Anthropomorphic Prosthetic Hand with Combination of Light Weight and Diversiform Motions

Abstract

Most prosthetic hands adopt an under-actuated mechanism to achieve dexterous motion performance with a lightweight and anthropomorphic design. Many have been verified in laboratories, and some have already been commercialized. However, a trade-off exists between the dexterity and the light weight of such prosthetic hands. In general, current commercially available prosthetic hands usually consider one aspect at the expense of the other, such as obtaining diversiform hand motions but an increased weight, or achieving lightweight design but with limited motion functions. This study attempts to attain a balance between the two factors, by realizing diversiform hand motions while reducing the weight as far as possible. An anthropomorphic prosthetic hand is proposed with only three servomotors embedded in a human-sized palm, with multiple functions, such as a stable/adaptive grasp and passive hyperextension. The proposed hand can achieve 13 grasp types with over 80% of the grasp motions under the Cutkosky taxonomy, while it weighs only 132.5 g, at less than 36% of the prosthesis weight limitation based on the study of Kay et al.

1. Introduction

Prosthetic hands that have been developed to date can primarily be categorized into two types: Fully actuated [1,2,3,4] and under-actuated [5,6,7]. The former type is usually equipped with actuators corresponding to every moving joint, which can achieve dexterous motions similar to those performed by a human being owing to its multiple degrees of freedom (DoFs). However, a multiple actuator configuration exhibits disadvantages such as the increased weight, bulky packaging, high power requirements, and complex control strategy. The weight of a prosthetic hand remains one of the most distinguishing factors limiting its adoption by amputees [8]. Therefore, research and design related to prosthetic hands have trended towards the under-actuated mechanism, which can significantly reduce the weight and packaging size, and much more easily realize human-like appearance, low power consumption, and simple control architecture compared to the fully actuated type. The under-actuated mechanism involves greater DoFs than degrees of actuation, usually including one to six actuators (compared to the 34 muscles of a human hand) [9]. The data from 1983 to 2016 have demonstrated that the majority of prosthetic hands are under-actuated [10]. However, even these under-actuated hands exhibit a trade-off between dexterity and light weight. That is, increasing the hand motion functions increases the weight, while reducing the weight leads to a simple mechanism that cannot achieve diversiform hand motions. Figure 1 presents a comparison between the achievable hand motion types and the entire weight of several under-actuated anthropomorphic prosthetic hands, covering a range of commercial to experimental uses. The comparison is based on the Cutkosky taxonomy as it is currently the most widely used approach in the field of robotics [11]. As illustrated in Figure 2, the human hand grasp motions are mainly categorized into power and precision grasps in the Cutkosky taxonomy, for a total of 16 types of grasp motions (labeled from 1 to 16). In Figure 1, it is clear that as the number of achievable types of motion increases, the entire weight increases. All of the hands that could achieve 13 types of motion weigh more than 600 g. Whereas, even though some of the light weight hands weigh under 400 g, they cannot achieve more than 6 types of motion. Therefore, there are mainly two inclinations: The focus is on reduced weight at the expense of fewer hand motions, or the focus is on diversiform motions at the expense of increased weight. This trade-off problem implies that combining dexterity and light weight will be a great challenge.

It is of great importance to consider both dexterity and light weight when designing a prosthetic hand, owing to two factors: (1) Amputees consider that the weight is important to relieve their burden [8,19], and (2) grasping is the most important task to restore the lost hand function as far as possible [10]. Therefore, the design objective of this study is to achieve a trade-off that can meet both dexterity and light weight requirements. Therefore, two design restrictions exist for the prosthetic hand: (1) Limited weight to reduce the burden of the user, and (2) realizing as many hand motions as possible. Firstly, the maximum weight of the prosthetic hand should not be more than 370 g. However, three different prosthetic hand weight limits exist, namely 370, 400, and 500 g, as presented by three different reports [20]. Here, the lightest weight limitation is adopted to minimize the influence of weight. Secondly, the scope of the target hand motions needs to be defined, because it is impossible to mimic every human hand motion for a prosthesis with the state of the art. As mentioned before, in this study, the Cutkosky taxonomy is followed to realize the grasp motion as much as possible, because it is the most widely used.

