A novel motion-coupling design for a jointless tendon-driven finger exoskeleton for rehabilitation

Mechanism and Machine Theory 99 (2016) 83–102

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A novel motion-coupling design for a jointless tendon-driven finger exoskeleton for rehabilitation Jianyu Yang∗ , Hualong Xie, Jiashun Shi School of Mechanical Engineering and Automation, Northeastern University, 110819 Shenyang, Liaoning, PR China

A R T I C L E

I N F O

Article history: Received 11 March 2015 Received in revised form 23 November 2015 Accepted 24 December 2015 Available online xxxx Keywords: Finger rehabilitation Hand exoskeleton Jointless tendon-driven Motion coupling

A B S T R A C T We have designed a new jointless tendon-driven exoskeleton plan for the human hand that provides a correct and stable motion sequence while keeping the structure lightweight, compact and portable. Before the development, anatomy analysis and a kinematics study of the human finger were performed, and bending angle relationships among the metacarpophalangeal (MCP), proximal interphalangeal (PIP) and distal interphalangeal (DIP) joints were analyzed. Detailed implementation is discussed, including the basic theory of the joint motion coupling method, related formula derivations and mechanical design of an experimental device. An experimental setup was built, and series of experiments was conducted to examine and evaluate the developed joint motion coupling plan.The results indicated that the new plan worked correctly as desired, that an incorrect finger motion sequence did not occur and that the new coupled tendon driven plan can drive finger bending as naturally as a human. The compactness and light weight of the entire structure of the device means that its parts can be arranged for a hand glove or fingerstall more easily than most bar-linkage exoskeleton structures. © 2015 Elsevier Ltd. All rights reserved.

1. Introduction A motion failure in a hand or finger can be cured by passive repetitive movement called therapy training for the suffering joints. Usually, these therapy movements are performed by a therapist; however, the boring training processes and shortage of therapists may cause the patient discontinue them [1]. On the other hand, major joints of affected body parts usually recover sooner than minor joints. Therefore, hand and finger joints normally experience the most difficult recoveries. To avoid the drawbacks of traditional manual therapy training, many exoskeleton devices have been developed for hand or finger motion rehabilitation. For example, H. Kawasaki et al. built a hand-assist robot with multiple DOF (degrees of freedom) for hand rehabilitation. The robot is an in-hospital device that can generate precise movements for each finger joints in the human hand [2,3,4]. Other devices for the same purpose with different mechanisms were developed by Y. Huang [5] and by L. Dovat et al., with a device called HANDCARE [6,7]. These devices were developed as in-hospital devices that sacrificed small size for ease in arranging complicated mechanisms. The advantage was obviously that with the complicated mechanisms, adjustment of more precise motion sequences and force outputs was easier, producing better rehabilitation performance. However, with in-hospital devices, patients had to come to the hospital for therapy training, which still limited the therapy duration. Therefore, various wearable devices that patients can take with them, have been developed for rehabilitation.

author. Tel./fax: +8602483671585. * Corresponding E-mail address: [email protected] (J. Yang). http://dx.doi.org/10.1016/j.mechmachtheory.2015.12.010 0094-114X/© 2015 Elsevier Ltd. All rights reserved.

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J. Yang et al. / Mechanism and Machine Theory 99 (2016) 83–102

An EMG controlled exoskeleton device for hand rehabilitation by M. Mulas et al. is a wearable device with a reduced mechanical structure that provides only basic and imprecise open-close movements for the hand [8] . A similar device developed by J. H. Bae uses an air piston to drive four fingers at distal phalanges to bend toward or away from the thumb, but ignores the angle relationships among finger joints while bending the fingers [9]. N. Ho et al. developed a more dedicated hand exoskeleton devece— a five-fingered pneumatic hand robot. In this device, piston-driven exoskeleton parts drive five fingers separately at their middle phalanges [10]. For more accurate and complex finger movement, exoskeleton devices with more joints were developed, that have more complicated mechanisms, usually a bar-linkage system or gear system, such as the device built by Andreas Wege and et al. [11,12,13]. They developed a five fingered tendon-driven bar-linkage exoskeleton system with EMG support for rehabilitation. Other jointed devices with bar-linkage or gear mechanical structures were also developed by B. L. Shields et al. [14], B. Choi et al. [15,16], T. Worsnopp et al. [17], HandEXOS by A. Chiri et al. [18], M. Fontana et al. [19], R. Riener et al. [20], B. Lee et al. [21], A. P. Tjahyono et al. [22], M. Cempini et al. [23], and J. Li et al. [24]. As mentioned above, Heo [25] noted that the current styles of wearable mechanisms used as hand or finger exoskeletons for matching the center of rotation or eliminating the need for precise alignment include: 1) a direct matching of joint centers, 2) linkages for a remote center of rotation, 3) a redundant linkage structure, 4) a serial linkage attached to distal segment, 5) a bending actuator attached to the joint. Mechanically, these devices were functionally successful in realizing or assisting the kinematics and dynamics aspects of human finger movements. However, unlike industrial-purposed devices, mechanical functional success is not enough for these human related devices: factors have to be considered more seriously such as cost, weight, size and appearance, safety, and man–machine interfacing [26]. From the portability and wearability points of view, current devices still need to be improved. Thus, jointless tendon-driven mechanisms were developed. In comparison with the formal five exoskeleton devices, jointless tendon-driven mechanism is the most compact, lightweight and portable. Therefore, in this paper, we focus on developing a new jointless tendon-driven exoskeleton design, with which humanly motion sequence among the finger joints can be acquired to avoid the drawbacks of the traditional one, which will be discussed in detail in the next section. With such wearable device, it is not only that therapy training can be brought into the patients daily lives, but additionally the devices can assist the patient to accomplish basic movements, improving living experience before the recovery of their disabled body part.

