Keywords

1 Introduction

The underactuated mechanical fingers who have little driver have some advantages such as simple structure, easy control and low manufacturing cost. And the underactuated mechanical fingers also have the good adaptive ability, which are good at enveloping grasp [1]. At present, the mainstream of the underactuated mechanical fingers are divided into two types, which are tendon drive and link drive. Linkage underactuated mechanical fingers have many advantages such as large output force, high load capacity, compact structure and so on. From the overall grasping effect, the performance of the link drive is better than the tendon drive [2]. At present, there are some literatures, such as paper [3], has a comprehensive simulated analysis on the grasping stability and mechanical properties of the tendon driven fingers in the process of grasping. Since the developing time is not longer, the analysis of the linkage underactuated fingers is still simple at present. Paper [4] only analyzed the contact force between the fingers and the objects, but the scope of the grab and others were not mentioned. Paper [5] which has added the stability of the fingers grab analysis, was not discussed the fingers stable grasping scope. Paper [6] estimated the fingers’ stable grasping scope, but did not analyze the relationship between grasping force and output torque. The overall analyses of linkage underactuated finger are important to test all aspects of the finger grasping performance and the finger design rationality, so it is necessary to proceed a comprehensive simulated analysis.

This paper simulates a linkage underactuated finger and analyzes the underactuated properties in the grasping process, motion coherence, mechanical property and so on, and the links whether inside the fingers in the process of the whole movement or not. And the paper also makes the quantitative analysis of the grasping scope and performance, so as to test the performance and rationality of the designed finger.

2 Full Rotation Joint-Linkage Underactuated Finger

The simulated finger of this paper is a kind of full rotation joint-linkage underactuated finger proposed by research group [7, 8]. In Fig. 1, the finger mechanism consists of eight links and two springs. Link 1 is the base, Links 2, 6, 8 respectively represent phalanx 1, phalanx 2 and phalanx 3. Points A, B, C, D, D, E, F, G, H are rotational joints. Spring 1 is fixed between link 3 and link 4 while Spring 2 is fixed between link 5 and link 7. The motor is mounted on the point B to drive link 3. Link DD’E uses a triangular structure (referenced in Fig. 2) to connect link DH and CD. The size of the overall finger and each phalanx are designed according to the ratio of 1:1 simulated by human index finger [9]. The designed sizes of each link bar and the phalanxes are as shown in Table 1.

Fig. 1
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The mechanism of full rotation joint-linkage underactuated finger

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Fig. 2
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Finger diagram and the position of link DD’E (Pureblack link)

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Table 1 The size of link and phalanx
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3 The Process and Results of Simulation

3.1 Settings of Simulation Parameter

The 3D model of finger is created by SolidWorks, and all parts of grasp are analyzed by the MOTION module. This paper simulates the process of grasping a variety of objects of different radius, which can be used to determine the radius of objects in grasping process. At the same time, the paper simulates grasping process of two different radius cylinders, and analyzes their changing curve of phalanx angle in each grasping process, torque motor and contact force.

Because the movement of the finger during the motion simulation is slow, the inertial force is not considered. And this paper only concerns the contact force between the finger and objects, and ignores the friction between joints. In order to make the movement of the finger easier to observe, the rotational speed of the driving link (BC) is taken as 1 rad/s in all the simulations in this paper.

It is estimated that the elastic coefficient of spring 1 is 2.00 N/mm and the damping coefficient is 10.00 N/(mm/s); the elastic coefficient of spring 2 is 1.00 N/mm and the damping coefficients 0.20 N/(mm/s). Finger can move stablely under this parameter. The recovery coefficient between the finger and object is set to 0, which means the contact between finger and object is the completely inelastic collision.

3.2 Grasping Performance of Finger on Different Size Objects

This paper stimulates grasping process of smaller object and bigger object. The finger has good envelope grasping performance on the object whose diameter equals to 0.106 times (i.e. 10 mm) of the finger length (excluding the base). And the finger can grasp the object whose diameter equals to 0.851 times (i.e. 80 mm) of the finger length (excluding the base) effectively.

In the following, the grasping process of these two kinds of cylinders in different position is emphatically simulated. And this paper uses the analysis of the coherence, grasping force changing curve, final grasping force, the relationship between grasping force of the finger and the motor output torque to analyze and verify the performance of the finger.

3.3 Grasping Performance of Finger on Smaller Object

In Fig. 3, the Cartesian coordinate is established with point B as the origin, and the horizontal extension direction of the finger is X axis. The simulation is divided into two situations, one is that the object locates in easy grasping position, another named limit position is that the object locates in difficult grasping position. The easy grasping position is that phalanx 1 near the middle of the phalanx bottom, and in the position where the finger can touch the object by rotating small angle. Limit position refers to the position where the object is in the phalanx root.

Fig. 3
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Grasping process of cylinder with a diameter of 10 mm at the easy grasping position

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3.3.1 Grasping Performance of Finger on Smaller Object at Easy Grasping Position

The object grasped is a rigid cylinder with a diameter of 10 mm, and the coordinate of the center of the circle is in the easy grasping position at (19.98−20.90 mm). Grasping process are as shown in Fig. 3, and point 1, 2, 3 are the contact points between phalanxes and object.