2. Related Grasp Extraction

Although a highly under-actuated mechanism can achieve greater DoFs with fewer actuators, it is extremely difficult to achieve all 16 grasp motions presented in Figure 2. Neuroscientists have established that the human brain does not control each joint individually to control the complicated hand mechanism, but rather uses several predefined synergies [9,21]. This means that a certain amount of relevance exists among different grasp motions. Thus, the minimum actuator configuration may be obtained by extracting the relatable grasp motions based on the Cutkosky taxonomy (Figure 2), which can lead to a significant weight reduction, while obtaining the maximum number of grasp motion types. As illustrated in Figure 2, the total of 16 grasp motions are divided into power and precision grasps, which are subdivided according to the object shape. To extract the related grasp motions, it is necessary to analyze the relationship of the finger joints that represent the DoFs of each motion.

2.1. Motion Analysis of Power Grasps

In general, power grasps are distinguished by large contact areas between the object and surfaces of the fingers and the palm to guarantee stability and security [23]. This group consists of nine grasp motions with two main divisions: Non-prehensile and prehensile motion. Only the platform push (grasp 15) belongs to the former, in which all of the digits (from thumb to little finger) are fully extended to form a flat plane. The remaining motions belong to the latter, as the object is seized and held within the hand. The lateral pinch (grasp 16) is also a special case, in which the four fingers flex completely but the thumb adducts slightly (rotates inwards) and flexes to hold a thin object such as a card. Depending on the geometric features of the object, the other seven motions are classified as circular or prismatic (left side in Figure 2).

There are two types of grasp motions in the circular group: disk (grasp 10) and sphere (grasp 11). These appear very similar, as both require all of the digits to flex together, and the thumb adducts to the opposite side of the index finger. However, the disk (grasp 10) is much more complex, as it requires the distal interphalangeal (DIP) joints to flex at different angles from the other two joints of the four fingers. The five other types of grasp motions (grasps 1 to 5) in the prismatic group can be divided into the following digits motions: (1) Flexion of the four fingers, (2) flexion/extension of the thumb, and (3) adduction/abduction of the thumb.

2.2. Motion Analysis of Precision Grasps

In precision grasps, the hand motions are also divided into circular or prismatic (right side in Figure 2). As opposed to the case of power grasps, the object is held with the tips of the digits in consideration of sensitivity and dexterity [23]. That is, precision grasps require finer adjustment with the finger joints, unlike power grasps, which surround or encompass the object. There are three circular grasp motions: disk (grasp 12), sphere (grasp 13), and tripod (grasp 14). Although an arch [24] appears to be necessary for the former two motions, in which every digit is required to surround the object, the combination motions of the digits’ flexion and thumb adduction can also be realized, particularly when the object’s diameter is sufficiently large. The tripod (grasp 14) is much easier to obtain by means of similar combination motions of the thumb and fingers, as only three digits are required in total.

There are four motions in prismatic, in which the thumb and four other fingers form an opposed posture. However, thumb-4 finger (grasp 6) and thumb-3 finger (grasp 7) are much more complex than thumb-2 finger (grasp 8) and thumb-index finger (grasp 9). In thumb-4 finger and thumb-3 finger, the fingers are required to flex at different angles to cause the fingertips to form a straight arrangement along the object shape. However, no such strict requirement exists for thumb-2 finger and thumb-index finger, because only one or two fingers are required to oppose the thumb, so that the finger joints can even flex at the same angle.

2.3. Achievable Grasp Motions

According to the previous analysis, the majority of the 16 grasp motions can be summarized as the following frequently used digits motions: (1) The joints of the four fingers usually flex/extend at the same angle, and (2) two independent DoFs of the thumb are often utilized in grasping, the flexion/extension and adduction/abduction. Therefore, in theory, all of the listed grasp motions are achievable if the three DoFs can be guaranteed, namely the flexion/extension of the four fingers, and the flexion/extension and adduction/abduction of the thumb. In

Table 1. Achievable grasp motions related to required digits motions (based on the Cutkosky taxonomy).

