Abstract
Two double-triangular mechanisms are introduced here. These are planar and spherical three-degree-of-freedom mechanisms that consist of two triangles moving with respect to each other. Moreover, each side of the moving triangle intersects one corresponding side of the fixed one at a given point defined over this side. The direct kinematic analysis of the mechanisms leads to a quadratic equation for the planar and a polynomial of 16th degree for the spherical mechanism. Numerical examples are included that admit two real solutions for the former and four real solutions for the latter, among which only two positive values are acceptable. All solutions, both real and complex, are listed.
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References
Craver, W.M.: 1989, Structural Analysis and Design of a Three-Degree-of-Freedom Robotic Shoulder, M. Eng. Thesis, The University of Texas at Austin: Austin.
Hunt, K. H.: 1983, ‘Structural Kinematics of In-Parallel-Actuated Robot Arms’, ASME J. of Mechanisms, Transmissions, and Automation in Design vol. 105, no. 4, pp .705–712.
Gosselin, C. and Angeles, J.: 1989, ‘The Optimum Kinematic Design of Spherical ThreeDegree-of-Freedom Parallel Manipulator’, ASME J. of Mechanisms, Transmissions, and Automation in Design vol. 111, no. 2, pp. 202–207.
Gosselin, C. and Angeles, J.: 1990, ‘Kinematic Inversion of Parallel Manipulator in the Presence of Incompletely Specified Tasks’, ASME Journal of Mechanical Design vol. 112, pp. 494–500.
Gosselin, C. M. and Sefrioui, J.: 1991, ‘Polynomial Solutions for the Direct Kinematic Problem of Planar Three-Degree-of-Freedom Parallel Manipulators’, Proc. of the Fifth Int. Conf. On Advanced Robotics, Pisa, pp. 1124–1129.
Gosselin, C. M., Sefrioui, J. and Richard, M. J.: 1992a, ‘On the Direct Kinematics of General Spherical Three-Degree-of-Freedom Parallel Manipulators’, Proc. of the ASME Mechanisms Conference. Phoenix, pp. 7–11.
Gosselin, C. M., Sefrioui, J. and Richard, M. J.: 1992b, ‘On the Direct Kinematics of a Class of Spherical Three-Degree-of-Freedom Parallel Manipulators’, Proc. of the ASME Mechanisms Conference, Phoenix, pp. 13–19.
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. 3, pp. 438–444.
Salmon, G.: 1964, Lessons Introductory to the Modern Higher Algebra (5th ed.), New York: Chelsea.
Stewart, D.: 1965, ‘A Platform with Six Degrees of Freedom’, Proc. of the Institution of Mechanical Engineers vol. 180, no. 5, pp. 371–378.
Tarnai, T., and Makai, E.: 1988, ‘Physically Inadmissible Motions of a Pair of Tetrahedra’, Proc. of 3rd Int. Conf. Eng. Graph. and Desc. Geom., Vienna vol. 2, pp. 264–271.
Tarnai, T., and Makai, E.: 1989a, ‘A Movable Pair of Tetrahedra’, Proc. of R. Soc. Lon. A432. pp. 419–442.
Tarnai, T., and Makai, E.: 1989b, ‘Kinematical Indeterminacy of a Pair of Tetrahedral Frames’, Acta Technica Acad. Sci. Hung. vol. 102, pp. 123–145.
Zsombor-Murray, P. J. and Hyder, A.: 1992, ‘An Equilateral Tetrahedral Mechanism’, J. of Robotics and Autonomous Systems vol. 9, pp. 227–236.
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© 1993 Springer Science+Business Media Dordrecht
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Daniali, H.R.M., Zsombor-Murray, P.J., Angeles, J. (1993). The Kinematics of 3-DOF Planar and Spherical Double-Triangular Parallel Manipulators. In: Angeles, J., Hommel, G., Kovács, P. (eds) Computational Kinematics. Solid Mechanics and Its Applications, vol 28. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8192-9_14
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DOI: https://doi.org/10.1007/978-94-015-8192-9_14
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