underactuated finger design

CHINESE JOURNAL OF MECHANICAL ENGINEERING Vol. 23,aNo. 2, 2010

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DOI: 10.3901/CJME.2010.02.***, available online at www.cjmenet.com; www.cjmenet.com.cn

Development of Gesture-Changeable Under-actuated Humanoid Robotic Finger

ZHANG Wenzeng*, CHE Demeng, CHEN Qiang, DU Dong

1 Key Laboratory for Advanced Materials Processing Technology of Ministry of Education, Beijing 100084, China 2 Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China

Received May 20, 2009; revised February 12, 2010; accepted February 25, 2010; published electronically February 28, 2010

Abstract: Robotic fingers, which are the key parts of robot hand, are divided into two main kinds: dexterous fingers and under-actuated fingers. Although dexterous fingers are agile, they are too expensive. Under-actuated fingers can grasp objects self-adaptively, which makes them easy to control and low cost, on the contrary, under-actuated function make fingers feel hard to grasp things agilely enough and make many gestures. For the purpose of designing a new finger which can grasp things dexterously, perform many gestures and easy to control and maintain, a concept called “gesture-changeable under-actuated” (GCUA) function is put forward. The GCUA function combines the advantages of dexterous fingers and under-actuated fingers: a pre-bending function is embedded into the under-actuated finger. The GCUA finger can not only perform self-adaptive grasping function, but also actively bend the middle joint of the finger. Based on the concept, a GCUA finger with 2 joints is designed, which is realized by the coordination of screw-nut transmission mechanism, flexible drawstring constraint and pulley-belt under-actuated mechanism. Principle analyses of its grasping and the design optimization of the GCUA finger are given. An important problem of how to stably grasp an object which is easy to glide is discussed. The force analysis on gliding object in grasping process is introduced in detail. A GCUA finger with 3 joints is developed. Many experiments of grasping different objects by of the finger were carried out. The experimental results show that the GCUA finger can effectively realize functions of pre-bending and self-adaptive grasping, the grasping processes are stable. The GCUA finger excels under-actuated fingers in dexterity and gesture actions and it is easier to control and cheaper than dexterous hands, becomes the third kinds of finger. Key words: robot technology, robotic hand, gesture-changeable under-actuation, pre-bending, self-adaptation

1 Introduction∗

Robotic hand is a very importart part of humanoid robot,

which can grasp objects and perform different operations as a terminal. Design of robot hand is a significant technology in the research of humanoid robot.

In recent years, dexterous hand has gained great achievements. A dexterous hand can perform dexterous grasping movements and operations. Each dexterous finger has 2–3 joints driven by multiple actuators. JACOBSEN, et al[1], designed Utah/MIT dexterous Hand, which can be used as a high performance research tool for the study of machine dexterity. The Shadow Robot Company[2], designed a series of Shadow dexterous hands as the terminal of Shadow robot arms. BUTTERFASS, et al[3–4], gave two kinds of DLR Hands with open skeleton structures and automatically reconfigurable palm. Many other dexterous hands are also designed, like Robonaut hand[5], UB Hand[6–7], Gifu Hand[8], and HIT Hand[9].

* Corresponding author. E-mail: [email protected] This paper is supported by National Natural Science Foundation of

China (No. 50905093), and National Hi-tech Research and Development Program of China (863 Program, Grant No. 2007AA04Z258)

Dexterous robot hands are capable of grasping objects agilely and stably, however, they cannot grasp different objects self-adaptively, which makes them highly depend on sensor and control system, simultaneously, the complexity of dexterous hand devices makes the hand high price and low reliability.

Since under-actuated robot hands can overcome some weaknesses of dexterous hands, they are more and more important in recent 10 years. In the research of under-actuated robot hands, HIROSE, et al[10], gave a soft gripper which can softly and gently conform to objects and hold them with uniform pressures. BIRGLEN, et al[11–13], designed many kinds of under-actuated grippers and gave force analyses on them. DOLLAR, et al[14–15], gave a SDM Hand which uses a singly actuator to drive 8 degrees of freedom (DOFs). Harbin Institute of Technology(LIU, et al[16]), Beijing University of Aeronautics and Astronautics (GUO, et al[17]), and Tsinghua University (ZHANG, et al[18–19]) have also made many achievements in this field. Under-actuated robot hands can grasp objects with different shapes and sizes self-adaptively, which makes them low requirements of sensor and control system.

