Robotics is a multi-disciplinary research filed of mechanical engineering, electrical engineering, computer science, etc.[1–6] A robot′s hand is an important part of the robot because most of its functions are achieved through hand operations. A robot hand generally should have more joint freedoms for a better and higher anthropomorphic performance. At the same time, to reduce the difficulty of controlling the robot hand, as well as its volume and weight, it is necessary to minimize the number of drives. Designing a robot finger with an underactuated mechanism can meet these two requirements simultaneously and allow the robot finger to adaptively grasp objects with different shapes and sizes. An underactuated robot finger also has less control difficulty and a lower production cost, and the feature of self-adaptive grasping is also suitable for envelope grasping and strong grasping. Thus, an underactuated finger mechanism has become an important aspect of a robot hand.
At present, the mainstream of the underactuated mechanical fingers are divided into two types, which are tendon driven and link driven. The tendon and link driven are the two main types of underactuated fingers, but the link driven is better than the tendon driven. Ceccarelli et al.  proposed numerous underactuated fingers based on the link driven, which uses a combination of a linear spring and a torsion spring to achieve the passive mechanical limit of the free joint. The link driven finger has many advantages such as a large output force, strong load capacity, and compact structure.
At present, domestic and foreign institutions have developed various link driven robot hands. For example, the self-adaptive robotic auxiliary hand (SARAH) underactuated hand (Fig. 1 (a)) developed by the Canadian MD ROBOTICS company and the University of Laval has been successfully applied in operations at the international space station[10, 11]. An underactuated robot hand was designed by Nazarbayev University (Fig. 1 (b)). The multiple passive joints (MPJ) hand developed by Tsinghua University and Beihang University in 2016 (Fig. 1 (c)) also uses a linkage driven mechanism. However, there are also many problems with this method, including a complex mechanism, a large size, and high manufacturing and maintenance costs.
The cost of machining a prototype is high, and it is not conducive to updating the parts in the design process. Producing parts by 3D printing not only greatly reduces the costs, but also increases the flexibility of the design, because it makes it easy to update parts at any time. At present, an increasing number of research institutions have chosen 3D printing to manufacture prototypes such as the Open Hand designed by Yale University (Fig. 1 (d)), underactuated robot hand designed by Nazarbayev University (Fig. 1 (b)), and robot hand designed by the National University of Singapore (Fig. 1 (e)). However, the need to add support for floating parts when using 3D printing[16, 17] will affect the accuracy and strength of the parts, and it also requires further post-processing to remove the supports.2 Underactuated finger and its improvement
The finger designed in this study is a full rotation joint-linkage underactuated finger proposed by our research group[18, 19]. As shown in Fig. 2 (a), the finger mechanism consists of eight links and two springs. Link 1 is the base, links 2, 6 and 8 respectively represent Phalanx 1, Phalanx 2 and Phalanx 3. Points A, B, C, D, D, E, F, G and H are rotational joints. Spring 1 is fixed between links 3 and 4, while Spring 2 is fixed between links 5 and 7. The motor is mounted at point B to drive link 3.
It was found that the CD link could easily contact the shaft that fixed the DE link, which significantly reduced the grasping range of the finger. In order to avoid that situation, we changed the DE link from a straight link to triangular link DD′E (Fig. 2 (b)). This made it possible to avoid the above situation. Besides, this change allowed the link mechanism to remain inside the finger during the movement. It also increased the movement space of the fingers, and facilitated the integration of the robot hand and robot arm.3 Three-finger robot hand design 3.1 Finger design
In this paper, the hand can be divided into the fingers and palm. The main function of the fingers is to grasp an object. The main function of the palm is to determine the distribution position of the fingers. The sizes of the entire finger and each phalanx were designed according to the 1:1 ratio found in a human index finger. The designed sizes of the phalanxes are listed in Table 1. We designed the finger 3D model (Fig. 3) according to the finger mechanism (Fig. 2 (b)). Here, A and B are fixed points; points E, F and G, whose positions relative to the joints are fixed, are connected to the phalanxes by the shaft; and the BC link is designed to allow the right angle link to facilitate the suspension of the spring.
The finger connecting link mechanisms BCADE and ED′H are relatively independent as a result of using the triangular link DD′E. As long as the relative position between E and the second phalanx is constant, the relative distance between points D and E does not affect the relative trajectory of point D′ with the second phalanx in motion. In other words, the relative motion trajectory of point D′ and the second phalanx has point E as the center of the circle, with ED′ as the radius of the arc. In a similar way, the relative distance between points D′ and E does not affect the relative trajectory of point D with the first phalanx in motion. Thus, the use of triangular link DD′E cannot only solve the problem of the link mechanism hiding inside the fingers, but also increase the flexibility of the finger designed.