2. Drawback of traditional tendon driven plans According to Heo [25], the tendon arrangement plans of most current jointless tendon-driven hand exoskeleton structures can be abstracted as in Fig. 1. One tendon cable on the dorsal side is fixed at the tip of the finger, simply passed through the sheaths mounted beside each joint and finally pulled by an actuator; the ventral side tendon cable, pulled by another actuator, is fixed and arranged in the same way. In this case, whole structure of the exoskeleton can be designed as compactly as possible; usually all the parts except the actuators can be integrated and hidden in a hand glove, such as the Tendon-Driven Glove [27], and the SNU Exo-Glove [28]. However, the above tendon-driven plan usually produces an incorrect bending sequence that the farther joints of the finger have higher priority in the moving sequence than the nearer. This non-human motion can be observed in Fig. 2, by simply using the tendon arrangement plan shown in Fig. 1, with a finger exoskeleton demonstrating setup. As seen in subfigures (a) through (d) of Fig. 2, the wrong bending sequence can be produced when the ventral tendon is pulled, the DIP joint of the finger bends first, the PIP joint would not bend until the DIP reached its limit, and the same happened between the PIP and the MCP joints. However, it can be easily observed from (a) through (d) of Fig. 3, showing the natural poses of a bending human finger, that as a finger bends naturally, all three joints should be coupled. Bending sequence of finger joints is important in the late recovering stage and for patients who had suffered from finger function failure sequelae 2–3 years after the recovering from the stroke. For these stages, patients usually receive rehabilitation trainings at home, and grasping as well

Driving tendons

Rotary center of PIP

Sheathes

Rotary center of DIP

Rotary center of MCP Fig. 1. Tendon cable arrangement plan of current jointless hand exoskeletons.

J. Yang et al. / Mechanism and Machine Theory 99 (2016) 83–102

(a)

(b)

(c)

85

(d)

Fig. 2. Tendency for incorrect motion produced by traditional tendon arrangement.

as handling movements are involved. Thus, it ’is necessary for the exoskeleton device to offer coupled motion sequence among the three finger joints, otherwise training of grasping movement would fail. By adjusting friction between the tendon cables and sheaths at every joint, the incorrect sequence can be fixed; however, it is predictable that as long as abrasion occurs, the scheme of adjusting friction will not keep the motion stable. Furthermore, adding friction will usually lower efficiency, which could be a challenge to actuators, such as shape memory alloy actuators [26,29,30], with the characteristics of small volume, low power input and low weight that are necessary for portability. Considering the above factors, it is necessary to develop a new tendon-driven plan for finger exoskeletons that can achieve the correct joint-bending sequence while satisfying portability demands. Note that, the goal of this research was not to develop one device for all stages during finger/hand rehabilitation, but exactly for helping patients in the late recovering stages at home as mentioned above, by rehabilitating and assisting ordinary grasping and handling movements. From this point of view, offering motion sequence is also meaningful. 3. Anatomy and kinematics studies of human fingers To find a good plan for tendon arrangement for our finger exoskeleton, that will couple joints’ movements efficiently while keeping the whole structure compact, studies of human finger structure characteristics and kinematics are needed. 3.1. Finger anatomy studies As shown in Fig. 4, the bone structure of the motion mechanism of the human finger is mainly determined by the metacarpal and phalanges. The metacarpal is located in in the palm of the human hand providing a rotating and fixing base to the finger, while phalanges make up the finger and are connected to the metacarpal. There are three phalange components, including the proximal phalanx, middle phalanx and distal phalanx. These bones are connected by three joints: the MCP joint, connecting metacarpal bone and proximal phalanx; the PIP joint, connecting proximal and middle phalanx, and the DIP joint, connecting the middle and distal phalanx. Four degrees of freedom (DOF) govern the motion of these three joints; the MCP has two DOFs as a universal joint allowing for both flexion/extension and adduction/abduction, while each of the other two has a single DOF as a normal rotary joint, supporting flexion/extension only. In this case, an index finger can be regarded as a four-DOF-bar mechanical system within which the DIP DOF is subordinated to that of the PIP, and the motion of DIP joint is usually coupled with the PIP when the finger does a natural bend. According to Levangie, the typical maximum motion range of the index finger is 90◦ for the MCP, 100◦ –110◦ for the PIP and 80◦ for the DIP in flexion/extension movements. For its adduction/abduction movements, the index finger has a range of motion of approximately 40◦ [31]. However, these motion ranges of the joints can vary between different fingers as well as different persons [28,32] because the factors that define the range of joint motion are not only bone geometry in the finger but also the tendon and muscle structural characteristics of the hand. Thus, the index finger has the greatest range of motion compared with the others; some people’s fingers may bend very far in the opposite direction of the palm side of the hand. Therefore, it is

(a)

(b)

(c)

Fig. 3. Natural poses of human finger movements.

(d)

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Phalanx

Extensor Hood Metacarpal bone

Distal

Middle

Proximal

MCP Joint

PIP Joint

DIP Joint

FDP Tendon

EDC&EIP Tendon

FDS Tendon

Lumbrical Muscle(LU)

Interosseous Muscle(IO)

Fig. 4. Anatomy of the index finger [26].

required to customize the dimensions as well as kinematics of an exoskeleton device according to measured data of each specific user. In this paper, the ranges of motion of the three joints came from index finger motion tests during the kinematics study. 3.2. Finger kinematics studies A kinematics study of the finger was undertaken to ensure that the following development of the exoskeleton device would provide the correct motion tendency when driving the disabled finger. The study was based on a series of measuring tests of the index finger. A type of exoskeleton device with rotary sensors was developed for measuring the bending angle vs. time relationships of all MCP, PIP and DIP joints. As shown in Fig. 5, the developed measuring device was worn on the left index finger; one rotary sensor was mounted at the MCP joint, and another two rotary sensors were mounted at the DIP and PIP joints on the other side of the finger. The device was custom designed to strictly match the dimensions of the tester left index finger; marked parts (1, 2, 3, 4) were affixed to the corresponding finger segments and the hand, ensuring fewer rotary errors during the tests. Proportional voltage signals were read by a data acquisition (DAQ) card. Note that, the translational motion of phalanges during bending is smaller than muscle’s and skin’s transformation values which affects the measuring more significant during finger flexing. For example, Florian Hess etal. have observed the translational motion was between 0.06 mm and 0.73 mm for the PIP joint in their experiments [33]. In this case, many current researchers had treated the finger joints as pure revolute joints [34,35,36,37]. Thus, it ’is reasonable to use rotary sensors to measure the angles of finger joints. With the measuring device, the test on the index finger was conducted by repeatedly making flexion/extension movements. The data of the flexion/extension angles of three joints vs. time were recorded as in Fig. 6, from which the maximum bending angles are listed in Table 1: 87◦ for the MCP, 110◦ for the PIP and 60◦ for the DIP. Note that the PIP joint usually reaches its limitation angle of 110◦ before the other two joints reach their respective limits; 87◦ and 60◦ are not the limits of the MCP or DIP, because if the tester used more force, the bending angles of MCP and DIP could go farther. The variation of force during the flexion movements caused the joint maximum angles to vary during the test.

