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International Journal of Humanoid RoboticsVol. 8, No. 1 (2011) 73–86c© World Scientific Publishing CompanyDOI: 10.1142/S0219843611002435

A DEXTEROUS AND SELF-ADAPTIVE HUMANOIDROBOT HAND: GCUA HAND

DEMENG CHE∗ and WENZENG ZHANG†

Department of Mechanical Engineering, Tsinghua University,Key Laboratory for Advanced Materials Processing Technology,

Ministry of Education,

Beijing 100084, China∗cdm07@mails.tsinghua.edu.cn

†wenzeng@tsinghua.edu.cn

Received 3 May 2010Accepted 3 August 2010

Gesture-changeable under-actuated (GCUA) function is put forward to make traditionalunder-actuated hands feel easy to grasp different objects and do simple operations dex-terously, simultaneously, this function can lower control difficulties of robotic hands.Based on GCUA function, a GCUA hand based on pulley-belt mechanism is designedin detail and manufactured. The Hand can grasp different objects self-adaptively andchange its initial gesture dexterously before touching objects. The hand has 5 fingersand 15 DOFs, each finger utilizes screw-nut transmission, flexible drawstring constraintand belt-pulley under-actuated mechanism to realize GCUA function. The analyses ongrasping static forces and grasping stabilities are given. The analyses and experimentalresults show that GCUA function is very nice and valid. The hands with GCUA functioncan meet the requirements of grasping and operating with lower control and cost, whichis the middle road between traditional under-actuated hands and dexterous hands.

Keywords: Humanoid robot; multi-fingered hand; passive adaptive grasp; gesture-changeable under-actuated function; dexterity.

1. Introduction

Humanoid robotic hand plays an important role as end-effecter of humanoid robot.Over the past 30 years, the study on dexterous hands has gained plentiful achieve-ments. In general, a dexterous hand has 3–5 fingers with 2–4 DOFs in each finger,whose joints are mostly driven by actuators actively. Examples of dexterous robothands are Utah/MIT Hand,1 Robonaut Hand,2 UB Hand,3 Gifu hand,4 BH serieshands by Beihang University and HIT series hands5 by Harbin Institute of Technol-ogy. Dexterous robot hands can grasp different kinds of objects agilely and stably.However, dexterous hands cannot grasp objects self-adaptively, which makes themhighly depend on their sensors and control system. The complexity of dexteroushands makes them high cost and low reliability.

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74 D. Che & W. Zhang

Since under-actuated robotic hands can overcome some weaknesses of dexter-ous hands whose joints are mostly driven by actuators actively, under-actuatedrobot hands are more and more important in recent 10 years. In the research ofunder-actuated robot hands, Laval University (Birglen et al.6) in Canada (Dollaret al.7) in USA, TIT (Hirose et al.8) in Japan, HIT (Liu et al.9), Beihang Univer-sity (Guo et al.10), and Tsinghua University (Zhang et al.11), have done many jobs.Under-actuated robotic hands can grasp objects with different shapes and sizesself-adaptively, which makes hands reduce the requirements of sensor and controlsystem.

The traditional under-actuated finger has the gesture which cannot be changed(mostly keep straight) until the finger touches objects, which makes the finger lesshuman-like and less stable to grasp different objects. For instance, with the con-straint of spring, each finger of TH-3 hand must keep straight (the angle betweenmiddle- and terminal-segment is straight angle) only if it is blocked by objects,which reduces the stability and dexterity of grasping.

2. Principle of GCUA Function

2.1. Concept of GCUA function

Gesture-changeable under-actuated (GCUA) function is put forward to make tra-ditional under-actuated hands feel easy to grasp different things and do simpleoperations dexterously, simultaneously, this function can lower control difficultiesof robotic hands. “Gesture-changeable” means that the finger can change its ini-tial gesture before grasping, and “under-actuated” means that the finger can graspobjects with the most important feature of under-actuated function: self-adaptivegrasping. The mechanism based on GCUA function can change the finger’s initialgesture flexibly according to different sizes and shapes of the grasped objects whichis essential to improve the stability of grasping and make the grasping movementmore humanlike. After changing initial gesture, the finger can grasp objects self-adaptively.

In fact, GCUA function comes from the grasping movements of human beings.When people want to grasp small objects or balls, they always firstly bend their toptwo phalanges and then grasp them self-adaptively, which makes people feel easyto grasp different things stably even without thinking about the rotating angle ofeach joint.

