State Classification for Human Hands

Journal of Bionic Engineering Suppl. (2008) 158–163

State Classification for Human Hands Jia-lun Yang1, Feng Gao1, Li-feng Shi1, Zhen-lin Jin2 1. State Key Laboratory of Mechanical System and Vibration, Shanghai Jiaotong University, Shanghai 200240, P. R. China 2. Robotic Research Center, Yanshan University, Qinhuangdao 066004, P. R. China

Abstract The human hand, which is a perfect model for dextrous hands, is a masterpiece of mechanical complexity. A full understanding of the human hand will provide more inspiration for the successful implementation and application of dextrous hands. The purpose of this paper is two-fold. First, the characteristic tree of the human hand is established for kinematic characteristics analysis. Second, a systematic classification for the human hand states is issued from the view point of topology. Moreover, the kinematic characteristics of the palm or finger tips are achieved via the Generalized Function (GF) set theory with the aim of achieving deeper insight into the capabilities of the human hand. Finally one application example is given to show the effectiveness of the exploitation of the GF set theory and the usefulness of this methodology for dextrous hands. Keywords: state classification, human hands, dextrous hands, kinematic characteristics tree, generalized function set Copyright © 2008, Jilin University. Published by Elsevier Limited and Science Press. All rights reserved.

1 Introduction For the last four decades, several multi-fingered hands have been developed for the application of handling objects, such as Standford/JPL hand[1], Utah/MIT hand[2], Belgrade/USE hand[3], Graspar hand[4], Robonaut robotic hand[5], and DLR/HIT hand[6]. Thanks to the advancement of technologies, the capability and dexterity of the dextrous hands have been enhanced dramatically and it is straightforward to expect that dextrous hands will be able to function quite similarly to the human hand in the future. Consequently, it is necessary to study the human hand to solve issues of design, control and motion planning of dextrous hands, since almost all of the dextrous hands are constructed through mimicking human hands. Along with further development, the desired tasks for dextrous hands will become more and more complicated, which leads to difficulties of the motion planning and control of dextrous hands. However, the analysis of the states of human hands may provide some hints, which is the main goal of this paper. The human hand is a masterpiece of mechanical Corresponding author: Feng Gao E-mail: [email protected]

complexity, capable of performing quite complicated manipulations. Three categories of grasping exist from the connectivity point of view[7], namely, power grasp, constrained motion grasp, and free motion grasp, respectively. However, we consider grasp from the geometry point of view and only such grasps, which make the finger tip contact the environment (including movable and immovable objects), are taken into account. The other cases, such as grasps using whole fingers and the palm will be issued in elsewhere. Generally, different states are used for different tasks[8]. For instance, the O.K. posture is quite different from the one of writing with a pen. Fig. 1 depicts several states of the human hand, from which we can see that using sketches to represent the states is somewhat cumbersome, especially when the number of the states is huge. Moreover, the quality of the sketch is closely related to the skill of the painter. In fact, the environment or the objects that the hand touches can be categorized into movable objects and immovable objects. For instance, the earth is an immovable object, while the tennis ball is a movable object. Furthermore, there are different contact types between

Yang et al.: State Classification for Human Hands

Fig. 1 Characteristics tree of the human hand.

the finger tips and the environment. However, in this paper only the fixed contact is considered, which means that as soon as the finger tips contact the environment, no relative motion exists between the finger tips and the environment. In this paper, to distinguish and fully understand those states of the human hand, we first classify all of the states into six categories from the view point of topology. Second, the Generalized Function (GF) set theory is introduced for achieving the kinematic characteristics of the palm or finger tips for each state, which can provide deeper insight into the capabilities of the human hand. The results might be useful for the successful implementation of dextrous hands.

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The theorems regarding the application of the GF set theory are as follows. (2) Theorem for serial mechanisms For a serial mechanism, the kinematic characteristics of the end effector of the mechanism are the union of all of the GF sets with such a sequence from the start to the end. (3) Theorem for parallel mechanisms The kinematic characteristics of the moving platform of the parallel mechanism are the intersection of the GF sets of each kinematic chain of the parallel mechanism. 2.2 Characteristics tree of the human hand The human hand contains 26 bones divided into three parts which are finger, metacarpal, and carpal. In our study, we abstract the skeleton of a hand as the sketch shown in Fig. 2. It is important to note that the difference between the right hand and the left hand has not been taken into account. As a matter of fact, the results of this paper can be applied to both hands directly.