Achievable Grasp Motions				Required Digits Motions
				Four Fingers	Thumb
Power	Non-prehensile		Platform Push (15)	Extension	Extension/Abduction
	Prehensile		Lateral Pinch (16)	Flexion	Flexion/Adduction
		Prismatic	Large Diameter (1), Small Diameter (2), Medium Wrap (3)	Flexion	Flexion/Adduction
			Adducted Thumb (4), Light Tool (5)	Flexion	Extension/Abduction
		Circular	Sphere (11)	Flexion	Flexion/Adduction
Precision	Prismatic		Thumb-2 Finger (8), Thumb Index Finger (9)	Flexion	Flexion/Adduction
	Circular		Disk (12), Sphere (13), Tripod (14)	Flexion	Flexion/Adduction

, we list the achievable grasp motions related to the required digits motions based on the Cutkosky taxonomy.

3. Hand Design

According to the grasp motion analysis presented in Section 2, a prosthetic hand is proposed that utilizes three actuators to realize the 13 grasp motions. As illustrated in Figure 3, all of the actuators are embedded in the palm, in which motor 1 drives the four fingers by means of tendon-driven transmission (labeled in yellow), motor 2 also adopts tendon-driven transmission to drive the thumb (labeled in red), and motor 3 drives the thumb to rotate inwards/outwards (adduction/abduction) directly (labeled in green). Furthermore, considering the anthropomorphic requirement, the prosthetic hand model is based on an adult’s right hand (an Asian female, 35 years old).

3.1. Finger Design

A three-segment design was adopted for the anthropomorphic finger, as in the case of a human finger, which consists of three phalanges and three joints: The proximal, intermediate, and distal phalanges; and the metacarpophalangeal (MP), proximal interphalangeal (PIP), and DIP joints. In particular, the connection and fixation of the finger differ from those of traditional methods, as only a connecting tendon without any mechanical fastener was used, known as a shaft-less connection. Moreover, because every finger was designed with the same structure, one finger is taken as an example here. As illustrated in Figure 4, all the phalanges are fixed together via a connecting tendon to form the finger. Furthermore, the connecting tendon crosses through the palm, with both ends fixed on the distal phalange, to fix the finger onto the palm. By means of this shaft-less connection, the contact condition of each joint can be changed significantly, for which the processes are as follows: (1) When the finger is fully extended, it maintains surface contact at each joint, which is helpful for limiting the maximum extension angle and providing a stable support for every phalange, and (2) once any joint starts to flex, the contact condition is transformed from the surface contact to line contact. The finger joint actually flexes along one contacted line between two phalanges. Thus, the greatest merit is that no frictional power loss occurs as there is no contact surface to provide friction. Furthermore, this shaft-less connection offers other advantages, such as reduced weight, compact structure, and easy assembly, owing to the small weight and volume of the tendon.

According to the grasp motion analysis based on the Cutkosky taxonomy, the four fingers usually flex at almost the same angle in most grasping situations. Moreover, if the finger joints flex at the same angle, the four fingers always flex along a certain trajectory in grasping and the adaptability can be limited. However, this is of great use for precise grasps owing to the predetermined joint motions. Thus, a tendon-driven transmission is proposed that could maintain the MP and PIP joints rotating at the same angular velocity, called the stable tendon-driven mechanism. As illustrated in Figure 5, the two tendons work as a unit: (1) The driven tendon crosses through the MP joints to connect to motor 1 through the driven pulley, with the other end fixed on the proximal phalange; (2) the passive tendon crosses through both the MP and PIP joints, fixed on the palm and the intermediate phalange, respectively; and (3) the two tendons are distributed symmetrically on both sides of the finger joints, as indicated in Figure 6 a, where a is the distance constant between the joint rotation center and tendon. As motor 1 rotates (M₁ in Figure 6b), the driven tendon is rolled up to flex the MP joint, and assuming that the travel distance variable of the motor is ∆S. Furthermore, the passive tendon occurs the same distance variable ∆S at the MP joint owing to the symmetrical geometry. Thus, the PIP joint flexes with the same angular velocity as the MP joint. That is, the flexion angle of the MP joint ${\theta }_i$ is equal to the flexion angle of the PIP joint ${\theta }_j$. Therefore, the stable tendon-driven mechanism ensures that the MP and PIP joints flex at the same angle, which provides a determined movement trajectory for the finger joints.

