition in addition to flexion/extension of MCP and interphalangeal (IP) joint. Kinematic analysis of the proposed finger has been carried out to verify the movable range of the joints. Simulations and experiments are carried out to verify the effectiveness of the proposed finger mechanism and the hand prosthesis.


Introduction
Hand prosthesis is an artificial device which replaces the missing hand of an amputee and is expected to fulfil the functional and aesthetic requirements of the amputated hand. The main problem that causes amputees not to accept the available prostheses is the unavailability of light-weight prostheses with acceptable controlling and functional properties [1]. It has been identified that the Engineering thumb and the index finger play an important role than the other fingers in most of daily grasping activities [2]. Therefore, many hand prostheses are based on three fingered configurations and finger abduction/adduction is not considered in the designs [3]. During activities of daily living (ADL), hand is arranged in different grasping patterns to handle objects with different geometries [4]. Metacarpophalangeal (MCP), Proximal Interphalangeal (PIP) and Distal Interphalangeal (DIP) are manipulated to obtain different configurations to generate different grasping patterns. Flexion/extension angles of these joints are arranged in different combinations to realize different grasping patterns. Subsequently, a hand prosthesis should also be developed with the ability of generating different grasping patterns to help the amputee during ADL. Studies presented in [5] [6], and [7] attempt to accommodate these requirements in their devices. However, very few demonstrate the ability to provide human alike motion in their mechanisms. Generally, a robotic hand prosthesis should be lightweight while providing required dexterity and functionality. In order to arrive at a suitable compromise, researchers are trying to reduce number of actuators while trying to achieve maximum functionality of the prosthesis. In view of that, under-actuated mechanisms have been developed and tested. When a mechanism has lesser number of actuators than the generated degrees of freedom (DOF) [8] the mechanism is said to be under-actuated. Several researchers [3] [9]- [16] [19]- [24] have proposed under-actuated finger mechanisms and hand designs. Most of the fingers are capable of generating human alike cylindrical grasping mode to grasp cylindrical objects. The Smart Hand [7] is a transradial prosthesis with under-actuated fingers. The finger mechanism proposed in [15] is capable of passively generating different angles for PIP and DIP joints for each flexion angle of MCP joint. The angles change according to the grasping object passively and the thumb has a single DOF. However, DIP joint is not capable of generating different angles for the same angle of PIP joint. Therefore, if an object directly touches with the middle phalange while grasping the self-adaptation ability of DIP joint is lost. Therefore, in this research a prosthetic hand comprises of under-actuated and self-adaptive fingers is proposed. The proposed finger is used as the index, middle, ring or little finger of the hand prosthesis. Modified mechanism of the proposed finger is used as thumb of the hand prosthesis which includes thumb opposition/apposition in addition to flexion/extension of MCP joint and interphalangeal (IP) joint. The proposed finger is capable of passively generating different flexion/extension angles for a PIP joint and a DIP joint for each flexion angle of MCP joint. In addition, DIP joint is capable of generating different angles for the same angle of PIP joint. In this study, abduction/adduction of MCP joint is not considered and only the flexion/extension is considered. The hand prosthesis assists user to grasp objects with various geometries by performing cylindrical grasp, hook grasp, lateral pinch and tip pinch and palmar pinch.
Next section of the paper proposes the under-actuated and self-adaptive finger

Under-Actuated and Self-Adaptive Finger
Proposed finger can generate flexion/extension of MCP, PIP and DIP joints. It can be used as an index, middle, ring or little fingers of a hand prosthesis. Main structure of the finger can be simplified to a mechanism which consists of two four-bar mechanisms which are combined at PIP joint and with a coupling linkage as shown in Figure 1. Linkage for distal phalanx is connected to the second four-bar mechanism at DIP joint. As shown in Figure 1, three torsion springs are attached between lower bar-1 (proximal phalanx) and palm at MCP joint, lower bar-1 and driving bar at first four-bar mechanism; lower bar-2 (middle phalanx) and the side bar-1 at PIP joint; respectively. Driving bar is coupled to the motor which generates the driving torque. Second torsion spring is used to limit each joint motion of the first four-bar mechanism in its predefined initial position and carrying out the under-actuation. Third torsion spring is used to keep the second four-bar mechanism as a rigid body relative to first four-bar mechanism. The ratio of spring constants of first, second and third springs is 6.4:10:1.

Under-Actuation of the Finger
Initially, when the torque is applied by the driving bar the finger operates as a single rigid body due to second and third torsion springs. Then, first torsion spring which has lower spring constant than second torsion spring starts to compress and the spring resistance increases. When the spring resistance of second torsion spring is overcome by the first torsion spring middle phalanx starts to rotate relatively to the proximal phalanx. Once the middle phalanx motion is restricted by the grasped object, third torsion spring is compressed and side bar-1 starts rotating relative to middle phalanx. Then, distal phalanx  In order to carry out the proper under-actuation; Third Spring First Spring Second Spring where K is spring constant.

Self-Adaptation of the Finger
Proposed finger incorporates self-adaptation ability which enables to grasp objects with different geometries. Figure

The Thumb
Proposed finger mechanism shown in Figure 1 can be modified and used for the thumb. The main structure of the thumb is shown in Figure 3. The thumb is similar to the proximal phalanx and middle phalanx of the finger in Figure 1. It consists of a four-bar mechanism and two torsional springs. Thumb can generate flexion/extension of its MCP and IP. Additionally, opposition/apposition of thumb can be generated as explain in Section 3 [refer Figure 7(c)]. When the motor torque is applied by the driving bar the thumb operates as a single rigid body due to second spring. Then, lower bar (proximal phalanx) rotates and first torsion spring starts to compress and the spring resistance increases. When the  spring resistance of second torsion spring is overcome by the first torsion spring, distal phalanx starts to rotate relatively to the proximal phalanx. The ratio of spring constants of first and second springs is 0.64:1.