Stuck point 2

1

3

4 Rotary Sensors (One for each joint) Fig. 5. Joint bending angle measuring device.

J. Yang et al. / Mechanism and Machine Theory 99 (2016) 83–102

87

140 PIP

MCP

DIP

120

Angles

100 80 60 40 20 0

0

2000

4000

6000

8000

10000

12000

Time(ms) Fig. 6. Joints’ flexion/extension angle vs. time on index finger.

Selected data were used to produce the angle relationships as in Fig. 7, in which the data from finger flexion and extension were processed separately. Fig. 7 (a) is the PIP vs MCP relationship in finger flexion, where the data seems disordered because there is no anatomically coupling between the PIP and MCP during flexion movements: the two joints can move independently. Fig. 7 (b) is the DIP vs. PIP relationship in finger flexion: the data became more focused, showing a coupling effect between the two joints. Between 40◦ and 80◦ of PIP, the data became more scattered, which means the coupling effect became weaker, allowing the DIP joint to have structural adaptability for different shapes the finger touched and forces it used. Compared to sub-figures (a) and (b), the data in (c) and (d), which are finger-extending PIP vs. MCP and DIP vs. PIP angle relationships, seem more regular. Anatomically, the arrangement of the EDC and EI tendons in Fig. 4 offers the finger a better movement-coupling mechanism for extension. EDC and EI are the main extensor tendons for a finger; they merge at the MCP joint with the extensor hood, while on the other side of the MCP they separate into three tendons, one linked to the middle phalanx, the other two rejoin at and attach to the distal phalanx. Note that in Fig. 7 (c) and (d), as long as the finger extended, the data were generated from the upper right to the lower left, and because of the data regularity, approximation became more meaningful. In Fig. 7 (c), when the MCP angle decreases in area [70◦ , 87◦ ] and [0◦ , 10◦ ], the PIP angle changes slightly. For the entire movement, a 4th degree polynomial approximation matches the data well, as in Eq. (1), where x represents the MCP angle and y represents the PIP angle. y = 6e − 06x4 − 0.0015x3 + 0.11x2 − 0.96x + 5.6

(1)

In Fig. 7 (d), the data presents a similar tendency as in Fig. 7 (c) as the PIP angle decreases in area [90◦ , 110◦ ] and [0◦ , 20◦ ], the DIP angle changes less than 5◦ . Eq. (2) is a 4th degree polynomial approximation to the entire motion, matching the data better. If u represents the PIP angle value and v represents the DIP angle value, the equations are: v = −1.7e − 06u4 + 0.00026u3 − 0.0053u2 + 0.17u + 0.52.

(2)

3.3. Considerations for a finger exoskeleton based on kinematics studies From the anatomical study and kinematics study, the following four conclusions can be drawn for the structural design of an exoskeleton: 1) During flexing, the MCP and PIP joints of the index finger have no anatomical coupling mechanism; the relationship between these joints could follow any possible rule. For the natural bending of the finger, the rule depends mainly on Table 1 Motion range of index finger. Joint name

Range of motion(degree)

MCP flexion/extension PIP flexion/extension DIP flexion/extension

87◦ 110◦ 60◦

88

J. Yang et al. / Mechanism and Machine Theory 99 (2016) 83–102

120

70 60 PIP angle value(degrees)

100

60

40

50

DIP angle value(degrees)

80

40 30 20

20

10 MCP angle value(degrees)

0

0

10

20

30

40

50

60

PIP angle value(degrees)

70

80

90

0

0

20

(a) PIP vs. MCP when flexing

40

60

80

100

120

(b) DIP vs. PIP when flexing

120

70 PIP vs MCP data

DIP vs PIP data

60

100

50

PIP angle value(degrees)

80

60

40

Approximation DIP angle value(degrees)

Approximation

40 30 20

20

10 MCP angle value(degrees)

PIP angle value(degrees) 0

0 0

10

20

30

40

50

60

70

(c) PIP vs. MCP when extending

80

90

0

20

40

60

80

100

120

(d) DIP vs. PIP when extending

Fig. 7. Angle relationships among MCP, PIP and DIP.

the finger-bending situation and the tester desires. For a mechanical finger or a finger exoskeleton, this translates to freer choices for controlling the bending relationship between MCP and PIP when flexing. 2) During flexing, DIP vs. PIP joint relationship shows a coupling tendency relative to that of PIP vs. MCP, but it becomes weaker when PIP bends into the area of [40, 80]. This gives the DIP joint the capability of adapting to the bending situation and the contact force at the finger tip. This means that it is unnecessary to strictly couple PIP and DIP through the entire flex because the finger has more adaptability for flexion movement. 3) During extension, DIP vs. PIP and PIP vs. MCP both have stronger movement coupling and a 4th degree polynomial approximation fits all data very well. Considering points 1) and 2), as well as the anatomy of human finger, these extension approximation curves can be used for controlling the finger bending. 4) Recovering the basic bending function of the fingers and normal grasping function of the hand should have priority over other precision and complex movement functions. It is also reasonable for the exoskeleton to subordinate the PIP DOF to the MCP joint when coupling the movements of all three joints while bending. This change will enhance the portability of the exoskeleton, simplify the mechanical structure of the exoskeleton, reduce the number of actuators and lower the weight as well.

4. Development plan and supporting mathematics Before mechanical design, a new plan of coupling movements of three joints is proposed in this section for a jointless finger exoskeleton using staggered tendons; these tendons impose an interactive constraint between two adjacent joints. The relative coupling method, mathematics and simulation results are also discussed.