As illustrated in Figure 3a, only one motor is used to drive all four fingers. Therefore, according to the limited space condition and output efficiency requirements, the driven pulley is designed as a synchronous winding structure. As indicated in Figure 6, two parallel pulleys are employed, the rotation centers of which are on the same horizontal line, and which are connected to one another by means of two tendons (marked in yellow and green) fixed on both. Figure 6a demonstrates the initial state, where the motor has not yet rotated and both pulleys are in standby mode. Once the motor rotates, it will enter the synchronous rotation state. As illustrated in Figure 6b, as motor 1 rotates clockwise (M1), the connecting pulley rotates ${\theta }_k$ degrees. Meanwhile, the green tendon is rolled up to travel a corresponding distance, and the same travel distance is transferred to the driven pulley to cause it to move synchronously with motor 1. In turn, when motor 1 rotates anticlockwise, the yellow tendon plays the same role as the green tendon to guarantee synchronous movement. Furthermore, the motor torque is transferred to the driven pulley to the greatest extent by setting the moment arm to the minimum value of 4.5 mm, as indicated in Figure 6a. The winding mechanism offers the advantages of a light weight and compact structure. Moreover, it can prevent actuator damage, as the load does not directly act on the motor.

The four fingers are connected to the driven pulley by means of four driven tendons. When motor 1 rotates clockwise, the driven pulley rolls up every tendon to drive the four fingers to flex simultaneously. When motor 1 rotates anticlockwise, each driven tendon is released on standby for the finger extension.

3.2. Thumb Design

The thumb is designed with four segments: The thumb base, metacarpal, and proximal and distal phalanges, as illustrated in Figure 7. As with the four fingers, all segments are connected to one another by means of the shaft-less connection via a connecting tendon. The thumb also has two flexional DoFs of the carpometacarpal (CMC) and MP joints.

The tendon-driven transmission is also employed here to provide the thumb with adaptability in grasping. Figure 8a illustrates the full extension state of the thumb, in which the driven tendon crosses through the CMC and MP joints, with the two ends fixed on the driven pulley (fixed on motor 2 in Figure 9) and proximal phalange. When motor 2 rotates (M2 in Figure 8), the driven tendon is simultaneously rolled up. Both the CMC and MP joints are involved, which causes a travel distance variable of ∆S in total. In the grasping process, ∆S is allocated to the CMC and MP joints according to the contact condition with the object, thereby providing adaptive flexion during grasping, which is particularly useful in power grasps. Figure 8 presents the adaptive flexion process: (1)(a) The thumb is in the full extension state and the motor has not yet rotated; (2)(b) as motor 2 rotates, the driven tendon becomes involved, while the thumb flexes to approach to the object, and the rotation angles of the CMC and MP joints are ${\theta }_m$ and ${\theta }_n$, respectively; (3)(c) the CMC joint is blocked owing to contact with the object, in which the two joints rotate to the angles ${\theta }_m^{\prime }$ and ${\theta }_n^{\prime }$ as indicated; and (4)(d) the CMC joint stops at ${\theta }_m^{\prime }$. However, the MP joint continues to flex until contact with the object, and the flexion angle increases to ${\theta }_n^{″}$. Then, when motor 2 rotates anticlockwise, the driven tendon is released on standby for the thumb extension.

In addition to flexion, the thumb exhibits another DoF, namely adduction/abduction. Therefore, a third motor is employed. As illustrated in Figure 9, motor 3 is configured alongside motor 2, and the thumb base is fixed onto it through a link bar. As motor 3 rotates clockwise/anticlockwise (M3 in Figure 10), the thumb is driven to adduct/abduct, where the rotation angle range ${\theta }_t$ is 0 to 90°.