This paper puts forward a fresh concept called gesture-changeable under-actuated function, and then

YZHANG Wenzeng, et al: Development of Gesture-Changeable Under-actuated Humanoid Robot Finger

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designs a finger to achieve this new function. The finger can grasp different objects self-adaptively, and has more human-like action forms and considerable dexterity than traditional under-actuated hands.

2 Gesture-Changeable Under-actuated

(GCUA) Function

In our research of traditional under-actuated finger, it is found that most traditional under-actuated fingers must grasp objects in a single designed order, which makes them hard to do various humanoid poses. Simultaneously, with under-actuated function, gestures of the fingers cannot be altered (mostly keep straight) until they are blocked by objects, which makes fingers less human-like and lower stability to grasp different objects.

For instance, TH-3 hand designed by Tsinghua University uses pulley-belt transmission, many middle- segments set on the shafts and spring constraint to achieve grasping function. With the constraint of return spring, each finger of TH-3 hand must keep straight (the angle between adjacent segments is straight angle) until it is obstructed by objects, which makes the hand instable to grasp things, like small objects and gliding things (like balls). In order to overcome the shortages of traditional under-actuated fingers, a new concept of “gesture-changeable under- actuated” (GCUA) function is put forward. 2.1 Concept of GCUA function

GCUA function includes two main functions: under-actuated grasping process and pre-bending motion. “Gesture-changeable” means that the finger can change its initial gesture before grasping, and “under-actuated” means that the finger can grasp different objects self-adaptively like a traditional under-actuated finger. The mechanism designed with GCUA function has an ability to change the finger’s initial gesture flexibly according to the different sizes and shapes of grasped things, and then does grasping movements with under-actuated function. GCUA function can make the finger pinch relatively small objects easily and stably, simultaneously, it makes the grasping process more humanlike (people always bend middle joints of their fingers to grasp relatively small objects). Moreover, GCUA function can change bending order of finger’s segments, which makes the finger be able to perform some humanoid operations and poses.

Since more actuators are required to achieve GCUA function, adding GCUA function makes under-actuated finger more like dexterous finger rather than traditional under-actuated finger. However, the function reserves under-actuated grasping process, which makes the finger grasp things self-adaptively, therefore, GCUA finger is a new type of under-actuated finger. GCUA finger adds the dexterity of dexterous hands to under-actuated mechanism by changing the finger’s initial gesture, at the same time,

eliminates the weakness that dexterous hands highly depend on sensor and control system by the self-adaptive grasping function.

To sum up, GCUA finger is the middle road between under-actuated finger and dexterous finger. 2.2 Skeleton design of GCUA finger

Fig. 1 shows sketch of the principle of 2-joint GCUA finger.

I joint-shaft is sleeved within base, and middle-segment is sleeved with I joint-shaft; II joint-shaft is sleeved within the top of middle-segment, and terminal-segment is fixed with II joint-shaft. I-motor is located in base; II-motor is located in middle-segment; active pulley is fixed with I joint-shaft, similarly, passive pulley is fixed with II joint-shaft; pulley belt connects active and passive pulleys; screw is fixed with II motor-shaft, simultaneously, it is connected with nut; flexible drawstring connects nut and terminal segment, and return spring connects middle and terminal segments respectively with its two ends.

Terminal-segment

Middle-segment

II-Motor

Passive pulleyRope pulley

Pre-bending transmission

Nut

Active pulley

Base

Belt

Flexible drawstring

I joint-shaft

II joint-shaft

Screw

Return spring

Under-actuated transmission

Fig. 1. Sketch of the principle of 2-joint GCUA finger

Under-actuated transmission mainly consists of active pulley, passive pulley, and belt. The under-actuated transmission makes the finger able to perform under-actuated function: the finger can grasp different objects self-adaptively. Pre-bending transmission mainly consists of II-motor, screw, nut, flexible drawing, and rope pulley. The pre-bending transmission make the finger able to perform pre-bending motion: the finger can change its initial gesture freely. Combining these two transmissions, the mechanism can achieve GCUA function. 2.3 Grasping process of the GCUA finger

2.3.1 Under-actuated grasping process Traditional under-actuated fingers can grasp different

things self-adaptively with under-actuated function, similarly, GCUA finger can also achieve under-actuated grasping process, which is shown in Fig. 2. There are three

CHINESE JOURNAL OF MECHANICAL ENGINEERING

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steps in this process.

Fig. 2. Under-actuated grasping process

of the GCUA finger Step 1: At the beginning of the grasping process, I-motor

fixed in base rotates, drives I-joint to rotate forward. Before first-segment contacts the surface of the grasped object, two return springs make I-joint and II-joint of the finger straight, so these three segments bend as a rigid body around I-joint.