2 Structure of the human hand and its kinematic characteristics tree 2.1 Brief introduction of the GF set theory The GF set theory was introduced for the structure synthesis of parallel manipulators[9,10]. Later its application has been extended to the field of humanoid robots[11]. It can be seen that the GF set theory is suitable for the analysis of the states of humanoid robots. Here we will recall the GF set theory briefly. (1) Definition The set contains one and only one element which represents the generalized function of the end effectors, and is called GF set. Note that the generalized function is the mapping between the specific structure of mechanisms and the kinematic characteristics of the end effectors of mechanisms.

Fig. 2 Typical states for the human hand.

All of the Interphalangeal (IP) joints feature one rotational Degree of Freedom (DOF). The Carpometacarpal (CMC) joint of the thumb and all of the Metacarpophalangeal (MCP) joints have two rotational DOFs. Furthermore, in Fig. 2, the one rotational DOF and the two rotational DOFs are denoted by the circle with bar and the circle with cross, respectively. We assign GF sets for each finger tip. In particular, the GF sets for the thumb, index finger, middle finger, ring finger, and little finger are GFt, GFi, GFm, GFr, and

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GFl, respectively. Moreover, the sketch accompanied with GF sets is called characteristics tree of the human hand. For different states, the kinematic characteristics can be achieved via the application of the GF set theory on the characteristics tree of the human hand. It is worth to note that all of the assigned GF sets for the fingers indicate the kinematic characteristics of the fingers with respect to the palm of the human hand. Basically, the states can be classified into six main categories according to the environment or the objects that the finger tips contact. In particular, for the state shown in Fig. 2, there is no contact between the finger tips and the environment and we name it H0 which is the first category. For such states that the finger tips contact the immovable objects, we name them Hb followed with numbers which are indicating different child states. On the other hand, if the finger tips have contacts with the movable objects, we have the other four main categories as follows: (a) self-connection loop contains two fingers; (b) self-connection loops contain three fingers; (c) selfconnection loops contain four fingers; and (d) selfconnection loops contain five fingers, respectively. Hereafter, we will use Hb, Hc, Hd, and He followed with different numbers to represent the above mentioned four categories of states for human hands related to movable objects.

3 State classification for human hands related to immovable objects The states related to immovable objects are commonly used by human hands, such as playing the piano. Fig. 1a depicts that the thumb touches the immovable object and Fig. 1b indicates that both the index finger and the middle finger touch the immovable object. The motion capability of the palm is changed due to the contact between the finger tips and the immovable object. So we use the kinematic characteristics of the palm with respect to the immovable object to represent the specific state. From the topology point of view, totally thirty-one states exist. Making use of the kinematic characteristics tree of the human hand and the GF set theory, all of the kinematic characteristics of the palm for different states are listed in Table 1. Note that the superscript R denotes

the reversion operation of the GF set. The readers are referred to Reference [11] for detailed description of the reversion operation of the GF set. The term Ha within the name of specific state denotes the basic state class for the human hand related to immovable objects and the number following the term Ha indicates the different states. It is not difficult to see that the state shown in Fig. 1a and Fig. 1b are named as Ha1 and Ha10, respectively. Table 1 Kinematic characteristics of the palm for such states that fingers have contact with the environment Name

