Abstract
The direct kinematic problem of \(n-n\ (n=2,3,4,5)\) underconstrained cable manipulators has been solved previously by exploiting the line geometric equilibrium condition and using optimization techniques, heavy algebraic or numeric algebraic computation. In this paper another solution method is proposed. It uses kinematic mapping, distance constraint equations and a local plane constraint. This method can be used for all cases of underconstrained cable manipulators and it is also applicable to the case of \(n-i\) equilibria of \(n-\)cable manipulators. Univariate polynomials are computed in examples for the \(3-3\) and \(5-5\) cases as well as for \(n-1\) equilibria of the \(5-5\) case.
Keywords
- Kinematic Function
- Distance Constraint Equations
- Direct Kinematic Problem
- Cable Operators
- Univariate Polynomial
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Notes
- 1.
The kinematic images of planar and spherical displacements subordinate completely to this description because both cases are obtained by three dimensional sub-spaces of \(\mathbb {P}^7\). The corresponding geometry of their image spaces and the algorithms to derive these geometries can be found in [3] p.393ff. resp. [11] p.60ff.
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Acknowledgements
The authors acknowledge the support of the FWF project I 1750-N26 “Kinematic Analysis of Lower-Mobility Parallel Manipulators Using Efficient Algebraic Tools”.
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Husty, M., Schadlbauer, J., Zsombor-Murray, P. (2018). A New Approach to the Direct Geometrico-Static Problem of Cable Suspended Robots Using Kinematic Mapping. In: Gosselin, C., Cardou, P., Bruckmann, T., Pott, A. (eds) Cable-Driven Parallel Robots. Mechanisms and Machine Science, vol 53. Springer, Cham. https://doi.org/10.1007/978-3-319-61431-1_9
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DOI: https://doi.org/10.1007/978-3-319-61431-1_9
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