The end of the finger part consists of the D′H link, DH link, and triangular link ED′D. To ensure that the finger has the underactuated characteristic, the elastic deformation of Spring 2 should be in an increasing state during the movement when the second phalanx contacts the object. The second phalanx will no longer move after it contacts the object, but the third phalanx continues to move. Then, the trajectory of point H (Fig. 4) should be a circular arc that has the center G. And the radius of the arc is the initial distance of GH. At the same time, the angle change between ED′ and D′H determines the elastic deformation of Spring 2, and the elastic deformation of the spring increases as ∠ED′H increases. ED′ and D′H are fixed in length, with a greater distance for EH leading to a greater ∠ED′H. In the unconstrained state, the trajectory of the H point should be an arc with E as the center and EH as the initial distance. To ensure that distance EH is increasing during motion, the part of Arc 4 after H point should be on the right side of Arc 3. The simulation results showed that the size of the link listed in Table 2 reached the above conditions.
3.2 Grasping simulation for finger
The 3D model of the finger was created by using Solidworks, and all parts for grasping were analyzed using the MOTION module. This study simulated the process of grasping a variety of objects with different radii, which could be used to determine the radius of an object during the grasping process. At the same time, the study simulated the grasping process for two cylinders with different radii, and analyzed their changing phalanx angle curves during each grasping process, along with the motor torque and contact force.
Because the movement of the finger during the motion simulation was slow, the inertial force was not considered. In addition, this study only considered the contact force between the finger and object, and ignored the friction between joints. To make the movement of the finger easier to observe, the rotational speed of the driving link (BC) was 1 rad/s in all the simulations reported in this paper.
It was estimated that the elastic coefficient of Spring 1 was 2.00 N/mm, and the damping coefficient was 10.00 N/(mm/s). The elastic coefficient of Spring 2 was 1.00 N/mm, and the damping coefficient was 0.20 N/(mm/s). The finger could move stably under these parameters. The recovery coefficient between the finger and object was set to 0, which meant the contact between the finger and object was a completely inelastic collision.3.2.1 Grasping performance of finger with different size objects
This paper simulated the process of grasping small and large objects. In Fig. 5, the finger had good envelope grasping performance for an object with a diameter equal to 0.106 times (i.e., 10 mm) the finger length (excluding the base). Moreover, the finger could effectively grasp an object whose diameter was equal to 0.851 times (i.e., 80 mm) the finger length (excluding the base).
The following section discusses how the grasping processes for these two kinds of cylinders in different positions were simulated. This study analyzed the coherence, grasping force changing curve, final grasping force, and relationship between the grasping force of the finger and the motor output torque to verify the performance of the finger.3.2.2 Grasping performance of finger on smaller object
In Fig. 6, a Cartesian coordinate system is shown with point B as the origin, where the horizontal extension direction of the finger is the X axis. The simulations were divided into two situations: one where the object was located in an easy grasping position and the other (limit position) where the object was located in a difficult grasping position. With the easy grasping position, Phalanx 1 was near the middle of the phalanx bottom, and the finger could touch the object after rotating by a small angle. The limit position referred to a position where the object was at the phalanx root.
|Fig. 6. Grasping process for cylinder with diameter of 10 mm at easy grasping position|
22.214.171.124 Grasping performance of finger on smaller object at easy grasping position
The object grasped was a rigid cylinder with a diameter of 10 mm, and the coordinate of the center of the circle was in the easy grasping position (19.98 mm, –20.90 mm). The grasping process is shown in Fig. 6, where points 1, 2 and 3 are the contact points between the phalanxes and object.
In Fig. 6, the finger envelops the object by contacting it gradually. In Fig. 7 (a), the final rotation angles of Phalanxes 1, 2 and 3 are 26.51°, 162.01° and 194.5°, respectively. Points 1, 2 and 3 in Fig. 6 are the contact points between the phalanxes and object. These contact points constitute a static grasping of the object. It can be seen that the phalanxes have no abrupt change in angular displacement during the grasping process, and the finger movement is stable. As a result, the finger showed good motion coherence and stability in the simulation.
|Fig. 7. Changing curve of cylinder with diameter of 10 mm at easy grasping position|
In Fig. 7 (b), when Phalanx 1 touches the object, the contact force between Phalanx 1 and the object increases rapidly, and then increases gradually, at which point the other phalanxes do not contact the cylinder. When Phalanx 2 contacts the object, the contact force between Phalanx 2 and the object increases rapidly. When Phalanx 3 contacts the object, the contact force between Phalanx 3 and the object will increase with the motor torque. The motor torque was not fixed, but the rotational speed of the drive was set in the simulation process. Therefore, the motor torque was constantly changing, while the rotational speed of the drive was maintained at 1 rad/s. After the completion of the grasping, if the motor torque continued to increase to 29.00 N·mm, the grasp was completed with phalanx contact forces of 4.80 N, 1.61 N and 4.89 N. During the grasping process, the contact force of Phalanx 1 in individual contact with the object first increased and then decreased because the displacement of Spring 1 increased in this process, and a portion of the energy was stored in Spring 1. The contact force of Phalanx 1 increased rapidly after Phalanx 2 contacted the object because Phalanxes 1 and 2 were distributed on both sides of the object, which constituted an opposite side clamping state. The contact force of Phalanx 2 first increased and then decreased because Spring 2 stored part of the energy during the movement.
