Super Under-Actuated Humanoid Robot Hand with Gear-Rack Mechanism Wenzeng Zhang1, Min Qiu2, Xiande Ma1, Yuan Yao3, and Qiang Chen1 1
Key Laboratory for Advanced Materials Processing Technology, Ministry of Education, Dept. of Mechanical Engineering 2 Dept. of Civil Engineering 3 Dept. of Automotive Engineering, Tsinghua University, Beijing 100084, China
[email protected]
Abstract. This paper proposed a design idea of a novel under-actuated finger mechanism, and analyzed its principle and designed the finger mechanism. The finger is designed based on a gear-rack mechanism, spring constraint and particular active middle-segment, which is passively adaptive in grasping objects. A new multi-fingered hand named as TH-3R Hand is designed based on the finger. TH-3R Hand has 5 fingers, 15 DOF. Its all fingers are similar. TH-3R Hand has many advantages: it is simple in structure, light in weight, easy in control and low in cost. TH-3R Hand can passively adapt different shapes and sizes of the grasped object. It can be mounted in humanoid robot hand to make the hand obtain more DOF with less actuators, and good grasping function of shape adaptation, decrease the requirement of control system. Keywords: humanoid robot, multi-fingered hand, passive adaptive grasp, under-actuated finger, gear-rack mechanism.
1 Introduction Humanoid robot must use its hands to take actions like a human. A human hand has many advantages, small volume, more fingers, more DOFs, strong grasp force, which make imitation of a human hand very difficult. In addition, all of the power supply, drivers, control system, sensors and information processing system are installed in the humanoid robot itself, which provides very strict requirement on many aspects, such as the weight, volume, power cost and real-time control as well as the humanoid appearance of the humanoid robot hand. Many robotic hands focus on simulating the overall appearance and action of a human hand while neglecting other equally important features such as the size, weight and real-time control. Conventional robotic devices are relatively complex, large, cumbersome and difficult to be installed in a humanoid robot arm. The complexity of conventional robotic devices also makes the hand be more expensive and difficult to manufacture and maintain. The special clamp in industry with 1 or 2 DOF are not competent in grasping objects with various shapes and sizes, since they have bad agility. In the recent 30 years, many achievements have been made in the research of dexterous robot hands. A dexterous robot hand has 3~5 fingers with 2~4 DOF in each finger, the joints of which are mostly active ones driven by actuators. Dexterous robot C. Xiong et al. (Eds.): ICIRA 2008, Part I, LNAI 5314, pp. 597–606, 2008. © Springer-Verlag Berlin Heidelberg 2008
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hands are capable of performing agile motions like human hands, including grasping objects and operating them. Examples of dexterous robot hands are Utah/MIT Hand [1], Shadow Dexterous C5 Hand [2], DLR Hand [3], Robonaut Hand[4], and domestic BH series hands by BUAA (Beijing University of Aeronautics and Astronautics) and HIT series hands by HIT (Harbin Institute of Technology). In most cases robot hands are only required to be able to perform grasping operation without being very agile. Thus under-actuated robot hands are more and more important in recent 10 years. The so-called under-actuated mechanism refers to that with drivers (such as motors) less than DOF of the joints. Under-actuated robot hands use less motors to drive more rotating joints, thus to simplify the mechanical structure, decrease the volume and weight and finally lower the difficulty of control and the cost. In the research of under-actuated robot hands, Laval University [5] in Canada, HIT [6], BUAA [7] and HIIM (Hefei Institute of Intelligent Machines) of Chinese Academy of Sciences, have made many achievements. HIT makes an under-actuated humanoid robot hand by four-bar linkage and springs, and BUAA by gear and friction decoupling devices. Tsinghua Univ. has developed humanoid robot hands with underactuated fingers named TH-1 Hand [8] and TH-2 Hand [9], separately. TH-1 Hand utilizes rotating board and accelerating gear-box mechanism to make an underactuated thumb. TH-2 Hand employs moveable slider and gear-rack to make underactuated finger units, which are placed in the 9 under-actuated joints of the hand. This paper designs a novel under-actuated finger mechanism using gear-rack and torsion spring, based on which TH-3R Hand is designed, with better self-adaptive grasping effect, more personified appearance and motions, and grasping function with mighty force by the distal phalanx.
2 The Under-Actuated Finger with Gear-Rack Mechanism 2.1 The Components of the Under-Actuated Finger The component of the novel under-actuated finger mechanism is shown in Fig. 1. The first joint-shaft is near the base, which is sleeved within the base; the lower part of the middle-segment sleeves the first joint-shaft; the second joint-shaft is far from the base, which is sleeved within the upper part of the middle-segment; the terminal segment sleeves the second joint-shaft. The active gear is fixed in the first jointshaft, while the passive gear is fixed in the second joint-shaft, and a rack meshes the active and passive gears. The two ends of the return spring connect the middle and terminal segments respectively. 2.2 The Motion Process of the Under-Actuated Finger The process of the finger grasping an object is like this: The motor inside the base rotates, driving the gear, and then the first joint-shaft rotates. Before the middlesegment touches the surface of the grasped object, the spring keeps the terminalsegment being static relative to the middle-segment as long as possible, resulting in rotation of the two segments as an rigid body around the first joint-shaft.