In Fig. 3, the finger envelops the object by contacting with the object gradually. In Fig. 4a, the final rotation angles of phalanxes 1, 2, 3 are 26.51°, 162.01° and 194.5°. Point 1, 2, 3 refered in Fig. 6 are the contact points between phalanxes and object. The contact points between each phalanx and object constitute a static grasping of the object. It can be seen that phalanxes have no abrupt change of angular displacement during the grasping process, and the finger movement is stable. As the result, the finger shows good motion coherence and stability in the simulation.

Fig. 4
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Changing curve of cylinder with a diameter of 10 mm at easy grasping position

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In Fig. 4b, 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 the phalanx 2 contacts the object, the contact force between phalanx 2 and object increases rapidly. When phalanx 3 contacts the object, the contact force between phalanx 3 and object increases as the motor torque increases. The motor torque is not setted while the rotational speed of the drive is setted in the simulation process. Therefore the motor torque is constantly changing while keeping the rotational speed of the drive is 1 rad/s. After the completion of the grasp, if the motor torque continues to increase to 29.00 N mm, the grasp will complete with the contact force of phalanxes are 4.80, 1.61 and 4.89 N. During the grasping process, the contact force of phalanx 1 in the individual contact with the object increases first and then decreases because of the displacement of spring 1 increases in this process and a portion of the energy is stored in spring 1. The contact force of phalanx 1 increases rapidly after phalanx 2 contacts object because phalanx 1, 2 are distributed on both sides of the object which amounts to opposite side clamping state. The contact force of the phalanx 2 first increases and then decreases, because the spring 2 stores part of the energy during the movement.

In Fig. 4c, since the mass of the finger is not considered, the initial motor torque is 0, and the motor torque increases as the finger contacts object. Phalanx 2 contacts object at position 2, and then the motor torque rises until phalanx 3 touches the object. Generally small DC micro-motor output torque is about 3000 N mm. If the maximum output torque is used, the force of the finger on the object can be about 500 N while general adult male finger force is about 100 N[10], and the Tendon-drive finger force is about 50 N [4, 11]. Therefore the finger can generate a large grasp force.

3.3.2 Grasping Performance of Finger on Smaller Object at Limit Position

The object grasped is a rigid cylinder with a diameter of 10 mm, and the coordinate of the circle center (The coordinate system is the same as Fig. 3) is in the easy grasping position at (−2.88, −26.17 mm). The finger envelops the object by contacting with the object gradually. The final rotation angles of phalanxes are 67.83°, 196.24° and 264.50°. It can be seen that phalanxes have no abrupt change during the grasping process. So it shows a good motion coherence and stability in simulation.

When phalanx 1 touches the object, the contact force between phalanx 1 and object increases rapidly, and then increases gradually, at which point other phalanxes do not contact with the cylinder. When phalanx 2 contacts 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 increases. After the completion of the grasping, if the motor torque continues to increase to 30.40 N mm, the grasp will complete with the contact force of the phalanxes are 7.50, 2.17 and 15.00 N.

3.4 Grasping Performance of Finger on Bigger Object

Because the cylinder with a diameter of 80 mm is large relative to the finger, the position of cylinder has little effect on grasping effect, so this paper simulates only one position of the cylinder with a diameter of 80 mm.

The coordinate of the center of the circle (The coordinate system is the same as Fig. 3) is in the position at (58.98, −50.11 mm), where the finger can touch the object by rotating small angle, and the first contact point is on phalanx 1. Grasping process are as shown in Fig. 6, and points 1, 2, 3 are the contact points.

In Fig. 5a, the final rotation angles of phalanxes are 8.60°, 38.72° and 64.52°. In Fig. 5b, if the motor torque continues to increase to 8.87 N mm, the contact force will complete on 0.10, 0.16 and 1.08 N. The contact force between phalanx 1 and object after phalanx 2 contacts object becomes small because spring 1 stores a part of the energy, and the contact force between phalanx 2 and object becomes smaller when phalanx 3 contacts object because spring 2 stores a part of the energy (Fig. 6).

Fig. 5
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Changing curve of cylinder with a diameter of 80 mm

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Fig. 6
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Grasping process of cylinder with a diameter of 80 mm

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The motor torque continues to rise after phalanx 2 contacts the object until phalanx 3 contacts the object. However, the motor torque drops when phalanx 3 contacts the object. The reason is that the object relative to the finger is bigger, which triggers Roll-back phenomenon [12] as the root phalanx tends to separate from the object in the case of increasing the grasp force. In Fig. 7, if the rotation is continued, the phalanx will separate from the object.

Fig. 7
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Roll-back phenomenon

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4 Conclusion

This paper uses Solidworks to simulate the grasp operation of the finger with different situation, 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 finger designed by the mechanism according to Fig. 1 can achieve good motion coherence and stability grasping. The finger can make suitable capability for grasping the cylinders whose diameter can vary from 0.106 to 0.851 respecting to finger length which means it has a large grasping range. And it can produce 5 times of hand grasping force by using small electromotor which means it can produce a larger grasping force. In Figs. 3 and 6, links are maintained within the phalanxes in grasping process which means the finger has a compact structure in whole process. The rationality of design is validated through the simulation. And the important data of finger such as grasping range and grasping force are obtained.