Step 2: When first-segment is unable to bend with blocking by the grasped object, active pulley drags passive pulley through pulley belt. With pulley-belt transmission, middle and terminal segments rotate forward as a rigid body against the elastic force of return spring, until middle-segment also touches the object.

Step 3: When middle-segment cannot bend around II-joint, terminal-segment bend forward with the same principle of Step 2.

By these three steps, the finger can achieve under- actuated grasping process successfully. When the finger needs to unbend, I-motor will rotate backward, driving II joint to rotate backward. With the decrease of the return spring’s deformation, terminal-segment will rotate backward, and then middle-segment will be back too. If I-joint keep rotating backward, three segments of the finger will turn back to the initial position as a rigid body.

2.3.2 Pre-bending motion When GCUA finger needs to make some humanoid

poses and operation, it can change its initial gesture freely according to different goals. The movement that the finger change its initial gesture is called pre-bending motion. Many times, the finger needs to do pre-bending motion firstly, and then grasp objects self-adaptively, which is shows in Fig. 3.

II-motor rotates to drive screw, so that the screw can rotate forward to make nut move down, which pulls down flexible drawstring. After that, flexible drawstring will pull the top two segments to bend against the elastic force of return spring. The top two segments have already rotated an angle before II-motor stops. With flexible feature, flexible drawstring can prevent the top two segments from rotating

backward, however, allow them to rotate forward with the driving of other actuators. This important feature is called single direction constraint. With single direction constraint, pre-bending motion has no any effect on under-actuated grasping process. The latter process of the GCUA finger is similar as under-actuated grasping process, which can make the finger grasp objects self-adaptively after pre-bending motion.

Fig. 3. Pre-bending motion and Under-actuated grasping

If the finger needs to return to initial position, I-motor

rotates backward to drive the finger to unbend. When the finger is back to the gesture which is given by pre-bending motion, II-motor needs to rotate backward, and in doing so, the screw will turn back to make nut raise, which makes flexible drawstring not restrict the top two segments any more. With the decrease of the return spring’s deformation, the top two segments will rotate backward to the initial position.

The foregoing processes: under-actuated grasping process and pre-bending motion can be used alone or combined under different requirements of grasping or operating. With under-actuated grasping process, GCUA finger can be self-adaptive to shapes and sizes of the grasped objects, simultaneously, with pre-bending motion, the finger can grasp special objects (small objects, light objects, or gliding objects like balls) stably and does some humanoid poses. 3 Force analysis of GCUA finger

3.1 Principle of pre-bending motion

When the finger changes its initial gesture to achieve pre-bending motion, forces and torques which are exerted on terminal-segment and passive pulley will vary with different parameters.

Force analysis on pre-bending motion is shown in Fig. 4. AO2 is middle-segment, O2B terminal-segment, O2 the center of II joint-shaft. AO2 also stands for the rotation axis of screw and nut.

When the finger has changed its initial gesture, the force system is in balance. As is very small compared to f, gravity of nut can be omitted. Let effective diameter of


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screw be d, mm, one obtains

m2 tanf f ψ= , m22df T= . (1)

Terminal-segment

Middle-segment

O2

B

Motor

Passive pulleyTs

fm2

Rope pulley


Nut

f

Tm2

ψ

θ

ObjectA

Return spring

Screw

Fig. 4. Force analysis on pre-bending motion

Tm2―Torque of II-motor to screw around AO2, N•mm; fm2―Force of screw exerted to flexible drawstring, whose magnitude is

equal to force of flexible drawstring to rope pulley, N; Ts―Torque of return spring between middle and terminal segments,

N•mm; f―Force of screw to nut, which is perpendicular to AO2, N; r1,r2―Radii of rope pulley and return spring, mm; θ―Rotational angle of terminal-segment, rad; ψ―Lead angle of screw, rad. Considering torque balance of rope pulley with regard to

O2, one obtains

m2 1 sf r T× = , s max 2T k rθ= , (2)

where k is stiffness factor of return spring, N/mm. Considering geometrical relationship, one obtains

max 1 maxr Lθ = , (3)

where L is relative displacement of nut to screw, mm. Combining Eqs. (1), (2), (3), one obtains

1max m2

2

2 tanr Tr kd

ψθ = , (4)

2

1max m2

2

2 .tanrL L T

r kd ψ=≤ (5)

Keep Tm2, d, r1, r2, ψ as constants, by choosing the return

spring whose stiffness factor is suitable, one can adjust terminal-segment bend in a designed anger interval. When Tm2, d, r1, r2, ψ, k are all decided, it is necessary to ensure that the maximum relative displacement of nut to screw is not more than Lmax, otherwise with the blocking of spring torque, II-motor may be out of action in a short time.