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Fig. 1. Sketch map of the principle of the under-actuated finger: 1-the base; 2-the first jointshaft; 3-the middle-segment; 4-the second joint-shaft; 5-the terminal-segment; 6-the active gear; 7-the rack; 8-the passive gear; 9-the return spring; 10,11-the first and second rotation
When the middle-segment is blocked by the grasped object and unable to continue rotating, the first joint-shaft drags the second joint-shaft through the gear-rack mechanism. The terminal-segment, fixed with the shaft, rotates against the elastic force of the return spring, until also touching the object. The process of the finger leaving the grasped object is like this: The motor rotates backward, driving the first joint-shaft, and finally the second joint-shaft. The deformation of the return spring turns smaller gradually, with the terminal-segment rotating backward to be originally straight. The first joint-shaft continues to rotate backward, until the middle and terminal segments turn back to the initial status as an rigid body. This under-actuated finger can be self-adaptive to the shapes and sizes of the grasped objects. According to the principle, multiple of this mechanism can be put in series to form fingers with 3, 4, or even more joints.
3 The Principle of the Under-Actuated Finger Fig. 2 shows the force analysis of the under-actuated finger when it grasps an object. O1O2 is the middle-segment, O2B the terminal-segment, O1 and O2 the centers of the first and second joint-shaft, respectively. Let O1O2=l1, O2B=l2. f1-the reaction force of the object against the middle-segment, whose magnitude is equal to the grasping force of the middle-segment to the object, N; f2-the reaction force of the object against the terminal-segment, whose magnitude is equal to the grasping force of the terminal-segment to the object, N; TM-the torque of the base joint motor to the active gear with regard to the point O1, motor torque for short, Nmm; TS-the torque of the return spring between the middle and terminal segments with regard to point O2, spring torque for short, Nmm; fM-the force of the active gear exerted to the rack caused by TM , whose magnitude is equal to the force of the rack to the passive gear, N; r1, r2- the radii of the active and passive gears, mm; θM-the rotational angle of the active gear, rad; θ1 - the rotational angle of the middle-segment, rad;
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θ2 - the rotational angle of the terminal-segment, rad; h1- the arm of force f1 with regard to point O1, mm; h2- the arm of force f2 with regard to point O2, mm. B
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Fig. 2. The force analysis of the under-actuated finger: 1-middle-segment; 2-terminal-segment; 3-base; 4-active gear; 5-passive gear
According to the force analysis, the moment of the whole finger with regard to point O1 is balanced, i.e. TM = h1 f1 + ( h2 + l1 cos θ 2 ) f 2
(1)
The terminal-segment and the passive gear is fixed together as a rigid body, the moment of which with regard to point O2 is balanced, i.e. TS + h2 f 2 = r2 f M
(2)
r1fM=TM is obvious. Let the radii ratio of the passive and active gear R=r2/r1, radii ratio for short, and we get h2 (1− R) − Rl1 cosθ2 ⎧ h + l cosθ2 TM + 2 1 TS , ⎪ f1 = h1h2 h1h2 ⎪ ⎨ ⎪f = RT − 1 T . ⎪⎩ 2 h2 M h2 S
(3)
When the finger grasps an object, f1>0 or f2>0 is required. f2>0 and that f2 is large enough are especially expected to realize the goal of large force by the terminalsegment. The grasping forces of the middle and terminal segment are analyzed respectively below. 1) According to eq. (3a), to get f1>0, the motor torque TM, the spring torque TS, and radii ratio R should satisfy ⎣⎡ h2 (1 − R ) − Rl1 cos θ 2 ⎦⎤ TM + ( h2 + l1 cos θ 2 ) TS > 0
(4)
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For different sizes of the grasped objects and various grasping angles, the tenable condition of eq. (4) is changed as a result. When the finger is designed, the extreme conditions should be considered, based on which the optimized conditions effective for various instances can be obtained. The introduction of the spring is to guarantee the under-actuation effect during the grasping process, i.e. the rotation of the first joint is prior before the second joint, and when the middle-segment is blocked by the contacting surface of the grasped object, the motor torque TM drives the terminal-segment rotate by the gear-rack mechanism. The deformation of the return spring counteracts a part of the motor torque. Generally speaking, the elasticity of the spring are selected to be moderate, making it just enough to gain the under-actuation effect, not too large to lost too much the torque acted on the terminal-segment. Thus, the spring torque TS is very small compared to the motor torque TM, and might as well be omitted. As a result, eq. (4) is approximately equivalent to
h2 (1 − R ) − Rl1 cos θ 2 > 0
(5)
To obtain f1>0, eq. (5) should be satisfied. In eq. (5), the radii ratio R, the length of the middle segment l1 are determined after the finger is made, while the arm of the force of the terminal-segment h2 is related to the size, shape, relative location, and grasping angles θ1 andθ2. For instance, suppose h1=l1/2, h2=l2/2, and the lengths ratio of the segments S=l2/l1, and eq. (5) yields
S (1 − R ) − 2 R cos θ 2 > 0
(6)
Commonly, l2≤l1, r2
