IROS2019国际学术会议论文集Design of a 3-DOF Linkage-Driven Underactuated Finger ultiple Grasping

Abstract This paper presents a 3-DOF linkage-driven underactuated finger for achieving several different grasp modes. This finger mechanism is constructed by stacking one five-bar mechanism over one double parallelogram. This special architecture allows for installing all of the actuators on the base. A 2-finger robotic gripper having three actuators is developed for performing self-adaptive power grasping, parallel precision grasping, grasping during contact with the environment, and other grasping tasks through changing the orientation of the distal phalanx actively. The performance of the gripper is confirmed through both simulation and practical grasping experiment. I. INTRODUCTION So far, many different types of robotic hands have been developed to grasp a large variety of objects. To match the dexterity of human hand, numerous anthropomorphic hands with multiple degrees of freedom (DOF) and multiple actuators have been designed. The pioneer designs include: the Utah-MIT hand 1, the Shadow hand 2, the DLR hand 3, and many others. The aforementioned robotic hands have high dexterity to perform multiple grasping tasks. However, the design is bulky, the manufacturing is costly, and the control architecture is complex. Thus, in the meaning time, a lot of effort have been put into the design of robotic hands with simple mechanical and control architecture while relatively preserving the ability of versatile grasping. To this end, underactuated grippers/hands have received a particular attention in recent years. Compared with fully actuated hands, underactuated hands, or often referred to as self-adaptive, adaptive, hands reduce the number of actuators without decreasing the number of DOFs 4-6. The passive elements like springs or mechanical limits are commonly used to adapt the finger to the shape of the object to be grasped automatically. *Research supported by the Technology Innovation Program (or Industrial Strategic Technology Development Program) (20001856, Development of robotic work control technology capable of grasping and manipulating various objects in everyday life environment based on multimodal recognition and using tools) funded By the Ministry of Trade, Industry linkage-driven mechanism 13-19; gears 20-23; or some other combinations 24, 25. In addition to the above robotic hands used for grasping medium and large-sized objects, some researchers also proposed suitable designs for grasping and manipulation of small objects lying on flat surfaces 26, 27. Tendon-driven mechanisms have advantages of light weight and good adaptive property to envelop the object to be grasped. And all of the actuators can be remotely located at the base (palm) even for fully actuated fingers. Hence, less inertia would be added to the finger. However, the cable strength and pretension force on the cable may restrict the transmission force and the tendon has the possibility of loosening during operation. Thus, tendon-driven robotic hands generally are used to grasp objects with relatively light weights 28. Comparatively, rigid linkages can be used to transmit large force and the linkage-driven robotic hand has higher safety. However, linkage-driven robotic hands in general have smaller workspace than the tendon-driven or gear based robotic hands due to the interference of the planar linkages (the four-bar and five-bar mechanisms are frequently used to compose the linkage-driven robotic hand). Furthermore, to fully actuate a 3-DOF linkage-driven robotic finger with high dexterity, not all of the actuators can be placed on the base in general. Thus, large inertia will be added to the finger. This paper presents a linkage-driven finger which is constructed by combining a double parallelogram and a five-bar mechanism. Due to the special kinematic structure of the 3-DOF robotic finger, all of the actuators can be installed on the base even for fully actuation. Firstly, kinematic structure of the proposed finger mechanism is described in section II, followed by the grasping sequence analysis. Then, a 2-Finger robotic gripper having three actuators is developed and the three independent motions are illustrated in section III. In section IV, different types of grasping modes, such as the parallel precision grasping, self-adaptive power grasping, grasping during contact with the environment, and other versatile grasping tasks, are analyzed and verified through experiments. II. DESIGN OF UNDERACTUATED FINGER A. 3-DOF Linkage-Driven Robotic Finger Linkage-driven robotic fingers with three phalanxes have been widely investigated in last few decades. To the best of our knowledge, 3-phalanx fingers which can be fully actuated by placing all of the actuators on the base have been rarely reported. In this paper, we propose a linkage-driven robotic finger with three phalanxes as shown in Fig. 1(a). It is Design of a 3-DOF Linkage-Driven Underactuated Finger for Multiple Grasping* Long Kang, Jong-Tae Seo, Dukchan Yoon, Sang-Hwa Kim, Il Hong Suh, IEEE Fellow, and Byung-Ju Yi, Member, IEEE 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) Macau, China, November 4-8, 2019 978-1-7281-4003-2/19/$31.00 2019 IEEE5608 remarked that this finger mechanism is constructed by stacking one five-bar mechanism over one double parallelogram mechanism. This planar mechanism has three DOFs, which can be fully controlled by using three actuators to control the three independent links ( 1 l, 2 l, 3 l) pivoted to the same joint axis as shown in Fig. 1(a). B. Design Architecture of Underactuated Robotic Finger As mentioned above, this 3-phalanx robotic finger can be fully actuated to achieve high dexterity. However, in this work, we focus on designing an underactuated robotic finger which can perform both precision and power grasping with relatively simple control strategies. The schematic of