Abstract
In this paper a special type of symmetric Stewart-Gough platform is analyzed where the six attachment points in each of the two bodies are arranged symmetrically with respect to a centerpoint. The lengths of the six actuators, which connect the two bodies, are given, and the relative position of the two bodies to each other has to be computed (forward kinematics). In a preliminary step a particular symmetric platform with three pairs of equal actuator lengths is studied. It is shown that such a platform can pose in up to 24 different configurations, and that it can become finitely mobile if the geometric dimensions fulfill certain conditions which are provided in the paper. For the more general type of symmetric platform the forward kinematic analysis reveals again that there might exist up to 24 possible postures. A final numerical example even shows that all 24 postures might be real.
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References
Faugère, J. C. and Lazard, D., 1995: Combinatorial Classes of Parallel Manipulators, Mech. Mach. Theory 30, No. 6, pp. 765–776.
Gough, V. E., 1956–1957: Contribution to discussion to papers on research in automobile stability and control in tyre performance, by Cornell staff, Proc. AutoDiv. Inst. Mech. Eng. 1956, pp. 392–395.
Husty, M. L. and Zsombor-Murray P., 1994: A Special Type of Singular Stewart-Gough Platform, Advances in Robot Kinematics and Computational Geometry, Kluwer Academic Publisher, Dortrecht, pp. 449–458.
Innocenti, C., 1992: Forward kinematics in analytical form of the topologically-symmetric 4–4 fully-parallel mechanism, Robotics and Manufacturing, Vol. 4, ASME Press, New York, pp. 411–418.
Innocenti, C. and Parenti-Castelli V., 1993: Closed-form direct position analysis of a 5–5 parallel mechanism, ASME J. of Mechanical Design, Vol. 115, No. 3, pp. 515–521.
Lazard, D., 1993: On the representation of rigid-body motions and its application to generalized platform manipulators, Computational Kinematics (J. Angeles, P. Kovac and G. Hommel, eds), Kluwer Academic Publisher, Dortrecht, Boston, London, pp. 175–181.
Mourrain, B., 1993: Proc. of ISSSAC’93 (Kiew) (M. Bronstein, ed.), ACM Press, pp. 173–182.
Raghavan, M., 1993: The Stewart platform of general geometry has 40 configurations, ASME J. of Mech. Design, Vol. 115, pp. 277–282.
Ronga, F. and Vust, Th., 1992: Stewart platforms without computer?, Preprint. Université de Genève.
Stewart, D., 1965: A platform with 6 degrees of freedom, Proc. Institution of Mechanical Engineers, London, Vol. 180, Part l, No. 15, pp. 371–386.
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© 1996 Kluwer Academic Publishers
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Dietmaier, P. (1996). Forward Kinematics and Mobility Criteria of One Type of Symmetric Stewart-Gough Platforms. In: Lenarčič, J., Parenti-Castelli, V. (eds) Recent Advances in Robot Kinematics. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1718-7_38
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DOI: https://doi.org/10.1007/978-94-009-1718-7_38
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7269-4
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