Kinematic Analysis of the Finger
In order to understand the kinematic behaviour of the finger mechanism kinematic analysis is carried out. As shown in Figure 4 and Figure 5 the joints of the fingers are connected with nine mechanical links: AC, AB, CD, BD, EF, BF, BH, FG and GHI. Joint angle relationship between these linkages gives the respective motion between phalanxes of the finger. AC is rigidly connected to the wheel of the worm-and-wheel gear which is driven by the motor to drive the whole mechanism. Therefore, AC can rotate with respect to joint A when the motor rotates. Rotation of AC actuates CD. Then due to the compression of the torsion spring between AB and AC, AB is actuated by AC. EF and BD both are actuated by CD, and EF actuates both BF and FG. When BD actuates, due to the compression of torsion spring between BH and BD, BH starts to actuate. At the end, the GHI is actuated by FG. First, second and third springs are connected between, AB and the palm; AB and AC; and BD and BH. Initially even though the torque is applied to the AC, angle between AB and AC (θ) is kept constant due to the torsion spring between AB and AC. Then, angular velocity of AB becomes zero when its motion is restricted by the object. Initially, θ is known. Thus, β = 90 − (α + θ) for any α value. Assume that AC, AB, CD, DB, EF, BF, FG, BH, GH, HI, DE are l 1 to l 11 respectively. Considering ABDC four-bar mechanism;    The angle (δ) can be found from the above equation for the given α and β.
Therefore, can be found using and angle . Consider DE, EF, BF and BD.

Proposed Hand Prosthesis
The proposed finger and thumb is used to introduce a multi-functional hand prosthesis shown in Figure 6. Table 1 shows summary of specification of the proposed hand prosthesis.

Mechanical Design and Mechanism
The hand prosthesis consists of four main units: first finger unit, second finger unit, third finger unit and a palm [refer Figure 6]. Since the index finger and the thumb play an important role than the other fingers in most of daily grasping activities [2] those two are taken as separate finger units and the middle, ring and little fingers together are taken as a separate unit for the actuation.    shaft as shown in Figure 7(b). Third finger unit consists of thumb, its worm and wheel gears (reduction ratio 35:1) and two DC motors [refer Figure 7(c)] which are perpendicular to each other. All four motors of the prototype of hand prosthesis have the same specification shown in Table 2. Finger structures, shafts and gears are fabricated from Al7075, stainless steel and Nylon 101 respectively using CNC machine. All finger units are attached on the palm as shown in Figure 6. The proposed finger mechanism shown in Figure 1 is used to each finger in the first and second finger units. Motors of first and second finger units are connected to the MCP joint. Thumb can generate flexion/extension of the MCP and IP joints using motor −1 and opposition/apposition of thumb are generated using the motor −2 [refer Figure 6 and Figure 7(c)]. The hand prosthesis assists user to generate cylindrical grasp, hook grasp, lateral pinch and tip pinch and palmar pinch shown in Figure 8.

Experiment and Results
Simulations and experiments are carried out to compare and verify the motion generation of the proposed finger. Furthermore, experiments are carried out to verify the adaptation ability of the finger and hand prosthesis. The kinematic model is simulated in MATLAB/Simulink environment to achieve the fingertip motion. Index finger motion of prosthesis is captured using a camera by placing passive markers to each joint and captured data is used to derive joint angles.
The experimental set-up is shown in the Figure 9. As the controller, ATmega 2560 (Atmel) is used. The selected motor driver is a dual H-bridge motor driver (L298N). PD control is applied in the joint space to generate the torque command for the MCP joint. As the desired motion MCP motion shown in Figure  11 which is generated from the simulation is used.       Snapshots shown in Figure 15 and Figure 16 illustrate the adaptation ability of middle phalanx of index finger and distal phalanx of index finger respectively.

Simulation and Experimental Results
Cylindrical grasping of the hand prosthesis is shown from the sequence of snapshots in Figure 17 and Figure 18 shows sequence of snapshots for hook grasp generation. Figure 15, Figure 16 and Figure 17 have verified the adaptation ability of the hand prosthesis.      An under-actuated and self-adaptive finger was proposed together with a hand prosthesis. The finger consisted of mainly two four-bar mechanisms. Modified mechanism of the finger was used as the thumb mechanism. Furthermore, a hand prosthesis with the proposed fingers and thumb was introduced in the paper. The finger was capable of generating different passive angles for a PIP joint and a DIP joint for each flexion angle of MCP joint. In addition, DIP joint was capable of generating different angles for the same angle of PIP joint.

Discussion and Conclusions
Thumb mechanism allowed for powered articulated thumb opposition/apposition.  and experiments. The developed hand prosthesis offers a grasp adaptation using four actuators.
The hand prosthesis can be used to substitute a lost hand part of an amputee or can be used a terminal device for an arm prosthesis such as trans-radial prosthesis of trans-humeral prosthesis. Electromyography signals or electroencephalography signals of the wearer can be used to identify the motion intentions of the user to control the hand prosthesis, accordingly.