Since GCUA function introduces new actuators to achieve the initial changingmovements, adding GCUA function makes under-actuated finger more like dexter-ous finger rather than traditional under-actuated finger. However, GCUA functionholds the important feature of traditional under-actuated finger: self-adaptive grasp-ing, which makes it be a new part of under-actuated function. GCUA mechanismadds the dexterity of dexterous hands to under-actuated mechanisms by changingthe finger’s initial gesture, at the same time, by self-adaptive grasping function,GCUA mechanism gets rid of the weakness that dexterous hands highly depend on

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A Dexterous and Self-Adaptive Humanoid Robot Hand 75

MT MT MTMT

Proximal phalange

Middle phalange

Terminal phalange

Base

Fig. 1. Under-actuated grasping process of GCUA finger.

their sensor and control system. In a word, GCUA hand will be the middle roadbetween under-actuated hands and dexterous hands.

2.2. Grasping process of finger with GCUA function

Figure 1 shows the under-actuated grasping process of a finger based on GCUAfunction. The motor rotates on the base to drive the gear, and then the proximaljoint-shaft rotates. Before proximal phalange touches the grasped object, a springbetween proximal phalange and middle phalange and another spring between middlephalange and terminal phalange keep middle phalange and terminal phalange beingstatic relative to proximal phalange as long as possible, which makes them bendaround proximal joint-shaft as a rigid body.

When proximal phalange is blocked by the grasped object and unable to con-tinue rotating, the motor keeps rotating and drives middle phalange and terminalphalange to rotate against the elastic force of the return spring as a rigid body, untilmiddle phalange also touches the object. After middle phalange is blocked by thegrasped object, terminal phalange continues to rotate until it touches the object.In this way, the finger achieves the under-actuated grasping process.

Figure 2 shows the second movement process of GCUA function: the fingerchanges the initial gesture firstly and then grasps the object self-adaptively. Themovement of changing finger’s initial gesture is called pre-bending motion. The

MT

Proximal phalange

Middle phalange

Terminal phalange

BaseMT MT MT MT

Fig. 2. Pre-bending motion and under-actuated grasping process.

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76 D. Che & W. Zhang

motor located in middle phalange rotates to drive the gear. With screw-nut trans-mission and flexible drawstring, the motor actuates middle phalange to rotateagainst the elastic force of the return spring around middle joint-shaft, simulta-neously, with the constraint of the spring between middle phalange and terminalphalange, the terminal keeps static relative to middle phalange and rotates aroundmiddle joint-shaft. With the rotation of the top two phalanges, the finger achievespre-bending motion dexterously. With single direction constraint, the flexible draw-string can prevent middle phalange from rotating backward, on the contrary, allowmiddle phalange to rotate forward with the driving of other actuators. Therefore,pre-bending motion has no effect on the under-actuated grasping process, and thefinger can grasp objects self-adaptively with under-actuated grasping process afterpre-bending motion.

Pre-bending motion and under-actuated grasping process can be used alone ortogether under different requirements of grasping. GCUA function can not only beself-adaptive to different shapes and sizes of the grasped objects with the under-actuated grasping process, but also grasp small size and light objects or glidingobjects stably with the combination of pre-bending motion and under-actuatedgrasping process.

3. Design of the GCUA Hand Based on Pulley-Belt Mechanism

The principles of two different GCUA finger have been put forward above, in fact,almost all the traditional under-actuated finger can be transformed into GCUAfinger. In this chapter, the detailed design of a GCUA hand based on pulley-beltmechanism will be described. The hand has 5 fingers and 15 DOFs (6 active DOFs,5 pre-bending DOFs, 4 passive DOFs).

This hand is the double size with an adult’s hand, with a length 350mm, palmlength of 180mm, palm width of 152mm, palm thickness of 30mm, all the fingerscan rotate angle range of 0–90 for all joints. The details of the hand and theplacement of components are shown in Fig. 3.

3.1. Design of the 2-joint finger

The component of the 2-joint finger mechanism is shown in Fig. 4. The first motoris fixed with the base, whose output shaft is fixed with the first bevel gear, thefirst bevel gear is meshing with the second one which is fixed with the base joint-shaft, the base joint-shaft is sleeved within the base. The first straight gear is alsofixed with the base joint-shaft, which meshes with the second one fixed with thefirst joint-shaft. The first-shaft is sleeved within the base, the second joint-shaft issleeved within the middle-segment- and fixed with the terminal-segment.

