Front. Mech. Eng. China (2006) 1: 33–39 DOI 10.1007/s11465-005-0015-6
RESEARCH ARTICLE
ZHANG Wen-zeng, CHEN Qiang, SUN Zhen-guo, XU Lei
Superunderactuated Multifingered Hand for Humanoid Robot
# Higher Education Press and Springer-Verlag 2006
Abstract A novel underactuated finger mechanism was designed. Finger mechanism was incorporated into a humanoid robot hand to obtain more degrees of freedom with less actuators and good grasping functions with shape adaptation, therefore decreasing the requirements for the control system. A novel superunderactuated multifingered hand (TH-2 Hand) for a humanoid robot was designed based on a previous underactuated finger mechanism. The TH-2 Hand was attached to a humanoid robot because of its high personification, superunderactuation, compactness, easy real-time control, small volume, light weight, and strong grasping function. Keywords robot technology, humanoid robot, multifingered hand, underactuated mechanism
1 Introduction A humanoid robot must use its hands to perform actions like those performed by humans. A human hand has many advantages: small volume, more fingers, more degrees of freedom (DOF), and strong grasp force—characteristics that make imitation of a human hand very difficult. In addition, power supply, drivers, control system, sensors, and information processing system are installed in the humanoid robot itself, which provides very strict requirements (such as weight, volume, power cost, and real-time control, as well as the humanoid appearance of a humanoid robot hand) on many aspects.
Translated from the Journal of Tsinghua University(Scienceand Technology), 2004, 44(5) (in Chinese) ZHANG Wen-zeng (*), CHEN Qiang, SUN Zhen-guo, XU Lei Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China E-mail:
[email protected]
Many robotic hands focus on simulating the overall appearance and actions of human hands while neglecting other equally important features such as size, weight, and real-time control. Conventional robotic devices, such as the hand [1], are relatively complex, large, cumbersome, and difficult to install in a humanoid robot arm. The complexity of conventional robotic devices also makes the hand more expensive and difficult to manufacture and maintain. A key point concerning humanoid robot hand design is how to decrease volume, weight, and power cost. Too much volume may influence appearance, and too much weight and power cost may add to the burden of the robot’s arms and legs, thus adding to the total power cost. A hand’s DOF, driver style, transmission type, joint mechanism, link material, and kinematics character are quite important. At present, the hand’s driver and control system must be gigantic. The hand is difficult to control if it has greater DOF; thus, fewer drivers should be designed for the hands. The above-mentioned two aspects are partly contrary to each other. In addition, an important feature of a human hand—particularly of a finger—is the ability to bend around an object and adapt to its shape. It is better if some fingers are passively adaptive to the shape and size of objects with regard to object grasping. Some mechanical hands possess an architecture that combines three cases: taking advantage of them through the concept of underactuation. Their design is based on a large number of DOF, but with a reduced number of actuators. Indeed, underactuated hands are defined as those that have more degrees of freedom than actuators. This leads to flexible grippers without the complexity associated with a large number of actuators. Underactuation can be achieved using tendons, but grasping forces are limited and tendons give rise to friction and compliance. The hands in Gosselin and Laliberte [2], Dechev et al. [3], Laliberte and Gosselin [4], and Guo et al. [5] also have underactuated functions. Those underactuated mechanisms are commonly large in volume, heavy in weight, cumbersome in appearance, and difficult to manufacture and maintain.
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2 Traditional underactuated finger Traditional design ideas [5] on an underactuated finger are basically concentrated on how to transfer force from the root of the palms to the end joints of the fingers, but do not consider intermotion and interforce between the finger and the object grasped. A design idea of a novel underactuation (different from the previous one) considers the palm, the fingers, and the object to be grasped as one whole system. In grasping, some fingers bend and touch the object through their drivers, and then the object brings pressure forces to the other fingers. If these pressure forces can be utilized to “drive” some joints in the latter fingers and can make these joints bend like active joints, an underactuated effect will be achieved. The TH-1 Humanoid Robot has been developed successfully in Tsinghua University. The hand of the TH-1 robot is called TH-1 Hand. The TH-1 Hand [6,7] has the following features: 1 kg in weight; 0.5 kg in working load; three drivers; two fingers (which look like five fingers); appearance, size, and action similar to those of a human hand; and ability to perform actions such as extending, making a fist, and grasping some ordinary objects. Based on the previously proposed idea, a new underactuated mechanism is applied on the TH-1 Hand’s thumb. There is a large gearbox at the underactuated joint of the TH-1 Hand’s thumb. The active board of the thumb rotates and makes one end of the thumb much thicker than the other end (like a cone), which is not similar in appearance to the finger of a human hand. Therefore, the underactuated mechanism cannot simulate other fingers well. Furthermore, if a finger is composed of multiple underactuated mechanisms, arranging them in series will make it much different from the index, middle, ring, and little fingers of a human hand.
