為因應產品少量多樣化及複雜化之市場需求，以機器人為主的自動彈性裝配系統因應而生。而機械臂於裝配過程中，插配元件難免與插孔元件相碰撞，及機械臂本身之精確度、重現度和解析度的問題，而產生不可預期的位置誤差與角度誤差，造成插配之失敗。為解決此問題，利用被動式遙軸順應性裝置遂成為最常採取的方法之一。
傳統之遙軸順應性裝置(Remote Center Compliance Device, RCC)大都是在解決圓棒插配之工作，而本研究主要針對具有方向性考量的四邊形棒之插配，作深入研究、提出解決之辦法。所提出的被動式多遙軸順應性裝置(The Passive Multiple Remote Center Compliance Device, MRCC)，除了具有傳統RCC之性能外，並且具有方向性之順應性，以適合有方向性棒之插配。另外，可調節彈簧之機制設計對非上對下之水平插配更能勝任。經由能量法也驗證了此裝置之穩定性，而對不同形狀之插棒及插孔之實際測試，示範了其優越的插配性能。
四邊形棒因具有方向性，插配時更具有變化性及挑戰性。實際的插配過程可分為逼近、一點接觸、二點接觸、三點接觸、四點接觸、旋轉、離開導角面、以及插入等階段，本論文應用準靜態 (quasi-static) 方法提供了方棒插配過程的完整分析 。在裝配的幾何形狀與裝配的力量作用之問題上，發展提出能避免裝配時嵌住與擁塞現象的限制條件。此外，以幾何觀念探討，建立了方棒插配的有效區域圖。使得在未插配之前即能有效的預測能安全完成方棒插配的有效區域，以提高方棒成功插配的機率。

In order to meet production requirements of small quantity and large variety for versatile market demands, industrial robots with dexterous end-effectors are usually applied to the flexible manufacturing systems. However, owing to constraints of robot’s accuracy, repeatability, and resolution, assembled parts may experience collision during the insertion process. Both positional and angular errors, which cannot be easily predicted because of indeterminate collision situations, may cause failure of the assembly. One of the frequently applied strategies is to use a passive remote center compliance device.
Most traditional remote center compliance (RCC) devices aim to solve insertion difficulty for round peg insertion. This dissertation is devoted to analyze the insertion behavior and develop a new remote center compliance device for square pegs, which lack of the axial symmetry property of round pegs. The presented Passive Multiple Remote Center Compliance Device (MRCC) introduces a new azimuthal compliance over traditional passive compliance mechanisms that can effectively compensate the peg’s orientation deviation for polygonal assembly. Besides, a special feature of the adjustable compliance provides capability to overcome the gravity effect. Non-vertical insertions therefore become possible. A spring-supported object in space is also adopted for stability analysis of the compliant device. Actual experimental assembly processes demonstrate promising results on polygonal insertions in both traditional top-down and horizontal directions.
The assembly process of a square peg consists of approach, one-point contact, two-point contact, three-point contact, four-point contact, rotation, departure from chamfer crossing, and insertion. Full analysis of the square peg mating process, using a quasi-static approach will be presented. Constraints that can avoid the jamming and wedging phenomenon for successful assembly will also be established. Furthermore, a novel geometric insertion map, which is able to predict regions of failure and success before actual insertion takes place, is developed to improve efficiency of successful assembly for square pegs.

