Elmas ANLI, Hüseyin ALP, Sait N YURT, İbrahim ÖZKOL

Paralel mekanizmaların kinematiği,dinamiği ve çalışma uzayı

Bu çalışmada, paralel mekanizmaların genel özellikleri, kinematik, dinamik ve çalışma uzayları hakkında bugüne kadar yapılan çalışmaların bir özeti verilerek ileriye yönelik önerilerde bulunulmuştur. Havacılık sahasında, pilot adayları, uçakla uçuş eğitimine başlamadan önce simülatörlerde eğitim görmektedirler, böylece eğitim kayıpları ve zamanı en aza indirilmektedir. Simülatörlerdeki eğitimler esnasında, pilot adaylarının ötelenme ve dönme hareketlerini gerçeğe yakın hassasiyette algılamaları çok önemlidir. Gerçek bir uçakta uçarken pilotun maruz kalacağı hareket, simülatörün altında bulunan bir paralel mekanizma ile sağlanır. 1965 'te Stewart 'in uçuş simülatörü olarak önerdiği 6 serbestlik dereceli paralel platform mekanizmasının modifiye edilmiş hali bu işte kullanılmaktadır. Paralel mekanizmalar, mimarilerinden dolayı, seri mekanizmalardan daha yüksek doğal frekansa, katılığa, çalışma hızına, nominal yüklemeye ve hassasiyete sahiptir, ancak çalışma uzayları daha küçüktür. Stewart platform mekanizması, SPM, boyları prizmatik eklemler vasıtasıyla değişebilen 6 bacak ile birbirine bağlı altıgen biçimli bir sabit platform ve bir hareketli platformdan oluşmaktadır. Bacaklar platformlara genelde universal mafsallarla bağlı olmakla beraber, dönel veya küresel mafsallar da kullanılabilir. Bacakları hareket ettiren eyleyiciler sabit tabandadır. SPM üç yönde öteleme ve üç yönde dönme yapabilmektedir.

This paper summarizes the current state of affairs in the area of paralel mechanisms, their overall properties, kinematics, dynamics and workspace analysis; and makes suggestions on possible research areas that have not been explored yet. Piloting trainees train on flight simulators before flying the actual aircraft, so that training time and losses are minimized. It is vital for piloting trainees to sense the translation and rotation motions of the simulator just as they would in a real aircraft. The motion that a pilot would be exposed to while flying a real aircraft is provided by a paralel mechanism placed under the simulator. A slightly modified version of the 6 degree of freedom paralel platform mechanism suggested by Stewart in 1965 is used for this purpose. Due to their architecture, paralel mechanisms have higher natural frequencies, stiffness, speed, nominal loading capacity and precision, when compared to serial mechanisms, whereas their workspaces are smaller than those of serial mechanisms. The Stewart Platform Mechanism (SPM), is comprised of a hexagon shaped fixed base platform and a movable platform linked via six legs whose lengths can be changed using prismatic joints. The legs can be attached to the platforms using revolute or spherical joints, though universal joints are often used. The actuators that change leg lengths are on the base. SPM can move in three translational and three rotational directions.

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1.D.Stewart, "A Platform with Six Degrees of Freedom", Proc. Instn. Mech, Engrs, 180(15), 371-386,1965.

2.D. Ku, "Direct Displacement Analysis of a Stewart Platform Mechanism", Mechanism and Machine Theory, 34(3), 453-465,1999.

3.J. P. Merlet, "Direct Kinematics of Parallel Manipulators", IEEE Transactions on Robotics and Automation, 9(6), 842-846 (1993).

4.Y. K. Yiu, H. Cheng, Z. H. Xiong, G.F.Liu ve Z.X.Li, "On the Dynamics of Parallel Manipulators",, Proceedings of the 2001 IEEE International Conference on Robotics and Automation, 2001.

5.K. Liu, J. M. Fitzgerald ve F. L. Lewis, "Kinematic Analysis of a Stewart Platform Manipulator, "IEEE Transactions on Industrial Electronics, 40(2), 282-293, 1993.

6.K. Lee ve D.K. Shah, "Kinematic Analysis of a Three-Degrees-of-Freedom In-Parallel Actuated Manipulator", IEEE Journal of Robotics and Automation, 4(3), 354-360,1988.

7.X. Shi ve R.G. Fenton, "Solution to the Forward Instantaneous Kinematics for a General 6-dof Stewart Platform", Mechanism and Machine Theory, 27(3), 251-259, 1992.

8.C. Innocenti ve V. Parenti-Castelli, "Direct Position Analysis of the Stewart Platform Mechanism", Mechanism and Machine Theory, 25(6), 611-621, 1990.

