Abstract
The direct position analysis (DPA) of fully-parallel manipulators, basically comprises the analysis of fully-parallel kinematic chains (FPKCs) that feature two rigid bodies connected to each other via six binary links (legs) through spherical pairs. Some legs may share their endings, thus different leg arrangements are possible. The paper provides the state of the art of the DPA of all possible arrangements. In particular, the paper: i) reviews a procedure for identification and exhaustive enumeration of FPKCs, that led to the identification of twenty-one different FPKCs, and ii) after some basic ideas helpful for the DPA are outlined, reviews a technique that proved to be successful for the DPA solution of several FPKCs. Specifically, the technique focuses on the generation of the closure equations of the manipulator that is a basic stage for accomplishing the DPA solution in analytical form. Closure equations for one manipulator are also reported in order to outline the key role of the aforementioned technique.
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References
Gough V E 1956 Contribution to Discussion to Papers on Research In Automobile Stability and Control and in Tyre Performance, by Cornell staff. In: Proc. Auto. Div. Instn. mech. Engrs, pp 392–395
Stewart D 1965 A Platform With Six Degrees of Freedom. In: Proc. Instn. Meek Engrs., Part 1, 180 (15): 371–376
Hunt K J 1983 Structural Kinematics of In-Parallel Actuated Robot-Arms. Trans. ASME, J. of Mech. Tans, and Auto, in Design 105: 705–712
Earl C F, Rooney J 1983 Some Kinematic Structures for Robot Manipulator Design. Trans. ASME, J. Mech. Trans. Auto. Design. 105: 15–22
Merlet J P 1990 Les robots paralleles, Hermes, Paris
Innocenti C, Parenti-Castelli V 1994 Exhaustive Enumeration of Fully Parallel Kinematic Chains. In: DSC-VoL 55-2, Dynamic System and Control, ASME, pp 1135–1141
Faugere J C, Lazard D 1995 The Combinatorial Classes of Parallel Manipulators. Mechanism and Machine Theory 30 (6): 765–776
Innocenti C, Parenti-Castelli V 1992 Basic Ideas and Recent Techniques for the Analytical Form Solution of the Direct Position Analysis of Fully Parallel Mechanisms. Journal of Laboratory Robotics and Automation, LRA 4: 107–113
Salmon G D D 1885 Modern Higher Algebra, Hodges, Figgs, and Co., Dublin
Innocenti C, Parenti-Castelli V 1991 Direct Kinematics of the Reverse Stewart Platform Mechanism. In: IF A C ’91-SYROCO ’91, Wien, Austria, pp 75–80
Chen, N., and Song, S., 1994, “Direct Position Analysis of the 4-6 Stewart Platforms”, ASME Journal of Mechanical Design, Vol. 116, No. 1, pp. 61–66.
Dingra AD, Kohli D, and Xu YX, 1992, “Direct Kinematics of General Stewart Platforms,” Proc. of the 22nd ASME Biennial Mechanisms Conference, Scottsdale, AZ, DE-Vol. 45, pp. 107–112.
Gosselin, C.M., Sefrioui, J., and Richard, M.J., 1992, “On the Direct Kinamatics of General Spherical Three-Degree-of-Freedom Parallel Manipulators,” Proc. of the 22nd ASME Biennial Mechanisms Conference, Scottsdale, Arizona, DE- Vol. 45, pp. 7–11.
Griffis, M., and Duffy, J., 1989, “A Forward Displacement Analysis of a Class of Stewart Platform,” Journal of Robotic Systems, Vol. 6, No. 6, pp. 703–720.
Husain, M., and Waldron, K.J., 1992, “Direct Position Kinematics of the 3-1-1-1 Stewart Platforms,” Ptoc. of the 22nd ASME Biennial Mechanisms Conference, Scottsdale, Arizona, DE-Vol. 45, pp. 89–97.
Hust ML, 1996, “An Algorithm for Solving the Direct Kinematics of the Stewart-Gough Platforms,” Mechanism and Machine Theory, Vol. 31, No. 4, pp. 365–380.
Innocenti, C., 1992a, “Forward Kinematics in Analytical Form of the Topologically-Symmetric 4-4 Fully-Parallel Mechanism,” Robotics and Manufacturing, Vol. 4, ASME Press, New York, USA, pp. 411–418.
Innocenti, C., 1992b, “Direct Kinematics in Analytical Form of the 6-4 Fully- Parallel Mechanism,” ASME Journal of Mechanical Design, Vol. 117, No. 1, pp. 89–95.
Innocenti, C., 1995, “Analytical-Form Direct Kinematics for the Second Scheme of a 5-5 General-Geometry Fully Parallel Manipulator,” Journal of Robotic Systems, Vol. 12. No. 10, pp. 661–676.
Innocenti, C., 1998, “Forward kinematics in polynomial form of the general Stewart platform,” Paper N. DETC98/MECH-5894, 1998 ASME Design Engineering Technical Conference, Atianta, GA.
Innocenti, C., and Parenti-Castelli, V., 1990, “Direct Position Analysis of the Stewart Platform Mechanism,” Mechanism and Machine Theory, Vol. 25, No. 6, pp. 611–621.
Innocenti, C., and Parenti-Castelli, V., 1991a, “Direct Kinematics of the 6-4 Fully Parallel Manipulator with Position and Orientation Uncoupled,” EURISCON ’91, The European Robotics and Intelligent Systems Conference, June 23-28, Corfu, Greece.
