1. Department of Electrical Engineering Southern Taiwan University of Science and Technology Robot and Servo Drive Lab. 2016/1/3 Control of Three-Finger Gripper Student: Pei-Lin Tsai Adviser: Ming-Shyan Wang

2. Department of Electrical Engineering Southern Taiwan University of Science and Technology 2 Outline Abstract Introduction Kinematic Analysis of Homogeneous D-H Transformation Experimental Results Conclusions References

3. Department of Electrical Engineering Southern Taiwan University of Science and Technology 3 Abstract In this paper, a mechanical palm which includes three fingers with four degrees of freedom and four of 11 movable joints being independent, will imitate the movement behavior of mankind’s dexterous hands. Through the kinematics analysis, we get the workspace of every mechanical finger of the mechanical palm and derive out the useful postures for the reference of the claw design. It is the purpose for the palm to reach the function helping people to eat meals.

4. Department of Electrical Engineering Southern Taiwan University of Science and Technology 4 Introduction In recent years, though a lot of equipments of home automation are developed in succession, the equipments mostly offer the sound persons to enjoy designing more comfortably, but less likely to direct for the physically disabled patients. It is worse for the heavy degree the wounded or disabled persons. It is the basic behavior for people to maintain the life by having meals.

5. Department of Electrical Engineering Southern Taiwan University of Science and Technology 5 Introduction They are mostly unable to control their own arms (or even have no arms) to deliver the food into the mouths independently. Their relative or the medical personnel must help to have a dinner each time. This not only makes the patient personal inconvenience, but also causes relative heavy burden for a long time. So if there is a meal assistance robot to help patients to take food automatically, it enables patients to determine food and the time independently and keep their dignity.

6. Department of Electrical Engineering Southern Taiwan University of Science and Technology 6 Introduction The robot system combines each different system and is organized among them now, including mechanical head, mechanical arm, mechanical palm and one pair of feet system, etc. The technology of the mechanical palm has already been developed for a long time too. It is different to some extent on the function and organization that are developed. The main difference is the organizations of three fingers, four fingers or five fingers. There are two types of palm driving, built-in actuator and wire driving [1]. The latter is considered in this paper.

7. Department of Electrical Engineering Southern Taiwan University of Science and Technology 7 Kinematic Analysis of Homogeneous D-H Transformation In order to describe the relationship between the joint and link, the kinematics is introduced. The Denavit-Hartenberg (D-H) based homogeneous transformation matrix is used in the kinematics to describe the relationship between two axes systems A and B, Where represents the orientation of system B relative to system A; is the position information for the origin of system B relative system A; means perspective transformation; and is a scaling factor. (1)

8. Department of Electrical Engineering Southern Taiwan University of Science and Technology 8 Kinematic Analysis of Homogeneous D-H Transformation Where means the rotating axis of the joint i+1, represents the axis orthogonal to joint i and i+1, and is determined by the right-hand rule for and. is the intersection point of axes and ; is the origin of its axis system. As a result, we have the following parameters: link length, link distance, link twist angle, and link angle. Fig. 1. The definition for each link.

9. Department of Electrical Engineering Southern Taiwan University of Science and Technology 9 Kinematic Analysis of Homogeneous D-H Transformation Fig. 2. Sample Denavit-Hartenberg diagram [6].

10. Department of Electrical Engineering Southern Taiwan University of Science and Technology 10 Kinematic Analysis of Homogeneous D-H Transformation The D-H transformation matrix between (i-1)th link and its link is described as below: (2)

11. Department of Electrical Engineering Southern Taiwan University of Science and Technology 11 Kinematic Analysis of Homogeneous D-H Transformation Table 1. Parameters of each link. Joint i 101.7 cm0 20 0 30 0 Fig. 3. The axis systems. 1.7 cm (x，y；θ)(x，y；θ)

12. Department of Electrical Engineering Southern Taiwan University of Science and Technology 12 Kinematic Analysis of Homogeneous D-H Transformation According to Table 1 parameters of each link, and take them into D-H transformation matrix, which we can get the transformation matrix of each link as below: These equations are expressed the position and posture of the first to the third link. (4) (5) (3)

13. Department of Electrical Engineering Southern Taiwan University of Science and Technology 13 Kinematic Analysis of Homogeneous D-H Transformation As a result, the D-H transformation matrix is: (6)

14. Department of Electrical Engineering Southern Taiwan University of Science and Technology 14 Kinematic Analysis of Homogeneous D-H Transformation Take robot fingers joint angle, and into the above equation, we can know the element of the transformation matrix which is the position and orientation of the end- effector, the entire calculating process is the forward kinematics.