9.B. Dasgupta ve T.S. Mruthyunjaya, Mechanism and Machine Theory, 35, 15-40, 2000.

10.L. Romdhane, "Design and Analysis of a Hybrid Serial-Parallel Manipulator", Mechanism and Machine Theory, 34, 1037-1055, 1999.

11.T. Arai, K. Yuasa, Y. Mae, K. Inoue, K. Miyawaki ve N.Koyachi, "A Hybrid Drive Parallel Arm for Heavy Material Handling", IEEE Robotics and Automation Magazine, 45-54, 2002.

12.R. S. Stoughton, T. Arai, "A Modified Stewart Platform Manipulator with Improved Dexterity", IEEE Transactions on Robotics and Automation, 9(2), 166-173, 1993.

13.P. Nanua, K.J. Waldron, V. Murthy, "Direct Kinematic Solution of a Stewart Platform", IEEE Transactions on Robotics and Automation, 6(4), 438-444, 1990.

14.K. Wohlhart, "Displacement Analysis of the General Spherical Stewart Platform", Mechanism and Machine Theory, 29(4), 581-589,1994.

15.B. Dasgupta ve T.S. Mruthyunjaya, "A Canonical Formulation of the Direct Position Kinematics Problem for a General 6-6 Stewart Platform", Mechanism and Machine Theory, 29(6), 819-827,1994.

16.B. Dasgupta ve T.S. Mruthyunjaya, "A Constructive Predictor-Corrector Algorithm for the Direct Position Kinematics Problem for a General 6-6 Stewart Platform", Mechanism and Machine Theory, 31(6), 799-811,1996.

17.X. Zhao ve S. Peng, "Direct Displacement Analysis of Parallel Manipulators", Journal of Robotic Systems, 17(6), 341-345,2000.

18.D. Jakobovic ve L. Jelenkovic, "The Forward and Inverse Kinematics Problems for Stewart Parallel Mechanisms", International Scientific Conference on Production Engineering, 11-001 -11-012,2002.

19.M. S. Tsai, T. N. Shiau, Y. J. Tsai ve T. H. Chang, "Direct Kinematic Analysis of a 3-PRS Parallel Mechanism", Mechanism and Machine Theory, 38, 71-83,2003.

20.J. Kim ve F. C. Park, "Direct Kinematic Analysis of 3-RS Parallel Mechanisms", Mechanism and Machine Theory, 36, 1121-1134,2001.

21.R. Di Gregorio, "Kinematics of a New Spherical Parallel Manipulator with Three Equal Legs: The 3-URC Wrist", Journal of Robotic Systems, 18(5), 213-219, 2001.

22.M. Callegari ve M. Tarantini, "Kinematic Analysis of a Novel Translational Platform", Transactions of the ASME, 125, 308-315, 2003.

23.R. Di Gregorio, "Translational Parallel Manipulators: New Proposals", Journal of Robotic Systems, 19(12), 595-603, 2002.

24.Dasgupta, B. and Mruthyunjaya T.S., "Closed-Form Dynamic Equations of the General Stewart Platform Through the Newton-Euler Approach", Mechanism and Machine Theory, Vol.33, 1998, 993-1012.

25.Dasgupta, B. and Mruthyunjaya T.S., "Newton-Euler Formulation for the Inverse Dynamics of the Stewart Platform Manipulator", Mechanism and Machine Theory, Vol.33, 1998, 1135-1152.

26.J. Wang ve C. M. Gosselin, "A New Approach for the Dynamic Analysis of Parallel Manipulators", Multibody System Dynamics, 2,317-334,1998.

27.G. Lebret, K. Liu ve F. L. Lewis, "Dynamic Analysis and Control of a Stewart Platform Manipulator", Journal of Robotic Systems, 10(5), 629-655, 1993.

28.H. Pang ve M. Shahinpoor, "Inverse Dynamics of a Parallel Manipulator", Journal of Robotic Systems,.11.(8), 693-702, 1994.

29.M. J. Liu, C. X. Li, C. N. Li, "Dynamics Analysis of the Gough-Stewart Platform Manipulator", IEEE Transactions on Robotics and Automation, 16(1), 2000.

30.R. Di Gregorio, Journal of Robotic Systems 19(1), 37-43, 2002.

31.F. Pernkopf ve.M. Husty, "Workspace Analysis of Stewart-Gough Manipulators Using Orientation Plots", Proceedings of MUSME 2002, the International Symposium on Multibody Systems and Mechatronics, 2002.

32.El- M Dafaoui, Y. Amirat, J. Pontnau, C. Francois, IEEE Transactions on Robotics and Automation, 14(1), 1998.

