Since ancient times humanity is looking for solutions for people with disabilities and trying to help to solve their problems, so that their life can become more comfortable and they do not feel somewhat limited. This is especially applicable for the scope of designing prosthetic human limbs, which is actively developing in the past twenty years. Today prosthesis has achieved great success, in particular due to the development of electromechanical engineering and computer programming. What seemed fantastic in the past – today is a reality. Developments in industry served as a great impetus to the development of human prosthetics: scientists have developed different types of robot hands to assist and even to completely replace workers in some production processes. This in its turn let to gradual implementation of the innovation in the production became applied in medicine, more specifically in human limb prosthesis.
Scientists are trying to create prototypes that would be completely similar to human hand. The hand prosthesis should not only look similar to a human hand, but should also serve functions of human hand. There are prostheses that are close to this ideal. However the desire to replicate the appearance of a human hand, while maintaining the functionality leads to an increase in the cost of the prosthesis production, which is not always available to the end user.
Thus, the main task of this work will be the design of the prosthesis with a low production cost, while maintaining the maximum functionality. This will become possible through reducing the cost of materials for the production of the prosthesis, which will be achieved by a combination of two factors. Firstly, NU prosthesis will reduce number of fingers to three, forgoing appearance of the hand, but even more reducing the cost of materials, and, thus, making the prosthesis more affordable. Secondly, 3D printers will be used for the production of the prosthesis. This will not only reduce the cost of prosthesis production, but will also considerably decrease the weight of the prosthesis due to the fact that plastic will be used. Moreover, design of the prosthesis prototype printable on 3D printers will solve additional problems in prosthesis production - the design of NU prosthesis will simplify the prosthesis manufacturing process. That is, it is planned to put 3D model of the prosthesis in the public domain, thereby, making prosthetics much more affordable to general public, as everybody with access to a 3D printer will be able to print himself/herself prosthesis at a low cost. However, it should be noted that such a design would require additional simplification not only in manufacturing, but also in installation and use of prostheses, because users will independently perform all manipulations with prostheses without participation of any specialists.
This work will considered an under actuated (four-bar linkage) system. The given system allows using the least amount of actuators, while preserving the maximum degree of freedom. In order to understand how the system of the hand works it is sufficient to consider the kinematics and kinetostatics of one finger, as all the other fingers operate in the same way. Thus, this paper will focus on the analysis of work of one finger.
To develop a full understanding of the NU prosthesis design the structure of the work structure will be as following. Firstly, the paper will provide the background information, which will discuss the history of the hand prosthetics and anatomical structure of the human hand through evolutional and physiological points of view. Additionally, it will discuss the existing types of robotic grippers and compare and analyze the modern hand grippers. The second part of the paper will focus on NU prosthesis prototype through analysis of the possibilities of 3D printer in the production of the hands prosthesis. It will also address the kinematic and kinetostatic analysis of the finger, and its modeling. Lastly, the paper will discuss the results of the analysis and provide conclusions.
1. LITERATURE REVIEW
BRIEF HISTORY OF THE HAND GRIPPERS
The history of the modern hand grippers start in 1969, when a Mechanical Engineering student at Stanford University Victor Scheinman first time introduced his robotic arm . His hand gripper had six degrees of freedom, was equipped with electric motor, and could be controlled by laboratory computers . The working principle of the Stanford hand was based on hand a parallel grip. That is, it consisted of two fingers that performed the simplest actions of gripping and releasing the object . This type of gripper was improved in 1970s, when the grippers began to use angle grippers, which mechanism of work was similar to the claws of a lobster, closing on the object . The main difference of these two types of grippers is in the fact that in parallel grip the force is distributed equally over the length of two fingers available, whereas angle grip allows exerting more pressure at certain points . Additionally, parallel grippers are based on put a higher grip force at the shorter strokes, whereas angular grippers have lower grip force at longer strokes .