At the same time, the return spring around the second joint-shaft connects themiddle and terminal segment by its two ends, the active spring around the firstjoint shaft connects the active pulley and the first joint, which can eliminate thetorque produced when the active pulley reverses.

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A Dexterous and Self-Adaptive Humanoid Robot Hand 77

(a) design of the GCUA Hand (b) the GCUA Hand

Fig. 3. Details of GCUA Hand and placement of components.

The second motor is fixed in the middle-segment, whose output shaft is fixedwith the screw, and the screw is connected with the nut. The flexible drawstringconnects the nut and the rope pulley by its two ends, the rope pulley is fixed withthe second joint-shaft.

3.2. Design of the 3-joint finger

The 3-joint GCUA finger has two motors to drive 3 DOFs, which can change theinitial gesture (the angle between I-segment and II-segment) with the pre-bendingmotion and grasp different objects with the under-actuated grasping process self-adaptively.

Figure 5 shows the design of the 3-joint GCUA finger. The 3-joint GCUA fingeruses the same principle like 2-joint GCUA finger, which has the first motor locatedin the base to drive the finger to grasp different objects self-adaptively (Under-actuated grasping process), the second motor located in I-segment to drive thefinger to change the initial gesture (Pre-bending motion). The four 3-joint fingersof GCUA Hand have the same structure but different sizes, each of which can graspobjects independently.

4. Analyses of the GCUA Finger

4.1. Force analysis of pre-bending motion

Figure 6(a). shows the force analysis of 3-joint GCUA finger when it changes its ini-tial gesture. The letter “I” stands for the I-segment, “II” stands for the II-segment.

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78 D. Che & W. Zhang

1

6

2

3

4

15 514

17

7

16 10

11

9

8

18

20

19

21

8

21

12

179

1

2

7

13

(a) front cutaway view (b) side cutaway view (c) sketch map

Fig. 4. The GCUA finger with 2 joints. 1-base; 2-first motor; 3-first bevel gear; 4-second bevel gear;5-first joint-shaft; 6-second joint-shaft; 7-middle-segment; 8-terminal-segment; 9-second motor;10-screw; 11-nut; 12-flexible drawstring; 13-return spring; 14-active spring; 15-active pulley;16-passive pulley; 17-belt; 18-first straight gear; 19-second straight gear; 20-base joint-shaft; 21-rope pulley.

TM2-the torque caused by the second motor to the screw with regard toII-segment, second motor torque for short, Nmm;

FM2-the force exerted by the screw to the flexible drawstring, which is causedby TM2, N;

TS1-the torque caused by the return spring between I-segment and II-segmentwith regard to the II-segment joint-shaft, spring torque for short, Nmm;

FP-the grasping force exerted by the II-segment to the object, N;r3,rP-the radii of passive pulley and rope pulley, mm;hP- the arm of force FP with regard to the II-segment joint-shaft, mm;θP-the rotational angle of the II-segment, rad;ψ-the lead angle of the screw, rad.According to the static force analysis, when the II-segment touches the grasped

object, using the principle of virtual work, one obtains

FM2 = CTM2 (1)

FM2 · rP + TS1 = FP · hP (2)

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A Dexterous and Self-Adaptive Humanoid Robot Hand 79

III

II

I

(a) (b) (c) (d) (e)

Fig. 5. The GCUA finger with 3 joints. (a) front cutaway view; (b) side cutaway view; (c) frontview; (d) side view; (e) photo of three 3-joint fingers.

(a) changing the initial gesture (b) under-actuated grasping process

Fig. 6. Static force analysis of the GCUA finger.

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80 D. Che & W. Zhang

where C = 2/(d · tanψ), TS1 = −K1θP, K1 is the stiffness of the return spring.Combining Eqs. (1) and (2), one obtains

FP = JTP TP (3)

where JP = [2rP/(dhP tanψ) 1/hP]T, TP = [TM2TS1]. The main object of the pre-bending motion is changing the angle between I-segment and II-segment, at thesame time, it can also provide grasping force.