33.J.A. Carretero, M.Nahon, R.P.Podhoreski, Pr. of the 1998 IEEE/RSI International Conference on Intelligent Robots and Systems, 1998.

34.S. A.-Joshi ve L. W. Tsai, "Jacobian Analysis of Limited-Dof Parallel Manipulators",Transactions of the ASME, 124, 254-258, 2002.

35.C. Gosselin, J. Angeles, IEEE Transactions on Robotics and Automation, 6(3), 281 -290, 1990.

36.F. Pernkopf ve M. L. Husty, "Singularity Analysis of Spatial Stewart-Gough Platforms with Planar Base and Platform", Proceedings of DETC'02 2002 ASME Design Engineering Technical Conference, 1-8,2002.

37.C. L. Collins ve J. M. McCarthy, IEEE, 473-478, 1997.

38.J. Angeles, G. Yang ve I. M. Chen, IEEE/ASME Transactions on Mechatronics, 8(4), 469-475, 2003.

39.D.Kim ve W. Chung, "Analytic Singularity Equation and Analysis of Six-Dof Parallel Manipulators Using Local Structurization Method", IEEE Transactions on Robotics and Automation, 15(4), 1999.

40.J. Bessala, P. Bidaud, F. Ben Ouezdou, Proceedings of the 1996 IEEE International Conference on Robotics and Automation, 1996.

41.L. Romdhane, Z. Affî ve M. Fayet, Journal f Mechanical Design, 124, 419-426, 2002.

42.D. Zlatanov, R. G. Fenton ve B. Benhabib, "Singularity Analysis of Mechanisms and Robots via A Motion-Space Model of the Instantaneous Kinematics", IEEE, 980-985, 1994.

43.D. Zlatanov, R. G. Fenton ve B. Benhabib, "Singularity Analysis of Mechanisms and Robots via A Velocity-Equation Model of the Instantaneous Kinematics", IEEE, 986-991, 1994.

44.Z. Huang, L. H. Chen ve Y. W. Li, Journal of Robotic Systems, 20(4), 163-176, 2003.

45.L. J. Du Plessis, J. A. Snyman, International Journal for Numerical Methods in Engineering, 52, 345-369, 2001.

46.R. Di Gregorio, V. Parenti-Castelli, Journal of Mechanical Design, 124, 259-264, 2002.

47.G. Yang, I. M. Chen, W. Lin ve J. Angeles, "Singularity Analysis of Three-Legged Parallel Robots Based on Passive-Joint Velocities", IEEE Transactions on Robotics and Automation, 17(4), 413-422, 2001.

48.X. J. Liu, J. Kim ve K. K. Oh, "Singularity Analysis of the HALF Manipulator with Revolute Actuators", Proceedings of the 2003 IEEE International Conference on Robotics and Automation, 767-772, 2003.

49.G. Liu, Y. Lou, Z. Li, IEEE Transactions on Robotics and Automation, 19(4), 579-594, 2003.

50.D. L. Kim, W. K. Chung ve Y. Youm, "Geometrical Approach for the Workspace of 6-Dof parallel Manipulators", Proceedings of the 1997 IEEE International Conference on Robotics and Automation, 1997.

51.J. T. Wen, J. F. O'Brien, "Singularities in Three-Legged Platform-Type Parallel Mechanisms", IEEE Transactions on Robotics and Automation, 19(4), 720-726, 2003.

52.A. Wolf ve M. Shoham, "Investigation of Parallel Manipulators Using Linear Complex Approximation", Transactions of the ASME, 125, 564-572, 2003.

53.W. Dang ve T. Min, Proceedings of the 2001 IEEE International Conference on Robotics and Automation, 2001.

54.Z. Wang, Z. Wang, W. Liu ve Y. Lei, "A Study on Workspace, Boundary Workspace Analysis and Workpiece Positioning for Parallel Machine Tools", Mechanism and Machine Theory, 36, 605-622, 2001.

55.J. Angeles, G. Yang, I. M. Chen, 2001 IEEE/ASME International Conference on Advanced Intelligent Mechatronics Proceedings, 2001.

56.M. Z. A. Majid, Z. Huang ve Y. L. Yao,"Workspace Analysis of a Six-Degrees of Freedom, Three-Prismatic-Prismatic-Spheric-Revolute Parallel Manipulator", International Journal of Advanced Manufacturing Technology, 16, 441-449, 2000.

57.J. P. Merlet, "Determination of the Orientation Workspace of Parallel Manipulators", Journal of Intelligent and Robotic Systems, 13,143-160, 1995.

58.M. Badescu ve C. Mavroidis, "Workspace Optimization of 3-Legged UPU and UPS Parallel Platforms with Joint Constraints", Journal of Mechanical Design, 126, 291-300, 2004.