the underactuated finger is illustrated in Fig. 1(b). It can be found that the active link 1 l determines the orientation of the distal phalanx. The active link 2 l is used to control the open-close motion of the finger as shown in Fig. 2. To achieve the self-adaptive grasping, the link 3 l should be designed as a passive link to adjust different shapes of the grasped objects. One torsion spring is placed between the intermediate and proximal phalanxes to prevent the free rotational motion between them when no object makes a contact with the proximal phalanx. And one mechanical stopper is provided to prevent the excessive hyperextension of the finger (the maximum angle between the proximal and intermediate phalanxes is designed as 135 in this work). The grasping sequence can be explained as: The initial configuration of the finger is assumed to be far away from the object to be grasped. When the link 2 l is actuated, the proximal and intermediate phalanxes will move together as a single rigid body and the angle between them is maintained to be maximum if no external force is applied to the proximal phalanx. In this case, the precision grasping can be achieved as shown in Fig. 2(a). When the proximal phalanx makes a contact with the object, the continuous close motion will force the intermediate phalanx to move with respect to the proximal phalanx (from II to III in Fig. 2(b), i.e., the relative angle between proximal and intermediate phalanxes will be decreased to achieve the self-adaptive power grasping. After this phase, the orientation of the distal phalanx can be adjusted by controlling the link 1 l (from III to IV in Fig. 2(b) to achieve more stable power grasping if necessary. During this self-adaptive grasping phase, the actuator needs to produce additional actuation torque to twist the torsion spring. Thus, the stiffness of the torsion spring should be designed as small as possible, but sufficient enough to prevent the underactuated finger from collapsing. Furthermore, a preloading of the torsion spring is designed with the help of the mechanical stopper to avoid any undesirable motion due to the weight and inertia effects of the underactuated finger. III. DESIGN OF UNDERACTUATED ROBOTIC GRIPPER The proposed 3-DOF linkage-driven finger can be used to develop multi-finger hands with remote actuation. In this section, design of an underactuated gripper with two fingers is presented in detail. The developed underactuated gripper can be used to perform parallel pinching, non-parallel pinching, adaptive power grasping, and other versatile grasping tasks. A. Structure Description A gripper having two underactuated fingers is illustrated in Fig. 3. This gripper has three actuators. One actuator with large capacity is used to drive the open-close motion of the two fingers synchronously by using one common worm and two worm wheels (yellow color shown in Fig. 3) as the transmission mechanism. The other two actuators with small capacity are used to control the orientation of the distal phalanx of each finger, respectively, by using the worm gear (green color shown in Fig. 3) as the transmission mechanism. All of the motors are fixed inside the palm without increasing any inertia to the finger. The worm gear is used as the self-locking transmission mechanism because it is not back-drivable and thus can provide the safety grasping even when no power is applied. The specifications of the actuation Figure 1. (a) Schematic diagram of the 3-DOF linkage-driven robotic finger. (b) Underactuated finger having one torsion spring, one mechanical stopper, and two actuators. Figure 2. Grasping sequence of the underactuated finger. Figure 3. 2-finger underactuated gripper in CAD. 5609 system, including both motors and worm gear reduction ratios, are shown in Table I. And referring to Fig. 1(a), the detailed kinematic parameters of the finger are shown in Table II. The spring constant of the torsion spring shown in Fig. 1(b) is designed around 0.11 N. mm/deg. TABLE I. SPECIFICATION OF THE ACTUATOR DRIVING SYSTEM Motor 1 Motor 2 Motor 3 Motor type FAULHABER 1724T012SR FAULHABER 1717T012SR FAULHABER 1717T012SR Gearbox ratio 66:1 43:1 43:1 Worm gear ratio 30:1 20:1 20:1 Rated torque 4.5 mNm 2.1 mNm 2.1 mNm TABLE II. KINEMATIC PARAMETERS OF THE FINGER Length (mm) Length (mm) Angle (deg) AE 23.0l= BF 23.0l= KBC 135= FBG 45= KBA 135 (constrained by the stopper) AD 54.0l= BG 20.0l= AB 72.0l= BK 48.0l= BC 20.0l= GH 48.0l= CD 54.0l= KH 20.0l= EF 72.0l= KI 40.0l= B. Independent Output Motion As mentioned above, three actuators are employed to control the three independent output motions of this underactuated gripper. The most powerful actuator is used to control the open-close motion of the two fingers synchronously. The motions of proximal and intermediate phalanxes are coupled with each other due to the combined effects of underactuated architecture, torsion spring, and mechanical stopper. When there exists no contact at the proximal phalanx, the parallel precision grasping can be achieved as shown in Fig. 4. When there exists a contact at the proximal phalanx, the relative angle between proximal and intermediate phalanxes will be decreased to achieve the self-adaptive power grasping as shown in Fig. 5. The other two less powerful actuators are used to control the orientation of the distal phalanx of each finger, respectively, as shown in Fig. 6. C. Analysis of Precision Grasping Force As mentioned above, this gripper can perform precision grasping by using the most powerful actuator to control the open-close motion of two fingers as illustrated in Fig. 4. The precision grasping force can be evaluated by deriving its relationship with the actuation torque 29. Applying the principle of virtual work to the precision grasping model shown in Fig. 7(a), we have a =f v (1) where f represents the contact force, v is velocity of the contact point, a is the actuation torque