4.2. Force analysis of under-actuated grasping process

Although pre-bending motion can provide grasping force, the main grasping forceis provided by under-actuated grasping process. With the unilateral constraintof the flexible drawstring, pre-bending motion has little effect on under-actuatedgrasping process, therefore, we can consider under-actuated grasping process only.Figure 6(b) shows the static force analysis of 3-joint GCUA finger when under-actuated grasping process carries on. I stands for I-segment whose length is l1, mm,II stands for II-segment, whose length is l2, mm, III stands for III-segment whoselength is l3, mm.

F1-the grasping force caused by the I-segment to the object, whose magnitudeis equal to the reaction force caused by the object against the I-segment, N;

F2-the grasping force caused by the II-segment to the object, whose magnitudeis equal to the reaction force caused by the object against the II-segment, N;

F3-the grasping force caused by the III-segment to the object, whose magnitudeis equal to the reaction force caused by the object against the III-segment, N;

TM1-the torque caused by the first motor to the active pulley with regard to theI-segment joint-shaft, motor torque for short, Nmm;

TS1-the torque caused by the return spring between I and II segments withregard to the II-segment joint-shaft, first spring torque for short, Nmm;

TS2-the torque caused by the return spring between II and III segments withregard to the III-segment joint-shaft, second spring torque for short, Nmm;

r1, r2, r3- the radii of the active, first passive and second passive pulley, mm;θM-the rotational angle of the active pulley, rad;θ1-the rotational angle of the I-segment, rad;θ2-the rotational angle of the II-segment, rad;θ3-the rotational angle of the III-segment, rad;h1-the arm of force F1 with regard to the I-segment joint-shaft, mm;h2-the arm of force F2 with regard to the II-segment joint-shaft, mm;h3-the arm of force F3 with regard to the III-segment joint-shaft, mm.According to the principle of virtual work, one gets

TTΩ = FTV (4)

where T is input torque vector by the first motor and the return springs, F is thegrasping force vector by the three segments of the finger, V is the velocity vector

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A Dexterous and Self-Adaptive Humanoid Robot Hand 81

on the contact points, i.e.

T =

TM1

TS1 = −K1θ2

TS2 = −K2θ3

(5)

F = [F1F2F3]T (6)

where K1, K2 are the stiffness of the return spring located around the second joint-shaft and the third joint-shaft respectively.

V =

h1 0 0

l1 cos θ2 + h2 h2 0

l1 cos(θ2 + θ3) + l2 cos θ3 + h3 l2 cos θ3 + h3 h3

•θ1•θ2•θ3

(7)

Ω =[ •θM

•θ2

•θ3

]T

(8)

where•θM is the rotational velocity of the first motor,

•θ1 is the rotational velocity

of the I-segment,•θ2 is the rotational velocity of the II-segment,

·θ3 is the rotational

velocity of the III-segment. Let

AV =

h1 0 0

l1 cos θ2 + h2 h2 0

l1 cos(θ2 + θ3) + l2 cos θ3 + h3 l2 cos θ3 + h3 h3

. (9)

Considering the rotary process of the finger, one gets

θM = θ1 + α1 + α2, α1r1 = r2θ2, α2r1 = r3θ3 (10)

where α1 is the rotational angle of the II-segment after the I-segment is blocked bythe grasped object, α2 is the rotational angle of the III-segment after the II-segmentis blocked by the grasped object, from Eq. (10), one gets

θM = θ1 +r2r1θ2 +

r3r1θ3. (11)

Differentiating the Eq. (11), one can obtain•θM =

•θ1 +

r2r1

•θ2 +

r3r1

•θ3 . (12)

Combining Eqs. (8) and (12), one obtains

Ω = AΩΘ (13)

where

Θ =[ •θ1

•θ2

•θ3

]T

, AΩ =

1 r2/r1 r3/r10 1 00 0 1

.

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82 D. Che & W. Zhang

Combining Eqs. (4)–(7), (9), and (13), one gets

TTAΩ = FTAV . (14)

Calculate the determinants of matrix AΩ and AV , we know |AΩ| = 1 > 0, |AV | =h1h2h3, when hi is not zero, with matrix manipulation, one obtains

F = A−TV AT

ΩT. (15)

Let AF = A−TV AT

Ω, one obtains

F = AFT. (16)

Let ki = (li cos θ(i+1) + h(i+1))/(hih(i+1)) (i = 1, 2), Ri = r(i+1)/r1 (i = 1, 2) ands = l1 cos(θ2 + θ3)/h2, one gets

AF =

1 − h2k2R2

h1−R1k1 + h2k1k2R2 − sR2

R1

h2− R2k2

R2

h3

−k11h2

0

h2k1k2 − s− h2k2

h1−k2

1h3

T

. (17)

The return spring torques TS1 and TS2 is quite small compared to the motor torqueTM1, and might as well be omitted. From Eq. (16), one knows F3 is always largethan zero. Let li, hi, Ri, TM1 as constants (li = 2, hi, R1 = 2, R1 = 1, TM1 = 100,SI). The grasping stability area of the finger can get, shown in Fig. 7.