J. Yang et al. / Mechanism and Machine Theory 99 (2016) 83–102

Major extension

89

Sheaths 2

Auxflex

DPflex PMflex

4

1

3

1 Joint rotary centers Major flexion Fig. 8. New tendon arrangement plan for this paper.

4.1. Basic theory of the new plan for coupling the movements of joints To keep the mechanical structure compact, we propose a new plan for coupling movements of joints by adding one pair of staggered tendons to the traditional tendon-driven plan in Fig. 1. We call these staggered tendons DPflex and PMflex. They are used for coupling the movements of the PIP and DIP as well as the MCP and PIP during finger flexion. As shown in Fig. 8, the exoskeleton parts are driven by the major-flexion tendon and the major-extension tendon, which are separately mounted on the ventral and dorsal sides of the DIP part, respectively. These two tendons act identically as in the old plan in Fig. 1, which can produce high driving efficiency. Another auxiliary tendon we call Auxflex was added, and forces applied to this tendon will maintain the coupling effect of DIP vs. PIP as well as PIP vs. MCP during finger extension. When the major-flexion Tendon is pulled, the DIP part of exoskeleton produces a bending tendency towards the PIP part, which increases the distance between sheaths 1 and 2, as marked in the figure. Because the coupling tendon DPflex is fixed between sheaths 1 and 4, the distance elongation between sheaths 1 and 2 will cause a shortening between sheaths 3 and 4, which drives the exoskeleton part on the middle phalanx to bend toward the proximal phalanx. In this way, the flexion movement of the DIP and PIP joints is coupled. The coupling tendon PMflex acts similarly to DPflex when the major-flexion tendon is pulled. With this plan, the arrangement of circumferential and axial positions of the sheaths for coupling tendons is an issue that affects the coupling relationships of the joint movements. In Fig. 9 for example, consider sheaths 1 through 4, when sheaths 1 and 2 are mounted on the dorsal side of the finger; the distance between them toward the DIP bending angle can be maximized, and it decreases as the sheath circumferential positions are moved close to the joint bending axes. The same will happen to the distance between sheaths 3 and 4 toward the PIP joint. It is not possible to fix all 4 sheaths on the dorsal or ventral side of the finger because the distance variations are different due to the dimensions of the DIP and PIP joints being different. In addition, the sheath circumferential position arrangements also affect the friction between the coupling tendons and exoskeleton parts because the friction changes with the variation of circumferential distance between sheaths 2 and 3, as well as the axial distance. Therefore, sheath positions must be calculated carefully and optimized. Related issues will be discussed in the following sub-sections. The exoskeleton parts on the dorsal side of the human finger can be designed longitudinally longer than on the ventral side because human fingers have limited freedom of motion toward the dorsal side. Based on this idea, the design of the dorsal

Bending axis

Sheath 1 Sheath 2 Inter sheaths distance

Bending angle

Fig. 9. Distance variation is affected by sheaths’ circumferential positions.

90

J. Yang et al. / Mechanism and Machine Theory 99 (2016) 83–102

B O’

B’

α

C

A

β D A’

O

Fig. 10. Calculation of dorsal sheaths’ distance variation with the change of joint angle.

exoskeleton parts can be abstracted into two semi-cones, as in Fig. 10, such that when the joint is fully extended, two sectional  can be considered to coincide: this is also the approximate limited position for a  and arc OBO faces presented by arcs OAO natural human finger. At this position, the bending angle ∠ACB of the joint is zero, according to the figure, where points A and B are right the dorsal positions of the exoskeleton parts on the distal and middle phalanges separately. 4.2. Variation relationship between dorsal inter-sheath distance and joint angle 



In Fig. 10, segment OO represents the rotation axis of a finger joint, point C is the mid-point of OO , points A and B are    positions on the dorsal sheaths, and D is the intersection point of two vertical lines from A and B toward OO . Usually, ∠A CD    equals to ∠B CD, that A and B can be butted when the bending angle is zero. We treat the joint radius as a contant rd , as well as   the sheath position angles ∠A CD and ∠B CD as the constant bd , and define two variables: the bending angle ∠ACB as a, and the  B as l , which represents the inter-sheath distance. length of arc A d According to Fig. 10, the inter-sheath distance ld can be written as Eq. (3) for flexion movement, because the dorsal sides are active when the exoskeleton is bending: the inverse function of Eqs. (3) and (4) can be used for extension movement because all dorsal sides are passive during extension. 2

ld = fld (a) = rd arccos[1 − sin bd (1 − cos a)] a = fad (ld ) = arccos(1 −

1 − cos 2

ld rd

sin bd

)

(3)

(4)

In Eqs. (3) and (4), a, bd ∈ [0, p/2]. The sheaths’ position angle bd should be set to a value in the interval [0, p/2], depending on the requirements of the coupling method. If bd is set to 0, the two sheaths are located on both sides of point O, and the intersheath distance would be zero. An the other extreme, bd equals to p/2 means the two sheaths are located at a right angle in dorsal positions(positions A and B) of two exoskeleton parts and that the inter-sheath distance would be maximized. 4.3. Variation relationship between ventral inter-sheath distance and joint angle Unlike the dorsal side, the dimensions of the ventral parts of a finger exoskeleton are limited because finger joints have more motion range toward the ventral side that may produce interference between the parts. The rule for finding the maximum dimension of a part is that when the bending angle reaches 90◦ , two adjacent parts just contact each other. In this case, we abstracted ventral exoskeleton parts into two semi-cones that keep a distance from each other, as shown in Fig. 11. In the figure, the segment OO is the rotation axis of the finger joint, and point C is again the center of the joint. Points M and N are the centers of semi-circles of a cross-section of the exoskeleton parts, as two parts have been abstracted into semicones. Points E and F are the positions of tendon sheaths on the exoskeleton: the radii of the two parts are segments ME and

J. Yang et al. / Mechanism and Machine Theory 99 (2016) 83–102

C’

O

Z

N N’

91

M’

α

β

C

M O’ E

F

C’

l2

N’ e2

μ

μ α

0

M’’

l1

E’

F E

e1

M’

Fig. 11. Calculation of sheaths’ distance variation toward the change of joint angle on ventral side. 



NF designated as rv1 and rv2 . Segments EM and FN are the linear distances from E and F to their respective diameters. Sheath   position angles can be defined by ∠EMM and ∠FNN as bv . Based on the above, ∠ZCM is the bending angle a, and the segment EF is right the coupling tendon length that needed for a bending angle a. For convenient calculation, we re-drew some segments of the upper part of Fig. 11 to form the lower subfigure with some   auxiliary segments; points M and E represent M and E positions when the bending angle a equals zero. ∠FC E as l0 is the  initial angle when a = 0, and ∠FC E as l is the post-bending angle; both can be used for calculating the variation of a with the change of tendon length FE as lv , EM , FN , C  M and N C  are marked separately as e1 , e2 , l1 and l2 . During flexion, the ventral sides are passive; the changes of joint angles are caused by coupling tendons PMflex and DPflex. Then, the a to l relationship is needed for driving, which can be calculated by Eq. (5). a = gav (lv ) = l0 − l

(5) 

In Eq. (5), l0 can be calculated as Eq. (6), according to the figure, and after the finger joint bends through a, so that M and  E reach M and E: the new relation ship between l and lv can be calculated as Eq. (7). 