exerted on object by the input link 2 l, and represents the open-close angle of the finger with respect to the horizontal axis as shown in Fig. 7(a). As the distal phalanx moves as a rigid body, every point on the distal phalanx has the same velocity. During precision grasping, the motion of point K follows a circular trajectory with the center located at point A, as shown in Fig. 7(b). The linkage P OAKP forms a parallelogram. Then the motion of the contact point P follows a circular trajectory with the center located at point P O. The velocity of the contact point P can be found as AK vl= (2) Referring to Fig. 7(a), we have sinfv=f v (3) Figure 4. Open-close motion of the gripper. Figure 5. Self-adaptive power grasping sequence. (a) Start contact with the object. (b) After finishing self-adaptive grasping. Figure 6. Adjust the orientation of the distal phalanx of each finger. (a) Before changing. (b) After changing. 5610 By substituting (2) and (3) into (1), the parallel pinch force can be found as () AKsina fl= (4) Considering the efficiency of the driving system, the actuation torque exerted on the object by the input link 2 l can be derived as 2 am m wmw r r = (5) where m is the output motor torque. m r and w r are the gear ratio of the motor gearbox and the gear ratio of the worm gear respectively. m and w are the efficiency of the motor gear box and the efficiency of the worm gear, respectively. The actuator capacity could be selected in accordance with the task requirement by using the above relationship between the grasping force and the actuation torque. IV. EXPERIMENTAL EVALUATION To validate the proposed design, a gripper prototype was manufactured in aluminum alloy. Different types of grasping modes, such as parallel grasping, self-adaptive power grasping, and environmental contact-based grasping are analyzed and verified experimentally through integration with a commercially available 6-DOF robot arm. The parallel precision grasping is shown in Fig. 8. It can be found that this gripper has a wide span to grasp a variety of objects with different sizes. The maximum payload is around 2.5kg and the maximum span of the gripper is around 260mm. Fig. 9 shows the self-adaptive power grasping. When the grasped object makes a contact with the proximal phalanx, continuing activating the powerful actuator will make the intermediate phalanx bend with respect to the proximal phalanx until it contacts with the grasped object. Fig. 10 demonstrates grasping different objects with the help of the pinch motion of the distal phalanx. The object illustrated in Fig. 10(a) lies above the supported base, i.e., there exists spare space between the object and the base. Actively controlled pinch motion allows the finger to scoop the object up from the bottom side. The bowl-like object in Fig. 10(c) was grasped in a similar manner. Fig. 10(b) shows one example of grasping object through making contacts at two distal phalanxes and the palm. The Fig. 10(d) and (e) demonstrates the success of grasping objects with cone shape. It is noted that the grasping illustrated in Fig. 10(e) is not that stable and can only be used to grasp light objects due to the force closure of the grip force. Fig. 10(f) demonstrated using the closed distal phalanx to grasp objects having lifting ears. Fig. 11 illustrates the sequence of grasping a bowl-like object. As explained above, the orientation of the distal phalanx is decoupled and independently controlled by the actuator with small capacity. Thus, during the parallel grasping sequence, the distal phalanx can be maintained at the desired orientation even when it makes a contact with the external environment accidently. In this case, even though a collision happens, it is still possible to continue performing parallel grasping, i.e., Environmental contact-based parallel grasping. Because of the Figure 7. Parallel grasping model and kinematic simulation of the finger. Figure 8. Parallel grasping during contact with an environment. (a) When the fingertip initially makes a contact with the supported surface. (b) State when the parallel grasping is done. Figure 9. Reference state when the gripper moves upward with the robot arm but still in contact with the supported surface. Figure 8. Examples of Parallel grasping. Figure 9. Examples of self-adaptive power grasping. Figure 10. Examples of grasping by employing the pinch motion of distal phalanx. Figure 11. Sequence of grasping a bowl-like object. 5611 torsion spring, when the gripper is trying to leave the contact surface, the gripper might open, then the grasped object will fall down. There are several approaches which could be employed to solve this problem, such as installing a magnetic brake at the base joint connected to the proximal phalanx or installing an anti-moving back mechanism at the underactuated joint (i.e., the joint connected to the proximal and intermediate phalanxes) such as a rachet mechanism to preserve the angle between the proximal and intermediate phalanxes. However, in this prototype, we are trying to use a control algorithm-based method to simplify design. As the gripper is attached to a robot arm, we need to control the lifting speed of the robot arm and the closing speed of the gripper. It is necessary to ensure that the closing speed is faster than the opening speed caused by the lifting before the whole gripper completely leaves the contact surface. Then, the parallel grasping might be secured. Fig. 12 shows the sequence of parallel grasping during contact with the supported base. As the mathematical model presented in the last section, the closing speed of the gripper was controlled to be comparatively faster than the lift speed of the robot arm before the whole gripper completely leaves the supported surface. More details of the experiments can be referred to the video uploaded along with this manuscript. V. CONCLUSION In this paper, a 3-DOF