3.3. Unactuated Extension

To perform the hand extension motion, an elastic tendon (rubber band) is embedded in the back of each digit. The elastic coefficients of the elastic tendons need to be selected appropriately. The elastic tendon cannot provide a sufficient resilience force to extend the digit if the elastic coefficient is excessively small. Conversely, an excessive resilience force increases the energy consumption if the elastic coefficient is too large. Therefore, each constant of the elastic tendon is determined as follows.

Firstly, assume that the elastic coefficient is $k_n$, where, $n=1, 2, 3, 4, 5$ correspond to each elastic tendon set up on the back of the digit (from the thumb to little finger in turn). Figure 10 illustrates the full flexion state of the finger and thumb, in which the elastic tendon should overcome the gravity force of every phalange to drive the digit back to the fully extended position when the driven tendons are released along with the anticlockwise rotation of motors 1 and 2. This state can be regarded as a boundary state, because the elastic coefficient determined under this condition provides an appropriate resilience force for extension, while no further excessive consumption occurs.

Therefore, the elastic constant can be determined by the following equilibrium equation:

$${\displaystyle \sum }_{i=1}^3{{\displaystyle \int }}^{}-G_{ni}dy={\displaystyle \sum }_{j=1}^2\frac{1}{2}{k}_n{\left(x_{nj}-x_{n0}\right)}^2$$

(1)

where, i = 1, 2, 3 corresponds to the i-th phalange from proximal to distal, and j = 1, 2 corresponds to the maximum stretching on the j-th joint from proximal to distal, respectively, as indicated in Figure 11. Therefore, $G_{ni}$ is the gravity force of the i-th phalange on the n-th finger, $x_{nj}$ is the maximum stretching on the j-th joint of the n-th finger, and $x_{n0}$ is the initial stretching corresponding to each $x_{nj}$. Thus, the elastic coefficient of each digit can be obtained (see Appendix A.2.1).

3.4. Passive Hyperextension

Hyperextension of the fingertip is useful, particularly in precision grasping (grasps 8 and 9). As illustrated in Figure 11, hyperextension of the IP and DIP joints increase the contact area relating to the grasp stability.

The springs are embedded into the IP/DIP joints of the thumb, and index and middle fingers, to realize the hyperextension function, as these digits are frequently used in precision grasps. The maximum hyperextension angle is set to 30° for the thumb IP joint, and 10° for the DIP joints of the index and middle fingers, respectively [25]. The method for determining the spring coefficient is described below. Moreover, the spring embedded into the joint can enable the phalange to return to the extension position after releasing the object.

In a precision grasp, a two-point pinch formed by the thumb and index finger frequently occurs. Taking a two-point pinch with the thumb and index finger as an example, the hyperextension process is demonstrated in Figure 12.

Figure 12a illustrates the initial state, in which the two fingertips contact one another. The contact point (x, y) can be expressed as follows:

$$\left(\begin{array}{c}x\\ y-l_1\end{array}\right)=\left(\begin{array}{c}{l}_{11}\sin {\theta }_1+l_{12}\sin 2{\theta }_1+l_{13}\sin \left(2{\theta }_1+{30}^{°}\right)\\ l_{11}\cos {\theta }_1+l_{12}\cos 2{\theta }_1+l_{13}\cos \left(2{\theta }_1+{30}^{°}\right)\end{array}\right)$$

(2)

Figure 12b illustrates the full hyperextension state. As both the two fingertips are completely hyperextended, the contact point (x, y) can be expressed as follows:

$$\left(\begin{array}{c}x-l_0\\ y\end{array}\right)=\left(\begin{array}{c}{l}_{01}\cos \left({\theta }_0+{50}^{°}\right)+l_{02}\cos \left(2{\theta }_0+{50}^{°}\right)+l_{03}\cos \left(2{\theta }_0+{60}^{°}\right)\\ l_{01}\sin \left({\theta }_0+{50}^{°}\right)+l_{02}\sin \left(2{\theta }_0+{50}^{°}\right)+l_{03}\sin \left(2{\theta }_0+{60}^{°}\right)\end{array}\right)$$