59.M. Badescu, J. Morman ve C.Mavroidis, Proceedings of the 2002 IEEE International Conference on Robotics and Automation, 3678-3683, 2002.

60.I.A. Bonev, J. Ryu, Mechanism and Machine Theory, 36, 2001.

61.Y. Li, Z. Huang ve L. Chen, "Singular Loci Analysis of 3/6-Stewart Manipulator by Singularity-Equivalent Mechanism", IEEE, 1881-1886,2003.

62.J. P. Merlet, Proceedings of the 1996 IEEE International Conference on Robotics and Automation, 3726-3731, 1996.

63.B. Monsarrat, C. M. Gosselin, IEEE Transactions on Robotics and Automation, 19(6), 954-966, 2003.

64.Y. Jin, I. M. Chen ve G. Yang, "Structure Synthesis and Singularity Analysis of a Parallel Manipulator Based on Selective Actuation", Pr. of the 2004 IEEE International Conference on Robotics and Automation, 4533-4538, 2004.

65.S.H.Lee, J.B.Song, W.C.Choi ve D.Hong, Proceedings of the 2002 IEEE International Conference on Robotics and Automation, 3666-3671;,2002,

66.I. M. Chen, J.Angeles, Theingi ve C.Li.Oh, "The Management of Parallel-Manipulator Singularities Using Joint Coupling", Proceedings of the 2003 IEEE International Conference on Robotics and Automation, 773-778,2003.

67.T.Arai, K.Takayama, K.Inoue, Y.Mae, Y.Koseki, Pr. of the 2000 IEEE/RSJ, International Conference on Intelligent Robots and Systems, 2000.

68.K. Miller, "Maximization of Workspace Volume of 3-Dof Spatial Parallel Manipulators", Journal of Mechanical Design, 124, 347-350, 2002.

69.A. M. Hay ve J.A. Snyman, "Methodologies for the Optimal Design of Parallel Manipulators", International Journal for Numerical Methods in Engineering, 59, 131-152, 2004.

70.J. Cortes ve T. Simeon, "Probabilistic Motion Planning for Parallel Mechanisms", Pr. of the 2003 IEEE International Conference on Robotics and Automation, 4354-4359, 2003.

71.J. P. Merlet, IEEE, 2166-2171, 1994.

72.A. K. Dash, I.M.Chen, S.H.Yeo ve G.Yang, "Singularity-Free Path Planning of Parallel Manipulators Using Clustering Algorithm and Line Geometry", Proceedings of the 2003 IEEE International Conference on Robotics and Automation, 761-766, 2003.

73.R. Toogood, H. Hao ve C. Wong, "Robot Path Planning Using Genetic Algorithms", IEEE, 489-494, 1995.

74.Y. X. Su, B. Y. Duan, B. Peng ve R. D. Nan, "Singularity Analysis of Fine-Tuning Stewart Platform for Large Radio Telescope Using Genetic Algorithm", Mechatronics, 13, 413-425,2003.

75.Y. X. Su, B. Y. Duan ve C. H. Zheng, "Genetic Design of Kinematically Optimal Fine Tuning Stewart Platform for Large Spherical Radio Telescope", Mechatronics, 11, 821-835, 2001.

76.Y. X. Su, C. H. Zheng ve B. Y. Duan, "Singularity Analysis of a 6-Dof Stewart Platform Using Genetic Algorithm", IEEE, 2002.

77.C. Yee ve K. Lim, "Forward Kinematics Solution of Stewart Platform Using Neural Networks", Neurocomputing, 16, 333-349, 1997.

78.M. Durali ve E. Shameli, "Full Order Neural Velocity and Acceleration Observer for a General 6-6 Stewart Platform", Proceedings of the 2004 IEEE International Conference on Networking, Sensing and Control, 333-338, 2004.

79.S.V. Sreenivasan, K.J. Waldron, P. Nanua, "Closed-Form Direct Displacement Analysis of a 6-6 Stewart Platform", Mechanism and Machine Theory, 29(6), 855-864, 1994.

80.J. A. Carretero, R. P. Podhorodeski, M. A. Nahon ve C. M. Gosselin, "Kinematic Analysis and Optimization of a New Three Degree-of-Freedom Spatial Parallel Manipulator", Journal of Mechanical Design, 122, 17-24,2000.

81.P. Martin, J. R. Millan, Robotics and Autonomous Systems, 31, 227-246, 2000.

82.S. N. Yurt, 6-3 Stewart Platform Mekanizmasının Kinematik, Dinamik Analizi ve Kontrolü, Doktora Tezi, 2002.