Abstract
In a recent publication [10] the author showed that self-motions of general planar Stewart Gough platforms can be classified into two so-called Darboux Mannheim (DM) types (I and II). Moreover, in [10] the author was able to compute the set of equations yielding a type II DM self-motion explicitly. Based on these equations we present a basic result for this class of self-motions.
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Notes
- 1.
For \(e_0e_2-e_1e_3\neq 0\) this can be done w.l.o.g., as this factor belongs to the denominator of f i.
- 2.
Therefore we are looking for a common factor of Ω and Π, which depends on e 0.
- 3.
\(\varOmega: \sum\nolimits_{i=0}^3 c_i e_i^2 + c_4e_0e_3+c_5e_1e_2\) where \(c_0,\ldots,c_5\) only depend on the geometry of the SG platform.
References
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Acknowledgements
This research is supported by Grant No. I 408-N13 of the Austrian Science Fund FWF within the project “Flexible polyhedra and frameworks in different spaces”, an international cooperation between FWF and RFBR, the Russian Foundation for Basic Research.
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Nawratil, G. (2012). Basic Result on Type II DM Self-Motions of Planar Stewart Gough Platforms. In: Lovasz, EC., Corves, B. (eds) Mechanisms, Transmissions and Applications. Mechanisms and Machine Science, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2727-4_21
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