(3)

For the index finger (as indicated in Figure 13), using the angles in the initial (${\theta }_1$) and final (${\theta }_1^{\prime }$) hyperextension states, the energy $W_{F_{*}}$ as a result of the maximum output $F_{*}$ can be calculated.

$${\displaystyle \sum }_{i=a}^c{W}_{G_{1i}}+W_{k_1}+W_{F_{*}}=W_F$$

(4)

(1: index, a: DIP/IP, b: PIP/MP, c: MP/CM)

As indicated in Figure 14, in the complete hyperextension state, the energy $W_{F_{*}^{\prime }}$ owing to the maximum output force $F_{*}^{\prime }$ can be calculated in the same manner:

$${\displaystyle \sum }_{i=a}^c{W}_{G_{1i}}+W_{k_1}+W_{F_{*}^{\prime }}=W_F$$

(5)

(0: thumb, 1: index, a: DIP/IP, b: PIP/MP, c: MP/CM).

As $W_{F_{*}^{\prime }}$ includes the hyperextended spring energy $W_{k_{1e}}$ and maximum output force energy $W_{F_{*}}$,

$$W_{F_{*}^{\prime }}=W_{F_{*}}+W_{k_{1e}}.$$

(6)

Then, the hyperextended spring energy $W_{k_{1e}}$ of the index finger can be obtained.

Figure 15 illustrates the initial and final hyperextension states of the thumb. The hyperextended spring energy $W_{k_{0e}}$ of the thumb can be obtained in the same manner.

Based on the energy calculation of the two-point pinch formed by the thumb and index finger, the state of the three-point pinch can be analyzed in the same manner. Thus, the spring energy $W_{k_{2e}}$ of the middle finger can be calculated. The spring coefficient calculation process is presented in A.2.2 of the Appendix A.

4. Experiments

Two types of experiments were conducted to validate the proposed hand: (1) Grasp motion verification, which is operated by a motor controller for grasp tasks; and (2) a pick-and-place experiment, which uses an intuitive myoelectric signal. The prosthetic hand is equipped with a wrist, having DOFs of adduction/abduction.

4.1. Grasp Motion Verification Experiment

The purpose of this experiment was to test the hand motion performance. That is, to verify whether the hand could achieve the 13 grasp motions as expected. A prototype hand was developed. It was fixed using a vise to perform grasp tasks through a motor controller. The objects used are presented in

Table 2. List of experimental objects.

Object	Weight [g]	Shape	Size [mm]
Card	4.0	Thin plate	$54.0\times 85.7\times 0.6$
Wood block	34.5	Cylinder	$\varnothing$29.4$\times$119.6
Sponge ball	24.8	Sphere	$\varnothing$65.6
Foam balls (small)	0.7	Ellipsoid	$\varnothing$137.0; $\varnothing$230.0
Foam balls (big)	1.7	Sphere	$\varnothing$49.4
PET bottle	16.6	Cylinder	$\varnothing$66.4 $\times$ 162.5
Mark pen (big size)	8.3	Cylinder	$\varnothing$10.5 $\times$ 141.0
Mark pen (small size)	12.1	Cylinder	$\varnothing$17.0 $\times$ 118.0

. Moreover,

Table 3. Achievable motion types.

(grasp 1) Large Diameter	(grasp 2) Small Diameter	(grasp 3) Medium Wrap	(grasp 4) Adducted Thumb	(grasp 5) Light Tool
(grasp 8) Thumb-2 Finger	(grasp 9) Thumb Index Finger	(grasp 11) Sphere	(grasp 12) Disk	(grasp 13) Sphere
(grasp 14) Tripod	(grasp 15) Platform Push	(grasp 16) Lateral Pinch

summarizes the experimental results corresponding to each grasp motion.

The experimental results demonstrate that the prosthetic hand can realize 13 grasps, as expected. As indicated in Table 3, from top to bottom.