Fig. 1 Structural principle of the underactuated finger unit
anism consists of a rack fixed in the slip block and a gear fixed in the second segment, which are meshed together. The first segment could not only be connected with active joints driven by motors, but also be fixed on the palm. A concrete underactuated mechanical finger unit with passive shape adaptation has been designed, as shown in Fig. 2(a) – (d).
3 Novel underactuation finger unit 3.1 Structure of underactuated finger unit To avoid previous shortages of underactuation in the TH-1 Hand’s thumb, this paper proposes a novel underactuated finger unit with passive shape adaptation, whose structure is shown in Fig. 1. The underactuated finger unit is composed of the first segment (1), the second segment (2), and an underactuated joint (3). There is no actuator in this underactuated mechanism. An underactuated joint includes the following: slip block (4), transmission mechanism (5), and spring (8). The slip block is embedded and can slide in the first segment. A spring connects the slip block and the first segment, and always pushes the slip block outward when the finger does not grasp an object. Transmission mechanism can convert the small translation of the slip block to a large angle rotation of the second segment to realize an underactuated effect, as if there is an actuator in the underactuated joint. The transmission mech-
Fig. 2 Underactuated finger unit. a D-D cutaway view. b A-A cutaway view. c Side elevation. d Elevation. 1 First segment, 2 second segment, 3 underactuated joint, 4 slip block, 5 first segment frame, 6 right board, 7 back board, 8 spring, 9 slip block body, 10 slip block cover, 11 slip block board, 12 rack, 13 joint gear shaft, 14 cone pin
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3.2 Grasp processing of the underactuated unit Grasp processing of the underactuated finger unit is described as follows: 1. When the robot’s hand grasps an object, the motor rotates, which drives the root joint and the first segment to rotate. Then the slip block contacts the object to be grasped. Due to the reaction of the other fingers, the object presses (“drives”) the slip block to slide toward the inside of the first segment by a small displacement. The rack fixed in the slip block moves, driving the gear shaft mesh with the rack to rotate; thus, the second segment fixed with the gear shaft rotates. Since the diameter of the gear is relatively small, a small translation of the rack results in the rotation of a large angle; thus, the second segment can quickly rotate by a large angle to grasp the object as if there is a motor in the underactuated joint. The object can be stably grasped by the robot hand. 2. When the robot’s hand releases the object grasped, the motor rotates in reverse direction. The first segment rotates in reverse direction to depart from the object, and then the spring causes the slip block to slide outward, and the second segment rotates by a large angle in reverse direction through the gear rack transmission mechanism, until the whole finger completely leaves the object. If the size (such as diameter) of the object grasped is too small to be contacted by the slip block, the ends of the second segment can be used to pinch the small object. The object can be stably grasped in case the gear shaft does not rotate. When the underactuated mechanism is connected with an active joint, the finger grasps the object, as shown in Fig. 3(a),(b). Figure 3(c) shows that the finger grasps a small object in this case. When the underactuated mechanism is fixed on the palm, object grasping of the finger proceeds as shown in Fig. 3(d),(e). Figure 3(f) shows that the finger grasps a small object in this case. Several previous mechanisms can be arranged in series to produce a superunderactuated, highly passive-shapeadaptive finger mechanism. This feature can be utilized to design the index, middle, ring, and little fingers of a robot hand. Figure 4(a) – (c) shows a finger with two underactuated units grasping an object.