3.2 Analysis on finger when it grasps gliding objects Pre-bending motion can change the finger’s initial

gesture, but pre-bending motion has little effect on under-actuated grasping process or reaction force of the object against the finger. Therefore, when analysis on grasping movement is needed, under-actuated grasping process can give satisfying answer even if the function of pre-bending motion is omitted. Force analysis on 2-joint GCUA finger when under- actuated grasping process carries on is shown in Fig. 5. O1O2 is middle-segment, O2B terminal-segment, O1 and O2 the centers of I and II joint-shaft, respectively. Let O1O2 be equal to l1, O2B be equal to l2.

Terminal-segment

Middle-segment

Object

O1

O2

B

Base

Activepulley

Passivepulley

f1

f2

TS

TM1

fM1

Rope pulley


Fig. 5. Force status of the finger in under-actuated function

f1―Reaction force of object against middle-segment, N; f2―Reaction force of object against terminal-segment, N; Tm1―Torque of I-motor to active pulley with regard to point O1,

I-motor torque for short, N·mm; Ts―Torque of return spring between middle and terminal segments

with regard to point O2, spring torque for short, N·mm; fm1―Force of active pulley exerted to belt, N; r3, r4―Radii of active and passive pulleys, mm; θm―Rotational angle of active pulley, rad; θ1―Rotational angle of middle-segment, rad; θ2―Rotational angle of terminal-segment, rad; h1―Arm of force f1 with regard to point O1, mm; h2―Arm of force f2 with regard to point O2, mm. Considering torque and force balance of the whole finger,

one obtains[19]

(6a)

(6b)

Fig. 6(a) shows force analysis on gliding object in the grasping process.

( )2 1 2 2 1 21 m1 s

1 2 1 2

2 m1 s2 2

1 cos cos ,

1 .

h R Rl h lf T Thh hh

Rf T Th h

θ θ− −⎧ += +⎪⎪⎨⎪ = −⎪⎩


·5·

θ1

f1N

θ1

f3

(a) Middle and terminal segments

both touch the object (b) Only middle segments

touches the object

Fig. 6. Force analysis of the finger grasping gliding object

f1―Grasping force of middle-segment to object, N; f2―Grasping force of terminal-segment to object, N; f3―Friction force of ground to object, N; N―Holding force of ground to object, N; θ1―Rotational angle of middle-segment, rad; θ2―Rotational angle of terminal-segment, rad. Assume that gravity of the object is light enough to be

omitted, considering force balance on object, one obtains

( )1 1 2 1 2 3cos cosf f fθ θ θ+ + = , (7)

( )1 1 2 1 2sin sinf f Nθ θ θ+ + = . (8)

Considering physical nature of the ground, one obtains

3 sf Nμ≤ , (9)

where μs is coefficient of maximum static friction. Since spring torque TS is quite small compared to

I-motor torque Tm1, the result will be good enough when TS is omitted. Combine Eqs. (6–9), one obtains

( ) ( )s 1 2 1 22 1 2

1 1 1 s 1

sin coscos1cos sin

h lRh R h

μ θ θ θ θθθ μ θ+ − +−⎛ ⎞ +⎜ ⎟ −⎝ ⎠

≤ . (10)

As long as θ1 and θ2 satisfy Eq. (10), the object can keep static state when middle and terminal segments both contact the object. If gravity of the object is too large to be omitted, holding force N will increase to balance the gravity, the maximum static friction force fmax is larger than the one whose gravity is omitted. In this condition, if θ1 and θ2 still satisfy the relation which keep the object static, the object can also keep static state as same as a light one.

At the beginning of under-actuated grasping process, the finger must bend middle-segment firstly, when middle- segment contacts objects, according to force balance, one obtains

1 min sπ arctan .2

θ θ μ= −≥ (11)

When θ1 satisfies Eq. (11), the object is stable under the

grasping force exerted by middle-segment. When θ1 and θ2 satisfy Eq. (10), final state of grasping (two segments both contact object) is stable. If θ1 cannot satisfy Eq. (11), the finger cannot grasp object stably in the middle of the grasping process. Because under-actuated grasping process requires that the finger should bend its middle-segment firstly, and then bend terminal-segment, with this order, middle-segment has pushed object away before terminal-segment touches it. In this condition, one can use pre-bending motion to adjust finger’s initial gesture, so that middle-segment cannot touch object firstly, which can make finger grasp the object stably.