The easiest grasp is the platform push (grasp 15), as the four fingers simply extend owing to the elastic tendons. Furthermore, the metacarpals of the ring finger, little finger, and thumb form a plane to support the object.

The lateral Pinch (grasp 16) is a type of lateral grasp, which requires position adjustment of the thumb. The prosthetic hand includes an independent motor to drive thumb adduction or abduction. Thus, it can also adjust the thumb position in different lateral grasps. Although the metacarpals of the ring finger and little finger flex to form an arch along with the thumb, they will not obstruct the lateral grasp, as they are not in the same contact area.

In the circular grasps, the disk (grasp 10) power grasp is not achievable for the prosthetic hand, because the stable flexion transmission of the four fingers cannot drive the PIP and DIP joints independently, and the MP joints are ignored. However, the remaining grasps of sphere (grasp 11), disk (grasp 12), sphere (grasp 13), and tripod (grasp 14) are easy to realize, owing to the adaptive flexion of the thumb, stable flexion of the four fingers, and arch function.

In the prismatic grasps, only thumb-4 finger (grasp 6) and thumb-3 finger (grasp 7) cannot be realized, because the metacarpals form an arch along with the thumb adduction movement, in which the ring and little fingertips cannot remain in one straight line (as in grasp 6). Furthermore, as the metacarpals of the ring and little fingers always move together as a unit, it is impossible to obtain a posture of three fingertips in one line (as in grasp 7). Although thumb-2 finger (grasp 8) and thumb-index finger (grasp 9) also require the fingertips to contact the object, only two fingers and one finger are necessary, respectively. Hence, the thumb with the adaptive function can adjust the contact position in grasping. Furthermore, the medium wrap (grasp 3), adducted thumb (grasp 4), and light tool (grasp 5) are very similar, in which the four fingers are completely flexed to surround the object, but with a slightly different thumb position. Thus, these are easy to realize, owing to the stable function of the four fingers and adaptive function of the thumb.

Finally, large diameter (grasp 1) and small diameter (grasp 2) are similar to medium wrap (grasp 3). Thus, they can be realized in a similar manner.

4.2. Pick-and-Place Experiment

A pick-and-place experiment was conducted to investigate the stability and operability of the prosthetic hand. The hand was controlled through electromyography (EMG) signals acquired from an able-bodied male adult [26,27,28]. The experimental equipment included a socket for the subject to wear the hand, a microcomputer for recognizing the EMG signal and controlling the motors, a glove for covering the hand, myoelectric sensors, batteries, and the prosthetic hand, as illustrated in Figure 16. The prosthetic hand was attached to the right forearm of the subject by means of the socket.

Moreover, to investigate the performance of the prosthetic hand, the same experiments were conducted using previously designed hands [29]. Three types of previous prosthetic hands exist, as follows. (1) Joint fixed type—two motors are adopted, where motor 1 is connected to the MP joint for flexion and extension of the four fingers, and motor 2 is for adduction and abduction of the thumb. The remaining PIP, DIP, MP, and IP joints are unmovable and fixed at certain preset angles (shown in Figure 17). (2) Adaptive linkage type—two motors are adopted, as in the case of the first hand type, but the PIP and DIP joints can be driven to flex or extend passively by the MP joint, which can adapt to the shape of the object being grasped. A soft structure such as a sponge block is provided at each fingertip (shown in Figure 18). (3) Stable linkage type—this type is nearly the same as the adaptive type, but only the PIP joint can be passively driven by the MP joint, and the DIP joint is fixed at a preset angle, which can provide a certain trajectory of the finger joints in grasping (shown in Figure 19).

Before the pick-and-place experiment, the motion performance of these previous hands was also tested to verify how many types of motion can be achieved by these hands based on the Cutkosky taxonomy. The same motor controller as the one used in the grasp motion verification experiment was used to control each hand to perform the grasp tasks.

Table 4. Achievable motion types (joint fixed type).

(grasp 15) Platform Push	(grasp 16) Lateral Pinch
(grasp 4) Adducted Thumb	(grasp 14) Tripod

,

Table 5. Achievable motion types (adaptive linkage type).