Fig. 4 A finger with two units in series grasping an object. a Big object. b Middle object. c Small object
3.3 Force analysis of underactuated mechanism The forces brought on when the underactuated mechanism grasps an object are shown in Fig. 5(a). A coordinate frame has been established, of which the origin O is the rotation center of the root joint, y is the axis toward the end of the second segment when the hand does not grasp an object, and x is the axis toward the object to be grasped, perpendicular to the y axis. All forces brought on the object are shown in Fig. 5(b). Some main symbols in Fig. 5 are described as follows: f1 f2 ft fsum r2 l1 m s θ β α
The force brought to the object by the first segment [N] The force brought to the object by the second segment [N] The force brought to the object by other joints and other fingers [N] The total force brought to the object by the underactuated finger [N] The distance between f2 and the rotation center of the second segment [mm] The distance between the rotation center of the root joint and the rotation center of the second segment [mm] The moment of the root motor [Nm] The displacement mount of the slip block The rotation angle of the second segment relative to the first segment [°] The rotation angle of the first segment [°] The angle between fsum and f1 [°]
Fig. 3 Grasping process of the underactuated finger. a and b Active joint and big object. c Active joint and small object. d and e Fixed joint and big object. f Fixed joint and small object
36 Fig. 5 Forces at work in a finger grasping an object. a Hand grasping object. b Forces’ relation
A formula can be obtained according to the mechanism principle of gear rack transmission mechanism: ¼
2s dj2
(1)
Here, dj2 is the middle diameter of the gear [mm]. According to mechanics, transmission relation, and geometric relation, some formulas can be obtained: m f1 ¼ d cos l1 1 þ j22r2
f2 ¼
(2)
f1 dj2 md j2 ¼ d cos 2r2 2l1 r2 1 þ j22r2
fsum ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi f12 þ f22 þ 2f1 f2 cos
2 f 2 þ fsum f22 ¼ arccos 1 2f1 fsum
(3)
(4)
(5)
When m=2 Nm, r2=22.5 mm, and θ=30°, then the relationships of f1, f2, fsum, α, and l1, dj2 are shown in Fig. 6(a) – (d). The findings from these figures are listed below: 1. If l1 increases, then f1 and fsum will decrease distinctly, f2 will decrease a little, and α will basically keep the original value. 2. If dj2 increases, then f1 will decrease a little, f2 will increase, fsum will not change, and α will increase. Because α is the angle between fsum and f1, the increase of α will rotate fsum toward the direction of a stronger object grasp, which is much favorable. This phenomenon is equal to the force f2 of the second segment increasing when dj2 increases.
Fig. 6 Results of force analysis. a Relationships of f1 and l1,dj2. b Relationships of f2 and l1,dj2. c Relationships of fsum and l1,dj2. d Relationships of α and l1,dj2
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When m=2 Nm, l1=40 mm, and dj2=6 mm, then the relationships of f1, f2, fsum, α, and r2, dj2 are as shown in Fig. 7(a) – (d). Their findings are listed as follows: 1. If r2 increases, then f1 will increase but the increasing extent of f1 will decrease; f2 will decrease and its decreasing extent will decrease; and fsum and α will decrease and their decreasing extent will enlarge if θ increases. The contacting position r2 between the second segment and the object affects not only the distribution of grasping total force fsum between the first segment and the second segment, but also the grasping effect, namely, the mount and direction of fsum.
2. If θ increases, then f1 will decrease, f2 will increase a little, fsum will increase, and α will increase. The increasing extent of the latter two will decrease along with increasing r2. 3.4 Optimization of the underactuated finger The major rule in designing an underactuated finger is to give attention to the appearance and mechanics effects of passive adaptive grasps. The appearance effect of a passive adaptive grasp is defined here as the rotation angle of the second segment corresponding to a unit displacement brought on by sliding of the slip block. If the object presses the slip block to move by a specified small displacement, a bigger rotation angle of the second segment will be obtained; thus, the appearance effect of the underactuated finger becomes better. The mechanics effect of a passive adaptive grasp is defined here as the total grasping force of the underactuated finger. The bigger the total grasping force is, the better the mechanics effect will be. If dj2 is designed to be smaller, better appearance effects can be obtained. However, if dj2 is designed to be larger, better mechanics effects can be obtained. The two abovementioned aspects are directly in contrary to each other. In fact, this is a contradiction of this type of underactuated mechanism, implying that there is no actuator in itself. Therefore, a designer should find a proper balance between the two aspects. In designing, firstly, the realization of the appearance effects of the underactuated finger should be considered. If s is excessively large, the slip block will extrude more, the finger will be much thicker than a human finger, and the appearance of the finger before grasping will be much different from that of the finger after grasping. Thus, it is recommended that smax=3–10 mm. Corresponding to the value of smax, the finger should be completely bent by more than 80° (θmax=80–110°). dj2 can be calculated by formula (1) according to smax and θmax. Secondly, the mechanics effects of the underactuated finger should be considered. Formulas (2)–(5) can be used to determine whether the total grasp force is large enough to grasp an object. To obtain a stronger force, a smaller length of l1 should be designed. The grasp force of the second segment is commonly much smaller than that of the first segment; thus, the root motor should have bigger power to increase the moment of root joint. 3.5 Advantages of the underactuated finger
Fig. 7 Results of force analysis. a Relationships of f1 and r2,dj2. b Relationships of f2 and r2,dj2. c Relationships of fsum and r2,dj2. d Relationships of α and r2,dj2
Compared with a traditional underactuated finger mechanism, the finger mechanism has many advantages: better underactuated effect; absence of motor; stronger passive adaptation; less requirements for the control system; similarity in appearance to a human finger; simple structure, small volume, and light weight; and ease of
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integration into a series to obtain a superunderactuated finger as much as a superunderactuated hand.