Kinematic characteristics of the palm

Ha1

GFtR

Ha2

GFiR

Ha3

R GFm

Ha4

GFrR

Ha5

GFlR

Ha6

GFtR  GFiR

Ha7

R GFtR  GFm

Ha8

GFtR  GFrR

Ha9

GFtR  GFlR

Ha10

R GFiR  GFm

Ha11

GFiR  GFrR

Ha12

GFiR  GFlR

Ha13

R GFm  GFrR

Ha14

R GFm  GFlR

Ha15

GFrR  GFlR

Ha16

R GFm  GFrR  GFlR

Ha17

GFiR  GFrR  GFlR

Ha18

R GFiR  GFm  GFlR

Ha19

R GFiR  GFm  GFrR

Ha20

GFtR  GFrR  GFlR

Ha21

R GFtR  GFm  GFlR

Ha22

R GFtR  GFm  GFrR

Ha23

GFtR  GFiR  GFlR

Ha24

GFtR  GFiR  GFrR

Ha25

R GFtR  GFiR  GFm

Ha26

R GFiR  GFm  GFrR  GFlR

Ha27

R GFtR  GFm  GFrR  GFlR

Ha28

GFtR  GFiR  GFrR  GFlR

Ha29

R GFtR  GFiR  GFm  GFlR

Ha30

R GFtR  GFiR  GFm  GFrR

Ha31

R GFtR  GFiR  GFm  GFrR  GFlR

Yang et al.: State Classification for Human Hands

4 State classification for human hands related to movable objects Many states of the human hand exist for the finger tip grasps of movable objects or the finger tips contact each other directly. Several typical states are shown in Fig. 1. All of the four categories will be discussed in detail in the following subsections. 4.1 Self-connection loop contains two fingers For the case that two finger tips contact each other to form the self-connection loop, the total number of the states is 10 from the topological point of view. Four of the ten states are listed in Table 2. The term Hb denotes the states with self-connection loop containing two fingers. It is not difficult to see that Fig. 1c illustrates the state of Hb1. The kinematic characteristics of fingers for the four states are listed in Table 2, from which we can know the capabilities of the fingers. All of the kinematic characteristics of the fingers with respect to the palm can be Table 2 Kinematic characteristics of the finger for such states that the self-connection loop contains two fingers Name Hb1

Hb3

Hb8

Hb10

Finger Tips

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achieved by the application of the GF set theory on the characteristics tree of the human hand. For the sake of conciseness, not all of the states for this category are listed in Table 2. We will make the same arrangements for the following categories. 4.2 Self-connection loops contain three fingers In this case, three self-connection loops exist (see Fig. 1d). The total number of the states for this class is 10. Four typical states are listed in Table 3, as well as the corresponding kinematic characteristics of the finger tips with respect to the palm achieved via the GF set theory. The name of this state shown in Fig. 1d is Hd4. Table 3 Kinematic characteristics of the finger for such states that the self-connection loops contain three fingers Name Hc1

Hc4

Kinematic characteristics

Finger Tips

Kinematic characteristics

Thumb

GFt  GFi  GFm

Index finger

GFt  GFi  GFm

Middle finger

GFt  GFi  GFm

Ring finger

GFr

Little finger

GFl

Thumb

GFt  GFm  GFr

Index finger

GFi

Middle finger

GFt  GFm  GFr

Thumb

GFt  GFi

Ring finger

GFt  GFm  GFr

Index finger

GFt  GFi

Little finger

GFl

Middle finger

GFm

Thumb

GFt

Ring finger

GFr

Index finger

GFi  GFm  GFr

Little finger

GFl

Middle finger

GFi  GFm  GFr

Thumb

GFt  GFr

Ring finger

GFi  GFm  GFr

Index finger

GFi

Little finger

GFl

Middle finger

GFm

Thumb

GFt

Ring finger

GFt  GFr

Index finger

GFi

Hc7

Hc10

Little finger

GFl

Middle finger

GFm  GFr  GFl

Thumb

GFt

Ring finger

GFm  GFr  GFl

Index finger

GFi

Little finger

GFm  GFr  GFl

Middle finger

GFm  GFr

Ring finger

GFm  GFr

Little finger

GFl

Thumb

GFt

Index finger

GFi

Middle finger

GFm

Ring finger

GFt  GFl

Little finger

GFt  GFl

4.3 Self-connection loops contain four fingers If the self-connection loops consist of four fingers, then two sub-categories exist. Particularly, the first sub-category represents the four fingers contact at one common tip; and the second sub-category denotes that there are two common connection ends. Both two sub-categories will be covered as follows.

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4.3.1 Existing one common contact point The total number of this sub-category is 5 and one of the states is shown in Fig. 1e. The kinematic characteristics of the finger tips with respect to the palm for this state are listed in Table 4 with the name of Hd5. Table 4 Kinematic characteristics of the finger for such states that the self-connection loops contain four fingers Name Hd1

Hd5

Hd16

Hd20

Finger Tips

4.4.1 Existing two common connection ends The total number for this sub-category is 10 from the view point of topology. Fig. 1g depicts one of the states and its kinematic characteristics of the finger tips with respect to the palm are listed in Table 5. Furthermore, the name of this state is He1. Table 5 Kinematic characteristics of the finger for such states that the self-connection loops contain five fingers