Later, in 1990, the Massachusetts Institute of Technology introduced their own type of grasper, called the Barret hand. The innovation of that grasper was in the fact that it now was three-fingered, which allowed extra mobility with different type of grasps . This type of grasp became more multifunctional, unlike the two-finger models designed to perform a particular task.
One of the relatively recent developments in gripper innovation was made by Barrett Technology, who introduced the polymer-based SDM Hand, which is able to make manipulations over objects of different shape, size and weight .
1.2. ANATOMY OF THE HUMAN HAND:
Furthermore, in order to deeply understand the system of prototypes designing, it is necessary to consider in detail the anatomy and the functions of the human hand. The simple definition given by Cambridge dictionary  describes human hand as “the part of the body at the end of the arm that is used for holding, moving, touching, and feeling things.” It can be said that these definition fully satisfies our conception about the structure and functions that human hand perform. But is it really? In order to understand this it is necessary to delve in details of the anatomical structure of the human hand.
To begin with, the best way to consider the human hand is to start from its evolution and resemblance with limbs of other vertebrates. Apes and monkeys are considered to be mammals closest in the anatomical structure of their hands to human. This is due to the fact that the thumbs on both of their hands are opposable to other fingers, exactly the same as on a human hand. According to Richard W. Young  such structure of the hand provides an advantage in “throwing and clubbing”. However, despite such similarities, human hand has undergone significant changes in the last 7 million years, when the path of the evolution of man and the anthropoid apes went split . This is reflected in the fact that human has a long thumb and shorter fingers, while the closest biological relative of human chimpanzee has longer fingers and shorter thumbs  This is explained by the fact that in the course of evolution the human hand changed in order to make it easier to grab and hold objects, as the thumb easily contacts with the other fingers at any point, which makes it easier to grasp objects . At the same time, the longer fingers of chimpanzee allows it to easily climb the trees and to cling to branches . To be more precise, most scientists agreed that such structure of the human hand is the result of the beginning of the use of stone tools by man .
Considering evolution, the arising question is “why five fingers?” As many evolutionary studies shows, there is no exact answer to this question. Almost all tetrapods grew by five digits on each of the four limbs: even hoofed animals, such as horses, at an early stage of embryo development have five digits, which in the course of development of the embryo coalesce in the hoof . The only thing that can be said according to these studies is that although there are some individuals that are born with deviation in six fingers (1 out of
500 people) , evolution does not accept this variation of genes and does not take the reverse course. On the contrary, as Michael Coates , associate professor in the department of Organismal Biology and Anatomy at the University of Chicago and co-editor of Evolution & Development argues, over 360 million years of evolution tetrapods reduced the number of their fingers from six, seven and even eight to five, and it is likely that the process of reducing the number of fingers is continued. Another opinion regarding the reason human has five fingers is expressed by Frank Wilson a retired neurologist. He also states that six fingers are too many for standard function carried out by hands . Moreover, according to Wilson  modern developments in prosthetics engineering shows that the same functions can be performed with the same success and productivity rate by four-digitate and three-digitate hands. Therefore, we can conclude that argues, evolution moves towards simplification, which in the case of the hand implies reduction of the number of fingers without losing functionality of the hand, and, thus, a large number of fingers have advantage neither in terms of evolution, nor in terms of functionality.
1.3. ANATOMY OF THE HUMAN HAND: PHYSIOLOGY
In order to further understand where to begin modeling the hand prosthesis, it is necessary to consider the structure of the hand from the point of view of physiology. The figure 3 shows the detailed structure of the human palm. The metacarpal bones connected with the proximal phalanx is the first phalanx which connect the finger with a wrist, then comes middle phalanx and at the end the distal phalanx. Another feature of the thumb is that it consists of two phalanges: proximal and distal phalanx. The human hand also has metacarpophalangeal (MCP) joints, proximal interphalangeal (PIP) joints and the distal interphalangeal (DIP) joints that are shown in Figure 3.