4 TH-2 Hand An integrated multiple underactuated mechanism unit (a superunderactuated humanoid robot with a multifingered hand, with shape adaptation) has been designed and named TH-2 Hand. The kinematic structure of the TH-2 Hand is shown in Fig. 8. The joint mechanisms of the TH-2 Hand are divided into three kinds: modules A–C. Module A is the same underactuated mechanism unit mentioned above. Module B is the four-finger root joint mechanism to which a motor is attached, basically similar to the index root joint of the TH-1 Hand. Module C is the thumb root joint mechanism to which a motor is attached, similar to the thumb root joint of the TH-1 Hand. The TH-2 Hand is composed of a palm, a thumb, an index finger, a middle finger, a ring finger, a little finger, a four-finger root joint, and a thumb root joint. The thumb consists of a thumb root segment, a thumb end underactuated joint, and a thumb end segment. The index, middle, ring, and little fingers (written as “four fingers”) are composed of the root segment, middle underactuated joint, middle segment end underactuated joint, and end segment, respectively. The four fingers are dependent on one another in grasping objects. To make the hand agile, a novel fourfinger root joint mechanism was designed. The root segments of the four fingers in the same gear shaft of the four-finger root joint connect with the palm. The thumb root joint and the four-finger root joint are driven by motors embedded into the hollow palm. The same underactuated mechanism unit proposed and de-
Fig. 9 Appearance of the TH-2 Hand. a Appearance. b Grasping an object
scribed in detail previously in this paper was applied to the middle thumb end underactuated joint, the underactuated joint, and the end underactuated joint of the four fingers. A part is raised to the underactuated mechanism to bend the finger when there is no object to be grasped, which is necessary in making a fist. The surface of the fingers is covered with high-friction coefficient elastic materials, which are helpful to increasing the touch area between the fingers and an object through distortion and to increasing restriction force, friction force, and grasp stability. The appearance of the TH-2 Hand is shown in Fig. 9(a). Figure 9(c) shows the TH-2 Hand grasping a cylinder. The advantages of the TH-2 Hand are as follows: 1. Super personification: the appearance and size of the TH-2 Hand are similar to those of the human hand (TH-2 Hand: 5 fingers and 11 DOF). 2. Superunderactuated and compact hand: the same underactuated mechanism unit, which is compact and modularized, is applied to all nine joints of the TH-2 Hand; all motors, reducers, encoders, driver circuit boards, and basic control circuit boards are embedded into it. 3. Easy real-time control: there are only two motors in the TH-2 Hand; the TH-2 Hand needs much less requirements for the control system. 4. Small volume and light weight: few motors and reducers, simple transmission mechanisms. 5. Strongly passive adaptive grasp: the TH-2 Hand can grasp ordinary objects and has strongly passive adaptation to the shape and size of different objects.
5 Conclusions Fig. 8 Structure of the TH-2 Hand. a Kinematic structure. b Modules of the TH-2 Hand. 1 Palm, 2 thumb, 3 index finger, 4 middle finger, 5 ring finger, 6 little finger, J joint, S segment
This work proposed a design idea for a novel underactuated finger mechanism and concretely designed the finger
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mechanism. The finger has many advantages: better underactuated effect; absence of motor; stronger passive adaptation; less requirements for the control system; similarity in appearance to a human finger; small volume and light weight; and ease of integration in a series to obtain a superunderactuated hand. Based on the finger, a multifingered hand (TH-2 Hand) for a humanoid robot has been designed. The TH-2 Hand has many excellent features: high personification, superunderactuation, compactness, ease of real-time control, small volume, light weight, and strong grasping function. Acknowledgements This research was funded by the National Natural Science Foundation of China (No. 50275083) and the Education Prosperity Plan of the Ministry of Education, China.
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