⎛

⎞

e 1 e2 − l 1 l 2 ⎟ ⎜ l0 = arccos ⎝   ⎠ 2 2 2 2 l1 + e1 l2 + e2 ⎛ ⎞ 2 2 2 2 2 ⎜ l + e + l2 + e2 − lv ⎟ l = arccos ⎝ 1  1  ⎠ 2 l21 + e21 l22 + e22

(6)

(7)

During extension, the ventral sides become active: varying joint angle a produces the change of inter-sheath distance lv , facilitating the coupling tendons DPext and PMext driving the extension of the PIP and MCP joints. For calculation convenience,    the lowerpart of Fig. 11 can be drawn in a orthogonal coordinate system, with setting C as the origin and C N as the negative − → direction of the X axis. Thus the length of FE is the inter-sheath distance that can be solved by Eq. (8). − → −→ −→ FE = CE − CF

(8)

−→ −−→ − →  In Eq. (8), the vector C  E can be considered as the vector C  E rotating −a toward the pole C , and then the vector FE can be − → calculated as Eq. (9), and the inter-sheath distance lv is the modules of vector FE as in Eq. (10). − → FE =



l1 cos a − e1 sin a + l2 −l1 sin a − e1 cos a + e2

− → lv = glv (a) = | FE|

T (9) (10)

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J. Yang et al. / Mechanism and Machine Theory 99 (2016) 83–102

Table 2 Index finger parameter value list. Parameters

rd (mm)

l1 (mm)

l2 (mm)

rv1 (mm)

rv2 (mm)

MCP PIP DIP

12.5 10.5 7.5

12.0 9.0 6.6

12.5 10.7 8.3

12.0 9.2 6.8

12.7 10.8 8.5

According to the upper part of Fig. 11, the following conditions are satisfied in Eq. (5) through Eq. (10): ⎧ e1 = rv1 sin bv ⎪ ⎪ ⎨ e2 = rv2 sin bv ⎪ a, bv ∈ [0, p/2] ⎪ ⎩ l, l0 ∈ (0, p).

(11)

4.4. Motion coupling among three joints To facilitate mathematics modeling and testing, a experimental setup of a human hand model was developed, and all of the constant parameters needed for calculating the above equations were measured on it as listed in Table 2. Thus the maximum values of Dld and Dlv of the three joints can be calculated and are listed in Table 3 when bd and bv are set to p/2. Note that these maximum limits are values that the parameters could reach mechanically before the coupling, not the exact values acquired during coupling movements. Dld and Dlv are defined in Eq. (12). 

Dld = fld (a)

(12)

Dlv = glv (a) − glv (0)

As the coupling occurs, ld and lv of adjacent joints will vary the same amount but inversely,meaning Dld = −Dlv , neglecting any deformation of tendon cables: thin metal twisted wires were used in the experimental setup, and the wire stiffness was considered sufficient to ignore deformations. Therefore, according to the basic idea of the new plan, conditions should be satisfied as in Eq. (13), in which joint names in the parameter subscripts indicate the joints to which parameters belong.  Dld

dip

= −Dlv

pip

Dld

pip

= −Dlv

mcp

(13)

Following this idea, three joints can be coupled considering Eq. (3) and Eq. (5) together during the finger exoskeleton flexing. The angle relationships between adip and apip as well as apip and amcp can be calculated as in Eq. (14), in which joint names in the parameter subscripts indicate the joints to which the parameters and functions belong. 

apip = gav

pip (glv pip (0)

amcp = gav

− fld

mcp (glv mcp (0)

dip (adip ))

− fld

(14)

pip (apip ))

According to Table 3, the maximum values of Dld are smaller than those of Dlv of corresponding joints. Therefore, the value of the sheath position angle on the ventral side should be set to a smaller value than that on the dorsal side as in Eq. (15); if a full coupling movement is required, when a dorsal joint bends to the limited angle, the coupled ventral joint would also bend to the corresponding limit.  bv bv

< bd dip mcp < bd pip pip

(15)

Assuming that the finger joints will not flex to the angle limits listed in Table 1 when the exoskeleton device is worn, we reset the a angle limits to 60◦ for MCP, 90◦ for PIP and 57◦ for DIP, as listed in Table 4. These values were not set arbitrarily, Table 3 The maximum values of Dld and Dlv for three joints. Parameters

MCP

PIP

DIP

Dld (mm) Dlv (mm)

19.64 23.67

16.49 17.45

11.78 12.63

bv = bd = p/2.

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but were chosen using Fig. 7, following the observation that when the PIP angle was 90◦ , the MCP and DIP angles were usually near 60◦ and 57◦ . These values are also reasonable in that once they have been reached, the finger would be almost closed, as in holding a pen. To facilitate the movement coupling, bd angles were set to 60◦ for PIP and 90◦ for DIP; bv angles were set to 60◦ for MCP and 8◦ for PIP. In these conditions, the PIP joints would reach 90◦ when the DIP angle bends to 57◦ , and the MCP joints would reach 60◦ when the PIP angle bends to 90◦ . Consequently, Dld values were 7.46 mm for the DIP joint and 13.84 mm for the PIP joint, slightly smaller than Dlv values of 7.66 mm for the PIP and 13.88 mm for the MCP joints. With these values, movement coupling simulations were performed out and the results are presented in Figs. 12 and 13. In Fig. 12, the green scatter data came from measurements of the index finger as in Fig. 7 (a); the red curve is the approximation Eq. (1), for the PIP vs. MCP angular relationship during finger extension movements; the blue curve is the coupling movement simulation curve. The simulation curve remains in the general scatting area of the bending scatter plot, which means the setting of PMflex tendon would offer coupling effect between the PIP and the MCP, when the coupling method is applied. Note that every point in the scatter plot represents a possible natural bending pose of the joint, thus the scatting area can be considered to be similar to the working space of a mechanism. In this case, following the simulation curve remaining in general scatting area means sequential natural poses can be acquired. Fig. 12 also shows that the tendency of the coupling simulation curve varies from that of extension approximation curve for the PIP vs. MCP relationship. In this case, when the exoskeleton mechanism is extended at the MCP, the extension tendency will just follow the coupling simulation curve. Hence, the extension relationship between the PIP and MCP will differ from the natural active movements of the index finger. However, as discussed in Section 3.3, this tendency difference will not translate to a bad experience for the wearer. In one aspect there is no anatomical coupling mechanism between the PIP and the MCP in human fingers; the two joints can rotate independently. In another aspect, it is reasonable for a finger to perform reverse movements of natural flexion. In Fig. 13, the green points are also scatter data as in Fig. 7 (b); the red curve is the approximation Eq. (2), for the DIP vs PIP angular relationship during finger extension movements; the blue curve is the coupling simulation curve. It is clear that the simulation curve is also remaining in the scatting area of the scatter plot, which means the DPflex tendon would also offer coupling effect with natural poses between the DIP and the PIP. Besides, the extending approximation curve is also in the scatting area of flexing measurements, meaning the coincidence between the scatting areas of flexion and extension thus using the coupling equations will produce natural coupling effects between the DIP and PIP not only during finger flexion when driven at the DIP, but also during extension movements when driven extending at the MCP. Thus, the simulation results of the driving plan and coupling method developed in this section for the finger exoskeleton produce natural driving tendencies and good coupling effects for the PIP and MCP as well as for the DIP and PIP joints during both finger flexion and extension, solving the problem that was stated in Section 2.