In Fig. 7 (c), because the mass of the finger is not considered, the initial motor torque is 0, and the motor torque increases as the finger contacts the object. Phalanx 2 contacts the object at Position 2, and then the motor torque increases until Phalanx 3 touches the object. Generally, a small direct current (DC) micro-motor output torque is approximately 3 000 N·mm. If the maximum output torque is used, the force of the finger on the object could be approximately 500 N, while generally that of an adult male finger is approximately 100 N, and the tendon-driven finger force is approximately 50 N. Therefore, the finger could generate a large grasping force.126.96.36.199 Grasping performance of finger on smaller object at limit position
The object grasped was a rigid cylinder with a diameter of 10 mm, and the coordinate of the circle center (the coordinate system was the same as that of Fig. 6) was in the easy grasping position (–2.88 mm, –26.17 mm). The finger enveloped the object by contacting it gradually. The final rotation angles of the phalanxes were 67.83°, 196.24° and 264.50°. It can be seen that the phalanxes showed no abrupt change during the grasping process. Thus, it showed good motion coherence and stability in the simulation. The grasping process is shown inFig. 8, and points 1, 2 and 3 are the contact points.
|Fig. 8. Grasping process for cylinder with diameter of 10 mm at limit grasping position|
When Phalanx 1 touched the object, the contact force between Phalanx 1 and the object increased rapidly, and then increased gradually, at which point the other phalanxes did not contact the cylinder. When Phalanx 2 contacted the object, the contact force increased rapidly between Phalanx 2 and the object. And then, when Phalanx 3 contacted the object, the contact force between Phalanx 3 and the object increased with the motor torque. Finally, after the completion of the grasping, if the motor torque continued to increase to 30.40 N·mm, the grasping was completed with phalanx contact forces of 7.50 N, 2.17 N and 15.00 N.
As shown in Fig. 9 (b), when Phalanx 1 touches the object, the contact force between Phalanx 1 and object increases rapidly, and then increases gradually, at which point the other phalanxes do not contact with the cylinder. When Phalanx 2 contacts the object, the contact force between Phalanx 2 and object increases rapidly. When Phalanx 3 contacts object, the contact force between Phalanx 3 and object increases as the motor torque increased. After the completion of the grasping, if the motor torque continues to increase to 30.40 N·mm, the grasp will complete when the contact force of the phalanxes are 7.50 N, 2.17 N and 15.00 N. The contact force of Phalanxs 1 and 2 are reduced in the process of movement while Phalanx 2 has stopped during movement. The reason is that a part of drive force serves to overcome the pulling force of Spring 2, for driving Phalanx 3 to continue moving. And then the contact forces of three phalanxes increase, because the finger completes the envelope grasp, and Phalanxs 1 and 3 are distributed on both sides of the object which amounts to opposite side clamping state. As shown in Fig. 9 (c), since the mass of the mechanism is not considered, the initial motor torque is 0, and the motor torque increases as the finger contacts object. Phalanx 2 contacts the object at Position 2, and then the motor torque rises until Phalanx 3 touched the object.
|Fig. 9. Changing curve of cylinder with diameter of 10 mm at easy grasping position|
3.2.3 Grasping performance of finger on larger object
Because the cylinder with a diameter of 80 mm was large relative to the finger, the position of the cylinder had little effect on the grasping performance. Therefore, this study only simulated one position for the cylinder with a diameter of 80 mm.
The coordinate of the center of the circle (the coordinate system was the same as that shown in Fig. 6) was at a position (58.98 mm, –50.11 mm) that allowed the finger to touch the object after turned a small angle, and the first contact point was on Phalanx 1. The grasping process is shown in Fig. 10, and points 1, 2 and 3 are the contact points.
In Fig. 11 (a), the final rotation angles of the phalanxes are 8.60°, 38.72° and 64.52°. In Fig. 11 (b), if the motor torque continues to increase to 8.87 N·mm, the contact forces will finally be 0.10 N, 0.16 N and 1.08 N. After Phalanx 2 contacts the object, the contact force between Phalanx 1 and the object becomes smaller. The reason is that Spring 1 stores a part of the energy. Similarly, the contact force between Phalanx 2 and the object becomes smaller when Phalanx 3 contacts the object. The reason is Spring 2 stores a part of the energy.
