Abstract
The paper presents a new algorithm to solve in polynomial form the forward kinematics of the 6–6 fully-parallel manipulator that has a general-geometry platform, a base equal to the platform, and homologous points on base and platform joined by variable-length linear actuators. The forward kinematics is reduced to solving three univariate polynomial equations, one of degree 6 and the remaining of degree 2. Accordingly, the number of solutions for the considered kinematics problem is 24 in the complex domain. A numerical example is also provided.
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References
Dietmaier, P. (1996) Forward Kinematics and Mobility Criteria of One Type of Symmetric Stewart-Gough Platforms, Recent Advances in Robot Kinematics, Kluwer Academic Publishers, Dordrecht, pp. 379–388.
Griffis, M., Crane, C., and Duffy, J. (1994) A Smart Kinestatic Interactive Platform, Advances in Robot Kinematics and Computational Geometry, Kluwer Academic Publishers, Dordrecht, pp. 459–464.
Husty, M.L. (1996) An Algorithm for Solving the Direct Kinematics of General Stewart-Gough Platforms, Mechanism and Machine Theory, Vol. 31, No. 4, pp. 365–380.
Lazard, D. (1993) On the Representation of Rigid-Body Motions and Its Application to Generalized Platform Manipulators, Computational Kinematics, Kluwer Academic Publishers, Dordrecht, pp. 175–181.
Lee, H.Y., and Roth, B. (1993) A Closed-Form Solution of the Forward Displacement Analysis of a Class of In-Parallel Mechanisms, Proc. of the IEEE International Conference on Robotics and Automation, Atlanta, May 2–6, Vol. 1, pp. 720-724.
Mavroidis, C. (1997) Method to Determine the Displacement Screws Related to the Direct Kinematics of Parallel Mechanisms, Proc. of the 5th Applied Mechanisms & Robotics Conference, Cincinnati, Oct. 12–15.
Raghavan, M. (1993) The Stewart Platform of General Geometry Has 40 Configurations, ASME Journal of Mechanical Design, Vol. 115, No. 2, pp. 277–282.
Ronga, F., and Vust, T. (1995) Stewart Platforms without Computer?, Proc. of the Int. Conf. on Real Analytic and Algebraic Geometry, Trento, Sept. 21–25, 1992, W. de Gruyter Verlag, Berlin, pp. 197–212.
Salmon, G. (1964) Lessons Introductory to the Modern Higher Algebra, Chelsea Pub. Co., NY.
Wampler, C.W. (1996) Forward Displacement Analysis of General Six-in-Parallel SPS (Stewart) Platform Manipulators Using Soma Coordinates, Mechanism and Machine Theory, Vol. 31, No. 3, pp. 331–337.
Wang, G. (1992) Forward Displacement Analysis of a Class of the 6-6 Stewart Platforms, Proc. of the 22nd ASME Biennial Mechanisms Conference, Scottsdale, Sept. 13–16, pp. 113-117.
Wen, F., and Liang, C.G. (1994) Displacement Analysis of the 6-6 Stewart Platform Mechanisms, Mechanism and Machine Theory, Vol. 29, No. 4, pp. 547–557.
Yin, J.P., and Liang, C.G. (1993) 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.D., and Song, S.M. (1992) Forward Kinematics of a Class of Parallel (Stewart) Platforms with Closed-Form Solutions, Journal of Robotic Systems, Vol. 9, No. 1, pp. 93–112.
Zhang, C.D., and Song, S.M. (1994) Forward Position Analysis of Nearly General Stewart Platforms, ASME Journal of Mechanical Design, Vol. 166, No. 1, pp. 54–60.
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© 1998 Springer Science+Business Media Dordrecht
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Innocenti, C. (1998). Forward Kinematics of a 6-6 Fully-Parallel Manipulator with Congruent Base and Platform. In: Lenarčič, J., Husty, M.L. (eds) Advances in Robot Kinematics: Analysis and Control. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9064-8_14
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DOI: https://doi.org/10.1007/978-94-015-9064-8_14
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