4.5. Discussion on applying the method The joint motion-coupling plan can be used not only for the model mentioned in this paper, but also for models in different sizes of the same design. Usually, finger sizes vary in bone length values and joint diameters from person to person, thus exoskeleton part dimensions will vary accordingly. On the dorsal side of the finger, longitudinal or thickness changes in exoskeleton parts will not affect the flexing of the finger, because the adjacent parts just depart from each other while the joint is bending, as shown in Fig. 9. However, on the ventral side, the positions and the thicknesses of the parts may limit the finger bending. As in Fig. 11, the initial angle l0 is defined by the values of l1 , l2 , e1 and e2 , in which the former two variables are the distance between the bending center of the joint and the two ventral exoskeleton parts mounted aside; the latter two variables are relative to rv1 and rv2 listed in the Table 2, and also relative to the value of bv . In this way, if the value of l0 is too small, e.g. l0 ≤ 90◦ , the exoskeleton parts would block the joint from bending toward its limits. To avoid this, it ’is necessary to keep e1 ≤ l1 , and e2 ≤ l2 , meaning the exoskeleton part should not be too thick nor to be arranged too close to the bending center of the joint. The positions of the sheaths are decided by bd on dorsal side and bv on ventral side. The selection of these two values should firstly satisfy the requirements of Eq. (13), and then working out the simulation to see how well the results matching the natural flexing/extending tendency of a healthy human finger. Try to choose the pair of bd and bv values that making the best result.

Table 4 Variable limits for finger exoskeleton. Parameters

MCP

PIP

DIP

a bd bv Dld (mm) Dlv (mm)

60◦ – 60◦ – 13.88

90◦ 60◦ 8◦ 13.84 7.66

57◦ 90◦ – 7.46 –

Units: degree.

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PIP value

120

100

80

60

40 PIP vs MCP scatter

20

Coupling simulation

MCP value 0

0

20

Extension approximation

40

60

80

100

Fig. 12. Coupling effect simulation results of PIP vs. MCP. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

5. Mechanical design and experimental setup assembly Based on the foregoing theoretical analysis, an experimental device was developed, including a hand pattern (i.e., a robotic hand) on which to attach the exoskeleton parts and related actuating and sensing devices. Details are discussed in this section. 5.1. Mechanical design of the hand pattern The hand pattern was designed to be fitted with the exoskeleton parts, facilitating tests of the coupling plan mentioned above, because the exoskeleton device is jointless and cannot support itself. Fig. 14 presents the numerical model of the hand pattern including its three main parts: the arm bracket, the palm and the finger assemblies. The arm bracket provides space for sensors and actuators for further experiments. The palm is used to mount exoskeleton parts (not visible in the figure) for the hand and for connecting the finger assemblies. The finger assemblies receive the jointless finger exoskeleton parts (dark yellow parts). All key dimensions of the hand pattern such as the lengths and thicknesses of its fingers and those of each phalanx bone segment, as well as finger position arrangements, were taken from measurements of a human hand. The dimensions of the finger phalanx bones and the joint bending limits of the hand pattern are listed in Table 5. All joint bending limits were set to 90◦ , considering the variable limits listed in Table 4 in the theoretical analysis of the previous section. The yellow parts in Fig. 14 attached to the finger assemblies are the finger exoskeleton parts of the experimental setup. As shown in Fig. 15 each part was designed as a semi-cone dimensionally compatible with that of the finger phalanx to which it 70 DIP vs PIP scatter 60

Extension approximation Coupling simulation

50

DIP value

40 30 20 10

PIP value 0

0

20

40

60

80

100

120

Fig. 13. Coupling effect simulation results of DIP vs. PIP. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

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Finger assemblies

Arm bracket Hand pattern

Exoskeleton Parts

Fig. 14. 3D model of the hand pattern with exoskeleton parts mounted. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