(grasp 15) Platform Push	(grasp 16) Lateral Pinch	(grasp 3) Medium Wrap
(grasp 14) Tripod	(grasp 2) Small Diameter

and

Table 6. Achievable motion types (stable linkage type).

(grasp 15) Platform Push	(grasp 16) Lateral Pinch	(grasp 3) Medium Wrap
(grasp 14) Tripod	(grasp 2) Small Diameter

listed the achievable motions of each hand.

In order to compare the grasp performance of the proposed hand and previously designed hands, the same experiments were conducted. As illustrated in Figure 20, several objects of daily use were selected for this experiment.

Table 7. Experimental objects.

No.	Experimental Objects	Weight (g)	Shape	Size (mm)
(1)	Ball	11.1	sphere	$\varnothing$60
(2)	AAA battery	22.7	Cylinder	$\varnothing$14$\times$50
(3)	Spoon	7.9	Thin plate	3$\times$163
(4)	Signet	10	Cylinder	$\varnothing$12 $\times$58
(5)	Mark pen	14.3	Cylinder	$\varnothing$16 $\times$ 117
(6)	Wood block	60.9	Triangle	102$\times$29
(7)	Lighter	13.9	Cuboid	80$\times$24 $\times$11
(8)	Glue stick	19.6	Cone	$\varnothing$134$\times \varnothing$222 $\times$107
(9)	USB memory stick	9.2	Cuboid	61$\times$19.5 $\times$8
(10)	Plastic sushi	35	Cuboid	80$\times$ 22$\times$ 27
(11)	Nail enamel	43.9	Cylinder	$\varnothing$22 $\times$63
(12)	9 V battery	52.2	Cuboid	48$\times$26 $\times$17
(13)	PET bottle	235.3	Cylinder	$\varnothing$65 $\times$ 139

lists the weight, shape, and size parameters of the experimental objects. The subject was required to perform certain tasks. Firstly, mark two 15 $\times$ 15 mm square markers on a table at an interval of 300 mm. Secondly, for each object, control the prosthetic hand to pick up the object from one marker area and place it in the other repeatedly within 30 s. If the object was not dropped while moving it, it was recorded as one successful task. Figure 21 illustrates two successful tasks during the experimental process.

The experimental results are illustrated in Figure 22 (clockwise).

From the ball to spoon, only the proposed hand managed to perform each task successfully, and achieved a higher success rate than the other hands. Due to the limited DoFs of the thumb or the metacarpals, the stable linkage and adaptive linkage hands could not even pick up the PET bottle, and the joint fixed hand could not pick up the USB memory stick (see the Supplementary Material of Video S1). Thus, these hands did not have even a single successful record throughout the whole experiment. Furthermore, the proposed hand performed much better than the other hands with objects such as the ball, AAA battery, lighter, and USB memory stick, owing to the passive hyperextension function in the design. Therefore, the proposed hand is much more functional and dexterous, and it also improves the stability and operability in grasping.

5. Conclusions

The proposed hand achieves a significant improvement over other previous prosthetic hands because it can grasp much more stably and naturally, as shown in Figure 22. The proposed hand added more functions such as the arch and hyperextension, which results in integration in terms of both the motion performance and appearance. There are three servomotors embedded in the adult human sized palm, but the whole hand weighs only 132.5 g. Figure 23 summarizes the achievable types of motion and weights of the prosthetic and three previous hands. Clearly, the proposed hand is the lightest one, but can perform the most types of motion. It weighs 132.5 g, accounting for less than 40% of the weight limitation and it performs 13 types of motion, accounting for more than 80% based on the on the Cutkosky taxonomy. Thus, the proposed hand successfully combines dexterity and light weight, thereby addressing the trade-off issue between the two.

Nevertheless, several problems remain to be addressed. Although the stable function can provide a certain trajectory for the finger joints, reliability problems may still occur at times owing to tendon loosening. Furthermore, the proposed hand cannot provide high grasping power, as it employs small motors, owing to the weight and size limitations. Therefore, the directions for future work include addressing the above-mentioned problem, as well as realizing all 16 grasp motions.