The motor torque continues to increase after Phalanx 2 contacts the object until Phalanx 3 contacts the object. However, the motor torque drops when Phalanx 3 contacts the object. This is because the object is larger than the finger, which triggers the roll-back phenomenon because the root phalanx tends to separate from the object when the grasping force is increased. In Fig. 12, if the rotation is continued, the phalanx will separate from the object.
3.3 Palm design
To meet the needs of grasping, this study designed a robot palm that could change a finger′s position. The bottom of the palm was designed with a finger displacement device that could flexibly adjust the finger position.
As seen in Fig. 13 (a), the robot hand consists of three fingers and a palm. Fingers 1 and 2 can be driven by a pair of gears to achieve rotation, and the position of finger 3 is fixed. Because the two sides of the fingers are free to turn, the robot can achieve more grasping positions, with six possible kinds of grasping modes, in addition to the main mode of human grasping (Fig. 13 (b)).
The three-dimensional design of the robot hand is shown in Fig. 14 (a). The robot hand has 10 degrees of freedom and 4 input drivers. Each finger has a drive motor, and the palm is equipped with a motor. The drive motor is placed at the bottom of the palm. In order to ensure the efficiency of the robot hand, some of the necessary gears still need to use metal gears to ensure the accuracy and strength of the gear, using of standard gear can also reduce costs effectively. The parts of hand are produced by 3D printing except for gears, screws, optical axis and springs. However, 3D printing will add support for the floating part, so it will affect the accuracy and strength of parts, and it also needs further post-processing in order to remove the support of printed parts. So we try to avoid this situation in design. We finally produce a higher accuracy prototype hand (Fig. 14 (b)) by 3D-print, while the costs are significantly reduced.
4 Verification experiment for robot hand performance
A PC is used for motion control. On the base of research work, a prototype of underactuated robot hand has been designed. A smart control system has also been developed with the purpose to examine the research works in experiments. And we can control this hand in real time through the control system.
The robot hand′s performance of grasping objects with different sizes is shown in Fig. 15. Figs. 15 (a)–15 (c) show the performance of the robot hand while grasping large (232 mm × 63 mm), medium (97 mm×38 mm), and small (81 mm×19 mm) cylindrical objects, respectively. Fig. 15 (d) shows the performance of the robot hand while grasping irregular columnar objects. Figs. 15 (e) and 15 (f) show the performance of the robot hand while grasping large (diameter: 136 mm) and medium (diameter: 68 mm) size spherical objects, respectively. Fig. 15 (g) shows the performance of the robot hand while grasping an irregular shaped object. And Fig. 15 (h) shows the performance of the robot hand while grasping a fragile object such as a raw egg. The degree of bending of each finger depends on the shape of the object.
To verify the reliability of the grasping, we shook the hand heavily to test the grasping reliability after the grasping was completed. The results showed that the robot hand could perform stable grasping (a video of this experiment can be seen in ). We also conducted an experiment with raw eggs (Fig. 15 (g)), and the results showed that the robot hand could stably grasp raw eggs without damaging them, which meant the fingers had good underactuated characteristics, the mechanism was reasonable, and the spring parameters were moderate.5 Conclusions
In this study, the linkage for an underactuated mechanical finger proposed by our research group was improved. The rationality of the size design was verified by simulations. We use Solidworks to simulate the grasp operation of the finger in different situations, which can be used to analyze the range of the grasping, the underactuated characteristic, the coherence of motion and the mechanical property. It is simulated that the full rotation joint-linkage of underactuated finger designed by the mechanism according to Fig. 2 (b) can achieve good motion coherence and stability grasping. The finger can achieve suitable capability for grasping the cylinders whose diameter is between 0.106 and 0.851 respecting to the finger length which means the finger has a large grasping range. And the finger can produce 5 times of hand grasping force by using the small electric motor which means the finger can produce a larger grasping force. And links are maintained within the phalanxes in various situations of grasping process which means the finger has a compact structure in whole process. The palm of a robot hand was designed, which could change the relative positions between the fingers and increase the grasping range. 3D printing technology was used to produce a prototype, which allowed parts with a certain degree of flexibility. We designed the parts of the hand using Solidworks, and the design met the principles of 3D printing, which has advantages such as a low cost and design flexibility. Finally, we conducted experiments to verify the hand performance. The experimental results showed that the robot hand could stably grasp objects with different sizes, and verified the rationality of the design and the feasibility of fabricating the robot hand using 3D printing.Acknowledgements
This work was supported by National Natural Science Foundation of China (Nos. 51375504 and 61602539) and the Program for New Century Excellent Talents in University.
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