Figure 3. Structure of the human palm (Reference)
Furthermore, it is necessary to introduce the concept of degree of freedom, since it will often be used in this paper. There are many definitions given by the different sources, but generally of degree of freedom (DOF) can be defined as a number of parts involved in independent motion resulting in the ability of the hand to produce variety of movements. To clarify, in case the human hand DOF can be defined as the positions that fingers can take or movements that fingers can make in different directions. Figure 4 shows how degrees of freedom for each finger can be determined. Each finger, except thumb, has DOF equal to 4 as all of them can make hyper-extension, extension, flexion, and abduction movements . The thumb has a more complex structure, which enables it to perform an additional type of movement – opposition or retro-position, which makes its DOF equal to five .
Figure 4. Positions defining DOF of fingers 
In 1956 J.R. Napier classified basic movements of the human hand in the Journal of Bone and Joint Surgery. This classification is still widely used in medicine and science. According to Napier , basic movements of hands that people perform daily can be divided into two major types: prehensile movements that are based on the manipulation over an object by grabbing and holding it in hand, and non-prehensile movements that are based on the manipulation over an object by “pushing or lifting.” This paper will basically focus on prehensile movements since they are the most difficult to reproduce in the prosthesis.
The grasp can be considered as the most common type of the prehensile movements. In everyday life we use grasp to control different types of objects to perform different types of daily tasks. Napier divided grips into three different types according to the purpose of their use. They are “static grips, dynamic grips and gravity-dependent grips” . Rutter provides examples of the most common motions for each type of grip. According to him , the static grips are usually used for actions that require application of brute force, such as brandishing an ax, dynamic grips are necessary for movements that involves accuracy, such as holding a pen and writing, and last, but not the least, gravity-dependent grips are used for carrying things, such as shopping bags. Figure 3 shows the basic movements of the hands, which are most frequently used in everyday life. That is, lateral pinch, tip, and tripod provisions of the human hand on the Figure 3 illustrate types of dynamic grips, hook demonstrates gravity-dependent grip, whereas spherical and cylindrical grasps provide static grips examples. The platform and point provisions of the human hand on the Figure 5 shows non-prehensile movements that are commonly used for pushing and poking, respectively.
Figure 5. Basic provisions of the human hand (Skyler et all, 2012)
Another important decision that should be made when designing the desired prototype is how many fingers to include, on the necessary number of joints and their types, on sensors, degree of freedom, speed, strength characteristics and variation of movements of those joints. Everything is overcomplicated by the fact that it is necessary to arrange everything in a small space, as well as to choose the optimal weight and solidity construction. Since the extra weight adds stress on actuators, it leads to increase in costs, which in its turn leads to additional outlay of power, load on joints, which lead to more unstable work of arm. It should also be noted that the complexity of the prototype decreases its affordability. At the same time it would be difficult to a person to control an arm with a too complex system with many actuators. Thus, a control system should be as simple as possible. A system with under-actuated grippers is suitable for this.
1.4. MODERN TYPES OF GRIPPERS AND THEIR BRIEF DESCRIPTION
Currently, there are four major categories of grippers, which are in their turn also divided into several sub-categories.
The first category is mechanical grippers that include linkage grippers, gear and rack grippers, cam-actuated grippers, screw-driven grippers, and rope and pulley grippers . The simplest definition that at the same time fully conveys the entire mechanism of the mechanical gripper is given by McGraw-Hill Dictionary of Scientific & Technical Terms , which describes mechanical gripper as “a robot component that uses movable, fingerlike levers to grasp objects.”
The second category of vacuum and magnetic grippers, as its name said, consists of vacuum grippers, magnetic grippers, whose mechanism of work is based on application of distributed force for carrying out manipulations over an object . That is, vacuum grippers use rubber cups and pads, and move objects by creating a vacuum and suction (Figure 6) . The main disadvantage of this gripper is the impossibility of operations with rough objects . Magnetic grippers are used to lift and handle ferrous objects (Figure 7) .