ACKNOWLEDGMENTS……………………………….…………. i
CONTENTS…………………………………..….…………………. ii
LIST OF FIGURE CAPTIONS…………………………...……….. iv
LIST OF TABLE CAPTIONS……………………………………… vii
NOTATION….…………………………………………..…………. viii
CHINESE ABSTRACT...………………………………..………….. xiv
ENGLISH ABSTRACT……………………………………...….…. xv
CHAPTER 1 INTRODUCTION………………………..………… 1
1.1 Goals and Motivation…………………...……… 1
1.2 Background and Paper Review….……….….….. 2
1.3 Dissertation Outline…………………..…………. 8
CHAPTER 2 INSERTION BEHAVIOR ANALYSIS OF SQUARE PEGS……………………………………..…………. 12
2.1 Geometric Definitions...…………………..……. 12
2.2 Assembly Process and Motion Behavior…...….. 16
2.2.1 Insertion of Round Pegs………………….. 16
2.2.2 Insertion of Square Pegs………………….. 18
CHAPTER 3 MULTIPLE REMOTE CENTER COMPLIANCE (MRCC) DEVICE...……………………………….. 38
3.1 Structure of MRCC……….……………………. 38
3.2 Maneuver of MRCC……………………………. 40
3.3 Compliance Analysis of MRCC………………... 42
3.4 Stability Analysis of MRCC................................. 46
3.4.1 Mathematical Modeling…………………... 46
3.4.2 Stability Analysis…………………………. 48
3.5 Experiments………………………………..……. 53
CHAPTER 4 ASSEMBLY CONSTRAINTS FOR SQUARE PEGS 62
4.1 Insertion Constraints…………………………….. 62
4.2 Force Constraints for Assembly…………………. 67
4.3 Geometric Constraints for Assembly……………. 69
4.4 Geometric Insertion Map………………………... 71
CHAPTER 5 CONCLUSIONS………………………..…………… 84
5.1 Contributions…………..………………………… 84
5.2 Future Research Topics…..……………………… 85
BIBLIOGRAPHY………..…………………………………………. 87

Arai, T. and Kinoshita, N., “The Part Mating Forces that Arise When Using a Worktable with Compliance,” Assembly Automation, Vol. 1, No. 4, Aug. 1981, pp. 204-210.
Asada, H., “Teaching and Learning of Compliance Using Neural Nets: Representation and Generation of Nonlinear Compliance,” Proceedings of the 1991 IEEE International Conference on Robotics and Automation, Cincinnati, Ohio, USA, May 1991, pp. 2231-2237.
Balan, L. and Bone, G. M., “Automated Gripper Jaw Design and Grasp Planning for Sets of 3D Objects,” Journal of Robotic Systems, Vol. 20, No. 3, 2003, pp. 147-162.
Brussel, H. Van and Simons, J., “Automatic Assembly by Active Force Feedback Accommodation,” Robot Sensors, Vol. 2, A. Pugh ed., IFS Ltd., 1986, pp. 53-66.
Caillot, F. and Kerlidou, M., “Air Steam Compliance,” Assembly Automation, Vol. 4, No. 2, May 1984, pp. 22-24.
Cheng, C. C. and Chen, G. S., “Passive Multiple Remote Center Compliance Device,” U. S. Patent no. 5,909,941, issued Jun. 1999.
Cheng, C. C. and Wu, B. Y., “Intelligent Insertion Assembly by Fuzzy Control Rules,” Proceedings of the 2nd Asian Control Conference, Volume I, Seoul, South Korea, Jul. 1997, pp. 73-76.
Clark, D., Demmel, J., Hong, J., Lafferriere, G., Salkind, L., and Tan, X., “Teleoperation Experiment with a UTAH/MIT Hand and a VPL Dataglove,” Robotics Research 1989, presented at the ASME Winter Annual Meeting, San Francisco, California, USA, Dec. 1989, pp. 165-169.
De, A. and Tasch, U., “A Two-DOF Manipulator with Adjustable Compliance Capabilities and Comparison with the Human Finger,” Journal of Robotic Systems, Vol.13, No.1, 1996, pp. 25-34.
De Fazio, T. L., “Passive Mating System,” U. S. Patent no. 4,242,017, issued Dec. 1980.
De Fazio, T. L., “Deformable Remote Center Compliance Device,” U. S. Patent no. 4,337,579, issued Jul. 1982.
De Fazio, T. L., and Whitney, D. E., “Adjustable Remote Center Compliance Device,” U. S. Patent no. 4,477,975, issued Oct. 1984.