15. Department of Electrical Engineering Southern Taiwan University of Science and Technology 15 Kinematic Analysis of Homogeneous D-H Transformation The plane of three-axis robot fingers direct kinematic equations are: (7) (8) (9)

16. Department of Electrical Engineering Southern Taiwan University of Science and Technology 16 Kinematic Analysis of Homogeneous D-H Transformation Take the equation (9) into the equation (7) and (8), and then the inverse kinematic equations of the position of the end- effector can be obtained as below: (10) (11)

17. Department of Electrical Engineering Southern Taiwan University of Science and Technology 17 Kinematic Analysis of Homogeneous D-H Transformation The equation (10) and (11) are square, respectively, and then sum, we can get: (12)

18. Department of Electrical Engineering Southern Taiwan University of Science and Technology 18 Kinematic Analysis of Homogeneous D-H Transformation From the equation (12), we can get: (13) (14) （∵ cos(-θ) ＝ cos(θ) ）

19. Department of Electrical Engineering Southern Taiwan University of Science and Technology 19 Kinematic Analysis of Homogeneous D-H Transformation Modify the equation (10) and (11) to the simultaneous equations as below: (15) (16)

20. Department of Electrical Engineering Southern Taiwan University of Science and Technology 20 Kinematic Analysis of Homogeneous D-H Transformation We can get: (17)

21. Department of Electrical Engineering Southern Taiwan University of Science and Technology 21 Kinematic Analysis of Homogeneous D-H Transformation So, From the equation (9), we can get: Finally, we can accordance with the above calculating process calculated the results of the joint angle. (18) (19)

22. Department of Electrical Engineering Southern Taiwan University of Science and Technology 22 Experimental Results Fig. 4. 4-DOF Gripper.

23. Department of Electrical Engineering Southern Taiwan University of Science and Technology 23 Experimental Results Fig. 5. Futaba S3156MG Digital Servo [9]. Table 2. Parameters of Futaba S3156MG Digital Servo [9].

24. Department of Electrical Engineering Southern Taiwan University of Science and Technology 24 Experimental Results Fig. 6. The experimental setup. Power Supply 6 V 4 ‐ DOF Gripper SSC-32 Servo Controller Cyton Gripper Viewer USB to RS-232

25. Department of Electrical Engineering Southern Taiwan University of Science and Technology 25 Experimental Results ↑ Plastic spoon ; Less than 1g less.↑ Iron spoon ; 27 g.↑ Long-handled soup spoon ; 48 g. ↑ The glue 50 c.c. ; 68 g.↑ There is the paper cup fill with nine tenths of water ; 124 g. Fig. 7. The experimental results.

26. Department of Electrical Engineering Southern Taiwan University of Science and Technology 26 Conclusions Movements of the fingers can imitate the posture similar to human palm picking. It works functionally well to pick all kinds of the objects in daily life, for instance, various types of soup spoons, paper cups, etc. Its movement can seem to be similar to dexterous movements of the mankind’s hands and reach the function helping feeding meals.

27. Department of Electrical Engineering Southern Taiwan University of Science and Technology 27 References [1] Yuan-Kun Wang, Development of Humanoid Robot Hand, Master thesis, Department of Mechanical Engineering, National Taiwan University of Science and Technology, 2008. [2] Chun-Cheng Wang, Fast Inverse Kinematics by Least-Squares Approximation, Master thesis, Department of Automatic Control Engineering, Feng Chia University, 2009. [3] Chang-Hung Lai, Design and Control of an Anthropomorphic Robot, Master thesis, Department of Mechanical Engineering, National Cheng Kung University, 2003. [4] Shih-Han Lin, Innovative Design and Application of Walking Assist Device, Ph.d. Dissertation, Department of Mechanical Engineering, National Chiao Tung University, 2010. [5] Lung-Wen Tsai, Robot Analysis: The Mechanics of Serial and Parallel Manipulators, Wiley-Interscience, Taiwan, 2005. [6] Sample Denavit-Hartenberg Diagram, http://upload.wikimedia.org/wikipedia /commons/3/3f/Sample_Denavit-Hartenberg_Diagram.png. [7] Ching-Long Shih and Wen-Yo Lee, Mechatronics Control, Chuan Hwa Book Co., 2009 。 [8] Robai, www.robai.com. [9] Futaba, http://www.futaba-rc.com/. [10] Wen-Chou Yu, The Study of Robot Hands and its Applications, Master thesis, Department of Computer Science and Information Engineering, National Cental University, 2009. [11] Lynxmotion, Inc., http://www.lynxmotion.com.

28. Department of Electrical Engineering Southern Taiwan University of Science and Technology 28 Thanks for your listening!