Figure 6. Vacuum grippers  Figure 7. Magnetic gripper 
The third category of grippers – universal grippers - include inflatable grippers, soft grippers, and formless grippers. Inflatable grippers are designed to carry out manipulations over very small objects. Soft grippers are well-adjusted to the shape of the object, which allows to distribute pressure evenly across the entire object during manipulations over objects (Figure ) [. Three-Fingered Grippers. The mechanism of work of formless grippers is based on the property of soft materials to envelop around objects, and, in this way, to hold them (Figure ) .
Figure 8. Soft gripper  Figure 9. Fromless gripper 
The last category of grippers is multi-fingered hands. This category is the closest both in appearance and functionality gripper types to the human hand. There are two main types of multi-fingered hands. The first type is multi-fingered hand with parallel fingers. It usually consists of three or more fingers, which are arranged at an equal distance from each other along the rim . This type of the gripper will be discussed further in this paper.
The second type is multi-fingered hand with thumb. It usually consists of from two to four fingers installed in a raw, and one opposable finger, which serves functions of the human thumb .
Table 1. Comparison of robotic grippers 
Complexity of Grasp Planning
delicate objects Regrasping In-hand
(only through an
No Low (except for objects
with complex shapes)
Magnetic No N/A
No No Very Low
Universal Yes No
Yes (except for
(only through an
Multi-fingered Yes Yes Yes Yes Yes High
Table 2. Comparison Table for Prosthetic Hands
Name Developer Year Fingers DoF Type of Transmission Weight (g) Number of Joints Number of Actuators Actuation Method
Human hand - - 5 27 - - - - -
TUAT Hand  Forschungszentrum Informatik Karlsruhe 2000 5 19 - 125 20 1 Ultrasonic Motor
LO/Sh Southampton Hand  University of Southampton Hand 2001 5 4 - - 8 2 DC Motors
ACT Hand  University of Washington - 5 23 - - 15 4 Brushless DC Motors
RTR Hand [13, 15] ARTS / Mitech Laboratories (Pisa, Italy) 2002 3 9 Tendon 350 9 2 Electrical motor
Manus Hand  Spain/Belgium/Israel 2004 5 3 Tendon 1200 9 2 Brushless DC Motors
Keio Hand  Keio University, Yokohama, Japan 2008 5 15 Tendon 730 15 1 DC Motors
Barrett Hand [13, 15, 16] Barrett Technology, USA Since 1988 3 4 - 980 8 4 Rare-Earth brushless-DC servo motors
Robotiq hand [17-18] Robotiq, USA - 3 10 Resilient rigid linkage 2300 9 4 Servo motors and the control electronics
SDM Hand  - - 4 8 - 490 8 1
1.5. DESIGN OF TUAT PROTOTYPE
Forschungszentrum Informatik Karlsruhe (FZI) has developed the humanoid robot ARMAR (1) in 2000. Its main function was helping people at work and at home. Tokyo University of Agriculture and Technology (TUAT) had developed arm prosthesis for people with disabilities, which was integrated into ARMAR.
The parameters of a healthy 27-year-old Japanese man were used to create this prototype. His height was 165 centimeters and a weight was 55 kilograms. The prototype has the same hand geometry. The length from the tip of the middle finger to the end of the palm is 175 mm, the width is 130 mm, and the approximate weight is 125 grams. The rest of the parameters and proportions are kept similar to that of human model.
Figure 6. Structure of an arm prototype and its mechanism of work
Figure 4 shows the structure of the prototype of an arm and how does the mechanism work. It can be seen that four fingers have quite similar structure, where the first two interphalangeal joints (IP) have one DOF and metacarpal-phalangeal joint has two DOF. It should also be noted that a joint with two DOF can provide adduction-abduction movements. Figure 4 shows how the finger works and the connection between phalanx. Let\'s consider how the grasp works for a more detailed understanding. The link-rod (A) draw the link-plate (D) and finger starts to move and it goes until the proximal phalanges touches the object after that the link-plate (D) continue the movement until it grasp around the object by the link-rod (C). Disadvantage of the thumb is that it is designed in such way that it cannot copy all abilities of human-thumb. The prototype has 1 DOF, which is fixed on the base plate. It is located in a such way so it can be a fulcrum.