De Fazio, T. L., Seltzer, D. S. and Whitney, D. E., “The IRCC Instrumented Remote Centre Compliance,” Robot Sensors, Vol. 2, A. Pugh ed., IFS Ltd., 1986, pp. 33-44.
De Fazio, T. L., “Remote Center Compliance Device with Fully or Partially Coil-bound Springs,” U. S. Patent no. 4,848,757, issued Jul. 1989.
Du, K. L., Huang, X., Wang, M., and Hu, J., “Assembly Robotics Research: A Survey,” International Journal of Robotics and Automation, Vol. 14, No. 4, 1999, pp. 171-183.
Du, K. L., Zhang, B., and Hu, Z., “Robot Impedance Learning of the Peg-In-Hole Dynamic Assembly Process,” International Journal of Robotics and Automation, Vol. 15, No. 4, 2000, pp.107-118.
Gershon, D., “A Programmable RCC Hand,” Transactions of the ASME, Journal of Mechanical Design, Vol. 116, No. 3, Sep. 1994, pp. 884-889.
Goto, T., Takeyasu, K. and Inoyama, T., “Control Algorithm for Precision Insertion Operation Robots,” IEEE Transactions on Systems, Man and Cybernetics, Vol. SMC-10, No. 1, 1980, pp. 19-25.
Gullapalli,V., Grupen, R., A., and Barto, A. G., “Learning Reactive Admittance Control,” Proceedings of the 1992 IEEE International Conference On Robotics and Automation, Nice, France, May 1992, pp. 1475-1480.
Gurocak, H. B. and De Sam Lazaro, A., “Fuzzy Logic and Position Sensing for Precision Assembly,” Journal of Robotic Systems, Vol. 12, No. 2, 1995, pp. 135-146.
Guu, F. N., “On Design and Analysis of a Three-Dimensional Passive Compliant Machine Wrist,” Master’s thesis, Department of Mechanical Engineering, Feng Chia University, Taichung, 1990.
Hoffman, B. D., Pollack, S. H., and Weissman, B., “Vibratory Insertion Process: A New Approach to Non-standard Component Insertion,” Robot 8: Proceedings of 14th International Symposium on Industrial Robots Conference, Detroit, Michigan, USA, Jun. 1984, pp. 1-8.
Jung, C. M. and Gweon, D. G., “An Intelligent Wrist Mechanism for Robot Assembly of Chamferless Parts,” Robotics, Mechatronics and Manufacturing Systems, T. Takamori and K. Tsuchiya, ed., Elsevier Science, 1993, pp. 107-112.
Kang, H. and Vachtsevanos, G., “An Intelligence Strategy to Robot Coordination and Control,” Proceedings of the 1992 IEEE International Conference On Decision and Control, Honolulu, Hawaii, USA, Dec. 1992, pp. 2208- 2213.
Kim, W. K., Yi, B. J. and Cho, W. “RCC Characteristics of Planar/Spherical Three Degree-of-Freedom Parallel Mechanisms with Joint Compliances,” Transactions of the ASME, Journal of Mechanical Design, Vol. 122, No. 1 Mar. 2000, pp. 10-16.
Kung, S. H. and Cheng, C. C., “Supervisory Teaching and Learning for Peg Insertion,” Automation ’97, Proceedings of the 10th National Conference on Automation Technology, Volume I, Taichung, Oct. 1997, pp. 521-527.
Lee, S. H. and Kim, M. H., “Learning Expert Systems for Robot Fine Motion Control,” Proceedings of the 3rd IEEE International Symposium on Intelligent Control, Arlington, Virginia, USA, Aug. 1988, pp. 534-544
Mckerrow, P. J., Introduction to Robotics, Addison-Wesley Publishing Company, 1995, pp. 308-324.
Nevins, J. L. and Padavano, J., “Folded Remote Center Compliance Device,” U. S. Patent no. 4,355,469, issued Oct. 1982.