attached. Two semi-cones were required to drive one finger phalanx, attaching separately to its dorsal and ventral sides. For the experiments, these semi-cone parts were attached to the finger assemblies directly. To highlight the coupling effect of the driving plan during the experiment, all MCP joints of the finger assemblies were reduced to one degree of freedom (DOF) instead of the more realistic two by fixing the adduction and abduction DOFs to 0◦ . With the listed values listed in Table 5, the initial working space of the index finger of the hand pattern can be visualized as Fig. 16, which presents the initial reachability of the index finger mechanism before the exoskeleton device was applied. Once the coupling tendons were arranged, the working space of the index finger assembly was constrained to a fixed trajectory that obeyed the definitions of the equations and joint bending limitations discussed in the previous section, the black curve in Fig. 16. The hardware of the experimental setup was comprised with four components as shown in Fig. 17: the hand pattern and exoskeleton device, the controller and driving system, sensors and transducers,and a data acquisition (DAQ) system.The setup was built to measure the forces in the driving tendon and on the fingertip of the index finger of the hand pattern with the finger exoskeleton device actuated. The hand pattern was constructed by a stereolithography apparatus 3D printer using the numerical model of the previous subsection; the attached exoskeleton parts were made of aluminum, and the arm bracket and supporting parts were 3D printed or machined metal. A pressure sensor was placed against the fingertip of the index finger assembly for measuring the output force with the driving force applied, and a tension sensor was connected between the driving tendon of the exoskeleton device and the pulling tendon to the winch to sense the driving force along the driving tendon. The measuring range of both force sensors were the same at 5 kg, with a precision of 1 g/mV (gram per millivolt). The winch producing the driving force was actuated by a Leadshine 57HS22-A stepping motor, with 2.2 N • m maximum torque output. Because the radius of the winch winder was 1 cm, the winch had the capability of generating up to approximately 22.4 kg tension force. An Arduino Mega 2560 micro-controller was used as a pulse generator; it was capable of forward, reverse, fast forward and fast reverse pulse signals. An MD432C stepper driver was used to drive the 57HS22-A stepper. The DAQ card for data acquisition was a PCI8622 with 16 bits AD (analog to digital) conversion accuracy by Beijing Art Technology Development Co., Ltd. 5.2. Composition and fundamentals of the experimental setup The basic force experiment is shown Fig. 18. When the winch pulls the tendon, the index finger assembly is forced to bend, which is stopped by the pressure sensor against the finger tip. As long as the pulling force increases, the output force at the fingertip also increases. Thus, the input and output force relationship can be acquired by changing the bending angle of the fingertip as well as the position of the pressure sensor. Note that the bending angle of the fingertip is not any single bending angle value of the DIP, PIP or MCP, but their sum. To measure the bending angles of the DIP, PIP and MCP joints, another rotary-sensor-based measuring device was attached to the index finger assembly, as shown in Fig. 19. This device appeared similar to and worked the same as that in Fig. 5 for measuring the joint angles of a human index finger. In this way, real-time angle values could be gathered during the experiment Table 5 Length of each phalanx bone on index finger. Name

Length (mm)

Bending limit (degree)

Proximal phalanx Middle phalanx Distal phalanx

45 25 20

90◦ 90◦ 90◦

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Dorsal parts

Ventral parts Fig. 15. Exoskeleton parts for fingers.

while the finger was bending. The rotary sensors adopted were Murata model SV01A103 with a total resistance of 10 ky ± 30% and linear accuracy of 2%. 6. Tests and results Two series of experiments were conducted with the exoskeleton device. Tendon driving kinematics experiments were conducted to evaluate the performance of coupling effect to see whether and how the PIP vs. MCP and DIP vs. PIP results matched the simulation curve. Force relationship experiments were performed to evaluate the force performance of the new coupling plan. To facilitate the experiment, we rotated the hand pattern 90◦ about the longitudinal axis as presented in Fig. 20, thus leaving more space for the index finger assembly. Because there was no force load at the finger tip, the experiment could be performed by directly pulling the driving tendon (major flexion tendon) either manually or with the winch, which was actuated by the stepper. As the finger bent, three resistive rotary sensors on the joint-angle measuring device (see Fig. 19) converted the angular information into voltage signals, which were then acquired by the DAQ at 1000 samples/s. The rotary sensors were linearly resistive and were calibrated by dividing the output voltage range between the finger joint extreme positions of 0◦ and 90◦ into 90 divisions; thus, real-time joint bending angles could be acquired by measuring the voltage in real time. An adjustable stabilized voltage supply was used for +24 V, +12 V, and +5 V power sources for the stepper driver, the force sensors and transducers as well as the Arduino Mega micro-controller. Resistive rotary sensors on the finger angle measuring devices were also powered by +5 V voltage. 6.1. Driving kinematics experiment Tendons for finger bending were made of 0.5 mm stainless steel. They had flexibility to wriggle through the sheaths at different positions while having sufficiently strong axial strength to avoid large elastic deformation from friction with the sheaths and the force load applied at the fingertip. The kinematics of finger bending was much better than if an elastic tendon material, such as nylon, were used. Tests were repeated several times; the data acquired are presented as Figs. 21 and 22. In the two figures, green points are the data acquired during the experiment, the blue curves are coupling simulations, and the red curves are extension approximations 0 Working space scatter

mm

-10

Couple motion curve

-20 -30 -40 -50 -60 -70 -80 -90 -100 -50

mm -25

0

25

50

75

Fig. 16. Finger working space of the hand pattern design.

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To DAQ Arduino Mega

97

Transducers

Press sensor (blocked)

Wiring board Stepper Driver

Stepper

Tension sensor

Exoskeleton parts

Fig. 17. Hardware of the experimental setup.

as in Figs. 12 and 13. Both figures indicate the theoretical success of the designed coupling plan; the data scatter plots follow the simulation curves well enough to generate the desired joint motion, although errors still exist. We believed that the errors in Fig. 21 came mostly from mounting-position errors of the sheaths that the coupling tendons passed through because scatter curves from different tests were very close to each other and merged together, with the same deviation from the theoretical simulation. Errors also exist in Fig. 22; scatter-data curves from different tests, spread in the PIP range from 0◦ to 60◦ , then merged above 60◦ . We believed these errors were mostly due to friction between the sheaths and the tendons at the DIP part in addition to the reason mentioned above. On one hand, friction between the tendons and sheaths was larger at DIP joint because dimensions of the parts near this joint are relatively smaller than that of the PIP and MCP; both the coupling tendon and driving tendon need to bend much more to wriggle through the sheaths here than near the PIP and MCP. The tighter bend caused more friction. On the other hand, the coupling tendon DPflex acts only when the DIP part moves prior to the PIP. Then, when the PIP joint had a tendency to bend slightly before the DIP due to the greater friction on the coupling tendons at the DIP, the situation in Fig. 22 is to be expected. Certainly if the friction between the DPflex coupling tendon and related sheath is large enough to make the joint stick, or if there were an outer force applied at the distal and middle phalanges to simply stop the DIP part from bending toward the PIP, the PIP joint would bend independently itself with this plan. Nevertheless, in general situations this would not happen. Note that without our PMflex or DPflex coupling tendons, motion relationship between the PIP and the MCP as well as between the DIP and the PIP, would be presented as vertical segments, the X = 0◦ , 0◦ ≤ Y ≤ 90◦ , in Figs. 21 and 22, because as mentioned in the Section 2 of this paper, the DIP joint would bend the first, the PIP would not start to bend until the DIP reached the limit (90◦ for the hand pattern), and the MCP joint would bend finally after the PIP joint stopped at its limit (90◦ ).