1.6. MECHANISMS OF WORK OF THE ANATOMICALLY CORRECT TESTBED (ACT) HAND
The ACT Hand is designed to deepen our understanding of human hand and control mechanisms and to provide guidelines for building versatile prosthetic and dexterous hands.
This prototype was made of two types of materials: one part was made of steel beams and served as a bone. This material offers superior strength and durability as is required for durable work. Body is made of plastic shells fabricated using stereo-lithography. This plastic material is easy to work with and it is possible to remodel its shape for small time and monetary cost.
Table 3. Act hand phalange length 
The table 2 illustrates the length of the three fingers and their proportion. The fingers have 4 DOF, while the opposable thumb has DOF five. Non-orthogonal, non-intersecting DOFs. The thumb, index and middle fingers are actuated by anatomically routed tendons and muscle-equivalent actuators.
Figure 7. 
The examples analyzed above has not yet entered into a mass production. In the Joseph T. and Jacob L.’s “Mechanical Design and Performance of Anthropomorphic Prosthetic Hands” six prototypes that are mass-produced or popular around the world were review. There are: Vincent hand produced by Vincent system, iLimb hand produced by Touch Bionics, Bebionic hand v2 produced by RSL Steeper and Michelangelo hand produced by Otto Bock. The picture 5 illustrates all types of hands without their cosmetic gloves. The table 1 provides detailed description of each type of hand. It follows from the table that parameters and functionality of hands are almost similar, and the only serious difference between the prostheses is in the joint coupling methods: the joint coupling method for iLimb and iLimb Pluse is tendon linking, whereas the joint coupling method for Vincent Hand, Bebionic, Bebionic v2 is linkage spanning.
It should also be noted that almost all prostheses have distal finger segment. Therefore, in order to make the distal phalanges to move separately from the whole finger one more joint, called DIP, is added. Only Michelangelo fingers comprises of one integral finger part. That is, when MCP joint moves, the whole segment of the finger moves (Figure 8, d).
As it was mentioned above, almost all prostheses have distal phalanges and use four-bar linkage system to drive DIP joint. Thus, the need for additional actuators is eliminated. The Figure 6 (a, b, c) clearly shows how the distal segment connects with the system. To be more specific, Vincent finger’s (figure 8 (a)) distal part is connected by two wires to the base finger mechanism, the iLimb and iLimb Plus are attached to the base finger using tendon mechanism. The end of the tendon from one side is connected to the distal link and from another side to the finger base. It can be seen form the picture that base of the finger is connected with the end of the distal, and two small rollers drive them. The rollers help to control moment around PIP joint. The Bebionic finger uses four-bar linkage system, where the mechanism in the finger connects with single plastic rod, which connects distal and base segments.
All hands are shown without cosmetic glove.
Figure 8.(a) Vincent hand by Vincent Systems, (b) iLimb hand by Touch Bionics, (c) iLimb Pulse by Touch Bionics, (d) Bebionic hand by RSL Steeper, (e) Bebionic hand v2 by RSL Steeper, and (f) Michelangelo hand by Otto Bock. 
Figure 9. Commercial finger images (top) and kinematic models of finger joint coupling mechanism (bottom). (a) Vincent (Vincent Sys-tems), (b) iLimb and iLimb Pulse (Touch Bionics), (c) Bebionic v2 and Bebionic (RSL Steeper), and (d) Michelangelo (Otto Bock). θ1 = angle of metacarpal phalange joint, θ2 = angle of proximal interphalange joint. 
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