Kinematic characteristics Finger Tips

Kinematic characteristics

Thumb

GFt  GFi

GFi  GFm

Index finger

GFt  GFi

Ring finger

GFr  GFl

Middle finger

GFm  GFr  GFl

Little finger

GFr  GFl

Ring finger

GFm  GFr  GFl

Thumb

GFt  GFi

Thumb

GFt

Index finger

GFi  GFm

Middle finger

Name He1

He4

Little finger

GFm  GFr  GFl

Thumb

GFt  GFl

Index finger

GFt  GFi

Middle finger

GFm

Index finger

GFi  GFmGFr

Ring finger

GFr  GFl

Middle finger

GFi  GFmGFr

Little finger

GFr  GFl

Ring finger

GFi  GFmGFr

Little finger

GFt  GFl

Thumb

GFt  GFi  GFm GFt  GFi  GFm

Thumb

GFt

Index finger

GFi  GFm  GFr  GFl

He10

Middle finger

GFi  GFm  GFr  GFl

Index finger

Ring finger

GFi  GFm  GFr  GFl

Middle finger

GFt  GFi  GFm

Little finger

GFi  GFm  GFr  GFl

Ring finger

GFr  GFl

Thumb

GFt  GFi  GFm  GFr

Little finger

GFr  GFl

Index finger

GFt  GFi  GFm  GFr

Thumb

GFt  GFi  GFm  GFr  GFl GFt  GFi  GFm  GFr  GFl

He11

Middle finger

GFt  GFi  GFm  GFr

Index finger

Ring finger

GFt  GFi  GFm  GFr

Middle finger

GFt  GFi  GFm  GFr  GFl

GFl

Ring finger

GFt  GFi  GFm  GFr  GFl

Little finger

GFt  GFi  GFm  GFr  GFl

Little finger

4.3.2 Existing two common connection ends From the topology point of view, the total number of the states for such states consisting of two common connection ends and four finger tips is C51 u C42 / 2 15 . One of those states is shown in Fig. 1f whose name is Hd7 and its kinematic characteristics of the finger tips with respect to the palm are listed in Table 3.





4.4 Self-connection loops contain five fingers We also have two sub-categories for the states that the self-connection loops contain five fingers. The first one is that all of the five fingers contact at one common end. While the second one is that two common connection ends exist.

4.4.2 Existing one common connection ends Only one state exists for this sub-category and it is shown in Fig. 1h. The kinematic characteristics of the finger tips with respect to the palm for this state are listed in Table 5 with the name of He11. In summary, the total number of the states for the human hand can be computed by 1 + 31 + 10 + 10 + 20 + 11 = 51,

(1)

where 1 denotes the H0 state and all other numbers indicate the specific number of each category of the states. The capabilities of fingers for each state can be achieved via the GF set theory. Furthermore, several states are depicted in Fig. 1 and Fig. 2 and all the corresponding

Yang et al.: State Classification for Human Hands

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kinematic characteristics of the palm or fingers can be found in Tables 1 to 5.

teristics of the palm or fingers and the methodology used in this work can also be applied to the dextrous hands.

5 An application example

Acknowledgement

In the daily life of human beings, the given task to the human hand may consist of multi-states. It is also possible for the real application of dextrous hands, which means that it is necessary to find an easy way to describe the state changes. Suppose a given task for the human hand involves all of the states shown in Fig. 1, the corresponding working process of the human hand can be represented using the results achieved via the GF set theory in a systematic and standard manner. Consequently, Fig. 3 illustrates the whole process. It is not difficult to see that Fig. 3 is much more standard and can be understood universally compared to the sketches in Fig. 1, which is one of the main advantages of the introduction of the GF set theory to this field. Moreover, the name for each specific state could indicate the corresponding capabilities of the human hand, from which the deeper insight into the capabilities of the hand can be achieved.

This work is financially supported by the National Basic Research Program of China (Grant no. 2006CB705400) and the National Natural Science Foundation of China (Grant no. 60534020).

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6 Conclusions In this paper, we have made a systematic state analysis for the human hand. The main contributions of this paper are as follows. (1) The characteristics tree of the human hand is established; (2) The states of human hands are classified into six categories; (3) The kinematic characteristics of the fingers with respect to the palm of the human hand for all of the states are achieved and parts of them are listed in this paper; (4) An application example is given to show the advantages of the methodology of application of the GF set theory on the field of human hand. Furthermore, we can get better insight into the capabilities of the human hand via the kinematic charac-

Liu H, Meusel P, Seitz N, Willberg B, Hirzinger G, Jin M, Liu Y, Wei R, Xie Z. The modular multisensory

Fig. 3 Description of the changes of states using names.

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[10] Gao F, Zhang Y, Li W M. Type synthesis of 3-DOF reducible translational mechanism. Robotica, 2005, 23, 239245. [11] Yang J L, Gao F, Jin Z L, Shi L F. States classification for the humanoid robot platform SJTU-HR1. International Mechanisms and Machine Science Conference, Qinghuangdao, China, 2008.