When state point (θ2, θ3) is in the stable area, all the three grasping force arepositive, thus, the finger can grasp the object stably. On the contrary, if point(θ2, θ3) is in the unstable area, at least one force is negative, so the finger cannotgrasp the object stably. Figure 8 shows that the stability with different magnitudesof Ri.

Stable (F1>0; F2>0)

Unstable(F1>0; F1<0)Unstable

Unstable(F1<0; F2>0)

(F1<0; F2>0)θ 3(r

ad)

θ2(rad)

Fig. 7. Grasping stability area when R1 = 2, R2 = 1.

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A Dexterous and Self-Adaptive Humanoid Robot Hand 83

Stable (F1>0; F2>0)

Unstable(F1>0; F2<0)

Unstable(F1<0; F2<0)

Unstable(F1<0; F2>0)

θ 3(rad

)

θ2(rad)

Fig. 8. Grasping stability area when R1 = 1.5, R2 = 1.

(a) (b)

(c) (d)

Fig. 9. GCUA hand grasping different objects.

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84 D. Che & W. Zhang

(a) (b)

(c)

Fig. 10. Operations and poses of the GCUA hand.

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A Dexterous and Self-Adaptive Humanoid Robot Hand 85

5. Grasping and Operation Experiments

Figure 9 shows some pictures of the hand grasping experiments. The hand cangrasp objects of different sizes and shapes with under-actuated grasping process liketraditional under-actuated hand. Moreover, the hand can also grasp many small orgliding objects, like tennis ball, apple MP3, and so on. What’s more, the hand cando some operations or poses like touching keyboard, playing electronic organ, andso on, which in shown in Fig. 10.

With the GCUA function, the hands can not only grasp objects but also operateinstruments. Combining pre-bending motion with under-actuated grasping processmakes the finger more humanoid, more dexterous, easier to control, lower manufac-ture and maintenance cost.

6. Conclusions

This paper proposed a design idea of gesture-changeable under-actuated (GCUA)hand which can achieve pre-bending motion and under-actuated grasping pro-cess. The detailed design of GCUA hand based on pulley-belt mechanism is given.The analyses and experimental results show that the GCUA function is very niceand valid. GCUA hand can grasp different objects self-adaptively like traditionalunder-actuated hands. Furthermore, it can also operate some instruments or makehumanoid poses as a dexterous hand. Although it is less dexterous than dexteroushand, it can meet many needs of grasping or operating with a lower manufactureand maintenance cost. The hands with the GCUA function will be the middle roadbetween traditional under-actuated hands and dexterous hands.

Acknowledgements

This paper was funded by Hi-Tech R&D Program (2007AA04Z258) and theNational Natural Science Foundation of China (No. 50905093).

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Demeng Che, born in 1988, is currently an undergraduate stu-dent in the department of Mechanical Engineering, TsinghuaUniversity, China. His research interests include anthropomor-phic robot hand and humanoid robot. He received the Best PaperAward of the Second International Conference on IntelligentRobotics and Applications (ICIRA 2009). He is a recipient ofNational Research Innovation Program for University Studentssponsored by Ministry of Education of the People’s Republic ofChina.

Wenzeng Zhang, born in 1975, is currently an associate profes-sor in the Dept. of Mechanical Engineering, Tsinghua University,China. He received his B.E and Ph.D. from Dept. of Mechan-ical Engineering, Tsinghua University in 1999 and 2005. Hisresearch interests are in the areas of humanoid robot hand androbot vision. He has published more than 90 academic papers.He has obtained the authorities of more than 40 Chinese inven-tion patents. He received 5 Best Paper Awards of internationalconferences (ICFDM2004, ICIRA2008, ICIRA2009, ICFDM2010and ICSR2010).