Innocenti, C., and Parenti-Castelli, V., 1992a, “Analytical Form Solution of the Direct Kinematics of a 4-4 Fully In-Parallel Actuated Six-Degrees-of- Freedom Mechanism,” Proc. of the Ninth CISM-IFToMM Symposium on Theory and Practice of Robots and Manipulators, Ro.man.sy ’92.
Innocenti, C., and Parenti-Castelli, V., 1993a, “Closed-form Direct Position Analysis of a 5-5 Parallel Mechanism,” ASME Journal of Mechanical Design, Vol. 115, No. 3, pp. 515–521.
Innocenti, C., and Parenti-Castelli, V., 1993b, “Echelon Form Solution of the Direct Kinematics for the General Fully-Parallel Spherical Wrist,” Mechanism and Machine Theory, Vol. 28, No. 4, pp. 553–561.
Innocenti, C., and Parenti-Castelli, V., 1993c, “Direct Kinematics in Analytical Form of a General Geometry 5-4 Fully-Parallel Manipulator,” Computational Kinematics, Eds. J. Angeles, P. Hommel, and P. Kovacs, Kluwer Academic Publishers, pp. 141–152.
Innocenti, C., and Parenti-Castelli, V., 1994a, “Symbolic-Form Direct Position Kinematics of a 5-4 Fully-Parallel Manipulator,” Recent Advances in Robot Kinematics, Eds. J. Lenarcic and B. Ravani, Kluwer Academic Publishers, pp. 429–438.
Innocenti, C., 1995, “A New Algorithm for the Direct Kinematics of the 6-5 Fully-Parallel Manipulator”, Proceedings of the fifth National Applied Mechanisms & Robotics Conference, Cincinnati, Ohio, USA, Paper No. AMR97-039.
Liang, C., Han, L., and Wen, F., 1995, “Forward Displacement Analysis of the 5-6 Stewart Platforms,” Proc. of the Ninth World Congress on the Theory of Machines and Mechanisms, Milan, Italy, Vol. 1, pp. 184–187.
Lin, W., Crane, C.D., and Duffy, J., 1992, “Closed-Form Forward Displacement Analyses of the 4-5 In-Parallel Platform,” ASME Journal of Mechanical Design, Vol. 116, No. 1, pp. 47–53.
Lin, W., Duffy J., and Griffis, M., 1990, “Forward Displacement Analysis of the 4-4 Stewart Platforms,” ASME Journal of Mechanical Design, Vol. 114, No. 3, pp. 444–450.
Nanua, P., and Waldron, KJ., 1990, “Direct Kinematic Solution of a Special Parallel Robot Structure,” Proc. of the Eighth CISM-IFToMM Symposium on Theory and Practice of Robots and Manipulators, Ro.man.sy 90, Cracow, Poland.
Nanua, P., Waldron, K.J., and Murthy, V., 1990, “Direct Kinematic Solution of a Stewart Platform,” IEEE Trans, on Robotics and Automation, Vol. 6, No. 4, pp. 438–444.
Nielsen,J., and Roth, B., 1996, “The Direct Kinematics of The General 6-5 Stewart-Gough Mechanism,” Recent Advances in Robot Kinematics, Eds. J. Lenarcic and V. Parenti-Castelli, Kluwer Academic Publishers, pp. 7–16
Raghavan,M., 1991, “The Stewart Platform of General Geometry Has 40 Configurations,” General Motors Research Laboratories Publication, GMR- 7347.
Sreenivasan, S.V., and Nanua, P., 1992, “Solution of the Direct Position Kinematics Problem of the General Stewart Platform Using Advanced Polynomial Continuation,” Proc. of the 22nd ASME Biennial Mechanisms Conference, Scottsdale, AZ, DE-Vol. 45, pp. 99–106.
Wampler, C, W., 1996, “Forward Displacement Analysis of the General Six-In- Parallel SPS (Stewart) Platform Manipulators Using Soma Coordinates,” Mechanism and Machine Theory, Vol. 31, No. 3, pp. 331–337.
Wen, F.A., and Liang, C.G., 1994, “Displacement Analysis for the General Stewart Platform-Type Mechanism,” Mechanism and Machine Theory, Vol. 29. No. 4, pp. 547–557.
Wohlhart K, 1992, “Displacement Analysis of the General Spherical Stewart Platform,” Mechanism and Machine Theory, Vol. 29, No. 4, pp 581–589.
Yin, J.P., and Liang, C.G., 1994, “The Forward Displacement Analysis of a Kind of Special Platform Manipulator Mechanisms,” Mechanism and Machine Theory, Vol. 29, No. 1, pp. 1–9.
Zhang, C., and Song, S., 1992, “Forward Position Analysis of Nearly General Stewart Platforms,” Proc. of the 22nd ASME Biennial Mechanisms Conference, Scottsdale, Arizona, DE-Vol. 45, pp. 81–87.
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Parenti-Castelli, V. (1999). Classification and Kinematic Modelling of Fully-Parallel Manipulators — A Review. In: Boër, C.R., Molinari-Tosatti, L., Smith, K.S. (eds) Parallel Kinematic Machines. Advanced Manufacturing. Springer, London. https://doi.org/10.1007/978-1-4471-0885-6_4
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DOI: https://doi.org/10.1007/978-1-4471-0885-6_4
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