4 Design of GCUA finger

4.1 Design of 2-joint finger

Designed GCUA finger with 2 joints is shown in Fig. 7.

(a) Front cutaway view (b) Side cutaway view

Fig. 7. GCUA finger with 2 joints

1. Base; 2. Active pulley; 3. I joint-shaft; 4. Active spring; 5. Belt; 6. Middle-segment; 7. Flexible drawstring; 8. II joint-shaft; 9. Passive pulley; 10. Terminal-segment; 11. Return spring; 12. Nut; 13. Screw; 14. II-motor; 15. II-bevel gear; 16. I-bevel gear; 17. I-motor

I-motor is located in the base, its output shaft is fixed

with I-bevel gear. II-bevel gear meshes with I-bevel gear, and II-bevel gear is fixed with I joint-shaft. Terminal-segment is fixed with II joint-shaft.

At the same time, return spring around II joint-shaft connects middle and terminal segments, active spring around I joint-shaft connects active pulley and I joint-shaft by its two ends, which can eliminate torque produced when active pulley reverses.


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II-motor is located in middle-segment, its output shaft is fixed with screw, the screw is connected with nut. Flexible drawstring connects nut and terminal-segment.

4.2 Design of 3-joint finger

GCUA finger with 3 joints has two motors and 3 DOFs, which can change its initial gesture with pre-bending motion and grasp different objects self-adaptively with under-actuated grasping process.

Fig. 8 shows designed GCUA finger with 3 joints. Fig. 9 and Fig. 10 show some grasping pictures of the finger.

(a) Front cutaway view (b) Side cutaway view

Fig. 8. GCUA finger with 3 joints

(a) Grasping square bottle (b) Grasping flat object

(c) Grasping a set of wrench (d) Grasping a mouse

Fig. 9. GCUA finger with 3 joints grasping different objects

(a) Initial status (b)Middle process

(c) Final status

Fig. 10. Under-actuated grasping process of GCUA finger

5 Conclusions (1) Two main kinds of humanoid hands have been

compared: dexterous hand and under-actuated hand, their advantages and weak points have been given. Dexterous hand can operate and grasp dexterously, however, it has a high dependence on sensor and control system, which makes it hard to manufacture and maintain. Under-actuated hand can grasp things self-adaptively, with this humanoid feature, it is easy to design and control, nevertheless, the hand cannot be dexterous enough to satisfy many special requirements like making humanlike poses and movements.

(2) In order to overcome weak points of these two kinds of hands above, a new concept called GCUA function is put forward. This function make hands get important humanoid features: grasping things self-adaptively from traditional under-actuated hand, moreover, the function adds pre-bending motion to the new mechanism, which makes it more dexterous and easy to grasp objects stably.

(3) With force analysis on pre-bending motion, the relationship between parameters has been obtained, which gives some mechanical requirements when a new mechanism is designed. (4) When a finger tries to grasp gliding things like balls, problems on grasping stabilities have been discussed. The paper gives force analysis in this process, and the result shows that pre-bending motion can make the finger grasp gliding things more easily and stably. (5) Designs of 2-joint and 3-joint GCUA fingers are given, combining screw-nut transmission and drawstring, the mechanism can achieve pre-bending motion, simultaneously, pulley-belt transmission makes the mechanism achieve under-actuated grasping process.


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Drawstring’s single direction constraint feature is very important, which makes pre-bending motion and under-actuated grasping process have no effect on each other. (6) GCUA finger keeps advantages of two kinds of hands, moreover, overcomes some weak points of them. GUCA finger brings a new concept and starts a new way between dexterous finger and under-actuated finger. References

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Biographical notes ZHANG Wenzeng, born in 1975, is currently a lecturer in Department of Mechanical Engineering, Tsinghua University, China. He received his bachelor degree and PhD degree from Tsinghua University, China, in 1999, 2005. His research interests include robotic hands, robot vision and seam tracking. Tel: +86-10-62773860; E-mail: [email protected] CHE Demeng, born in 1988, is currently an undergraduate in Department of Mechanical Engineering, Tsinghua University, China. E-mail: [email protected] CHEN Qiang, born in 1956, is currently a professor in Department of Mechanical Engineering, Tsinghua University, China. E-mail: [email protected] DU Dong, born in 1963, is currently a professor in Department of Mechanical Engineering, Tsinghua University, China. E-mail: [email protected]

underactuated finger design

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