The stepper

Driving tendon

The rails

The winch

Tension sensor

Fig. 18. Basic setup.

Hand pattern

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Rotary sensors

Tendons

Connection bars

Fig. 19. Joint angle measuring device for the finger assembly.

6.2. Force relationship experiment The goal of this experiment is to evaluate the force performance of the tendon driven plan. It ’is important for further works such as the selection of actuators and the development of control methods. In this stage, we focused more on flexion than extension because most hand functions are facilitated by various finger flexions. As illustrated in Fig. 23, force performance tests were executed with the hand pattern palm down on the test board while driving the index finger assembly against a press sensor at its tip. The angle-measuring device mounted on the index finger transformed three joint angle values into proportional voltage signals, while the press sensor transformed the force values from the fingertip. The tension sensor between the winch and the major-flexion driving tendon transformed the tension force values. These various voltage values were then acquired by the DAQ, thus capturing the relationships between the input tension force along the driving tendon and the output pressing force against the fingertip. Fig. 23 also shows that the press sensor was mounted on a slope of a fixture that was jacked up by a cushion block. By using fixtures with different slope angles and cushion blocks, the press sensor could be mounted at various heights relative to the fingertip and with various orientations, matching various finger-bending situations. To facilitate this, various fixtures and cushion blocks with different slope angles and heights were 3D printed. Hence, force relationships were acquired in different finger-bending situations. During the experiment, we used the sum of the MCP, PIP and DIP joint angles to define the finger bending situations, meaning 0◦ was a full extension of the index finger assembly while 90◦ was the fingertip pointed vertically to the ground. Thanks to the adoption of stainless steel tendons, there was usually very little or no slide at the contact point between fingertip and the press sensor; this ensured the accuracy of the data acquisition. A series of repeated force tests was conducted for the force relationship experiment. Selected data series were collected in Fig. 24 for contrast, in which the x axis plots the input tension force on the Major flexion driving tendon, and y plots the output pressing force at the finger tip; data points from different finger-bending situations are plotted with different symbols. Breaks within data scatter curves with the same symbol were caused by the difference of pre-load force applied each time the test was repeated for the same finger-bending situation. From 0 to 4000 g of input forces were applied, consistent with the measuring scale of the tension force sensor between the winch and major-flexion driving tendon.

Fig. 20. Experimental setup for driving kinematics tests.

J. Yang et al. / Mechanism and Machine Theory 99 (2016) 83–102

99

100 PIP vs MCP scatters Coupling simulation

80

Extension approx.

PIP value (degree)

60

40

20

MCP value (degree) 0

0

10

20

30

40

50

60

70

Fig. 21. Kinematics test result of PIP vs. MCP. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

Eight scatter curves were acquired; it is obvious that the scatter points spread linearly in each curve, ignoring very few errors points. It is also significant that the slopes of the linear scatter curves increase when the finger bends, from 0.175 for 0◦ to 0.37 for 110◦ . When a 4000 gram input force was applied, approximately 700 to 1500 g of output pressing force was measured as the finger bent from 0◦ to 110◦ . Table 6 lists the slope values for linear scatter curves for all eight finger-bending situations. Thus, with a given input tension force, a larger output force could be acquired as the finger bent further, within the range of 0◦ and 110◦ . We did not continue the test beyond 110◦ , both because the experiment apparatus reached its physical limits at 110◦ , and because a finger-bending situation beyond 110◦ left too little space between the finger phalanges to arrange the force sensor conveniently.

7. Conclusion The main purpose of this work was to develop a new lightweight, compact and portable exoskeleton structure for finger motion assistance and rehabilitation by adding two coupling tendons to the traditional plan to avoid an incorrect driving tendency. Anatomy analysis and a kinematics study of the human finger were performed before the development; bending angle relationships among the MCP, PIP and DIP joints were analyzed as well. Detailed implementation is discussed, including the basic theory of the joint motion coupling method, relevant formula derivations and mechanical design of the experimental device. A

60 DIP vs PIP scatter 50

Extension approx. Coupling simulation

DIP value (degree)

40

30

20

10

PIP value (degree) 0

0

20

40

60

80

100

Fig. 22. Kinematics test result of DIP vs. PIP. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

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Fig. 23. Fundamentals of input-output force relationship test.

series of experiments was then conducted to examine and evaluate the developed joint motion coupling plan. Achievements of this research work were as follows: 1) The two new coupling tendons worked as desired: the incorrect driving tendency of the traditional plan was completely avoided, and the new coupled-tendon-driven plan can drive finger bending as naturally as a human finger. 2) The entire structure of the finger exoskeleton device is compact and lightweight and can be arranged to fit a hand glove or a fingerstall more easily than most bar-linkage exoskeleton structures. 3) The coupling tendons act only when the farther joint of the finger bends prior to the nearer; thus, if unexpected large friction occurs between the coupling tendons and relative sheaths, the nearer joints will bend independently. This will not happen in general applications. 4) As the finger bends farther, the output force increases for a given input tension force. From 17.5% to 37% of the input force will be converted to output force over the flexion range 0◦ to 100◦ . 5) The coupling method can be used for jointless exoskeleton devices in different sizes with the same design. When applying on a new model,the thickness and the longitudinal size of the ventral side exoskeleton parts should be considered carefully.

1600 Bending situations

0 degree 16 degrees 40 degrees 45 degrees 60 degrees 73 degrees 90 degrees 110 degrees

1400

1200

1000

Output force (g)

800

600

400

200 Input force (g)

0

0

500

1000

1500

2000

2500

3000

Fig. 24. Force output vs. input relationship of the exoskeleton device.

3500

4000

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Table 6 Slope values of linear data scatters from eight series of tests. Finger situation (degree)

Slope value

0◦ 16◦ 40◦ 40◦ 60◦ 73◦ 90◦ 110◦

0.175 0.194 0.21 0.218 0.23 0.285 0.33 0.37

Acknowledgments This paper was sponsored by the National Natural Science Foundation, No. 51505072 and The Fundamental Research Funds for the Central Universities Projects, No. N130403008, from P.R. China. The authors also would like to thank Dr. Jaydev P. Desai of the A. James Clark School of Engineering, University of Maryland, USA. Dr. Desai funded the early period of this research.

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