Nguyen, Van-Duc, “The Synthesis of stable Grasps in the plane,” Proceedings of the IEEE International Conference on Robotics and Automation, San Francisco, California, USA, 1986, pp. 884-889.
Quinton, B. P. and Scott, G. E., “Remote Center Compliance Device System,” U. S. Patent no. 4,720,923, issued Jan. 1988.
Rourke, J. M. and Whitney, D. E., “Remote Center Compliance Device,” U. S. Patent no. 4,556,203, issued Dec. 1985.
Shahinpoor, M. and Zohoor, H., “Analysis of Dynamic Insertion Type Assembly for Manufacturing Automation,” Proceedings of the IEEE International Conference on Robotics and Automation, Sacramento, California, USA, Apr. 1991, pp. 2458-2464.
Simons, J. Brussel, H. V., Schutter, J. De, and Verhaert, J., “A Self-learning Automation with Variable Resolution for High Precision Assembly by Industrial Robots,” IEEE Transactions on Automatic Control, Vol. AC-27, No. 5, 1982, pp. 1109-1113.
Simunovic, S. N., “An Information Approach to Parts Mating,” Sc.D. Thesis, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA, 1979.
Strip, D. R., “Insertions Using Geometric Analysis and Hybrid Force-Position Control: Method and Analysis,” Proceedings of the IEEE International Conference on Robotics and Automation, Philadelphia, Pennsylvania, USA, May 1988, pp. 1744-1751.
Strip, D. R., “A Passive Mechanism for Insertion of Convex Pegs,” Proceedings of the IEEE International Conference on Robotics and Automation, Scottsdale, Arizona, USA, May 1989, pp. 242-248.
Sturges, R. H. Jr., “A Three-Dimensional Assembly Task Quantification with Application to Machine Dexterity,” The International Journal of Robotics Research, Vol. 7, No. 4, 1988, pp. 34-78.
Sturges, R. H., Jr. and Laowattana, S., “Virtual Wedging in Three-Dimensional Peg Insertion Tasks,” Transactions of the ASME Journal of Mechanical Design, Vol. 118, No. 1, Mar. 1996, pp. 99-105.
Sturges, R. H. Jr. and Laowattana, S., “Design of an Orthogonal Compliance for Polygonal Peg Insertion,” Transactions of the ASME, Journal of Mechanical Design, Vol. 118, No. 1, Mar. 1996, pp. 106-114.
Tsuda, M., Higuchi, T., and Fujiwara, S., “Automated Precision Assembly Using Magnetically Supported Intelligent Hand,’’ Robotics Research 1989, presented at the ASME Winter Annual Meeting, San Francisco, California, USA, Dec. 1989, pp.195-201.
Tung, P. C. and Hsu, Y. P., “Application of Fuzzy Control to an Inserting Operation,” Fuzzy Sets and Systems, Vol. 66, No. 3, 1994, pp. 267-281.
Vaaler, E. G. and Seering, W. P., “A Machine Learning Algorithm for Automated Assembly,” Proceeding of the IEEE International Conference on Robotics and Automation, Sacramento, California, USA, Apr. 1991, pp. 2231-2237.
Watson, P. C., “Remote Center Compliance System,” United States Patent no. 4,098,001, issued Jul. 1978.
Whitney, D. E., “Quasi-Static Assembly of Compliantly Supported Rigid Part,” Transactions of the ASME, Journal of Dynamic Systems, Measurement, and Control, Vol. 104, No. 1, Mar. 1982, pp. 65-77.
Whitney, D. E. and Nevins, J. L., “What is the Remote Centre Compliance (RCC) and What Can it Do?” Proceedings of the 9th International Symposium on Industrial Robots, Washington D.C., USA, 1986, pp. 135-152.
Zafred, P. R. and Veronesi, L., “Remote Center Compliance Device,” United States Patent no. 4,627,169, issued Dec. 1986.